Q: Frequency response of a first-order system (τ = 1 min) A first-order process with time constant τ = 1 minute is tested at input frequency ω = 1 rad/min. What is the steady-state phase shift (in degrees) between output and sinusoidal input?

Introduction / Context: First-order dynamics are ubiquitous in process units (tanks, heat exchangers). Their frequency response is simple yet powerful: knowing the phase shift and attenuation at a given frequency helps in controller tuning and estimating closed-loop behaviour. This question focuses on computing the phase at a specific frequency using the well-known formula for a first-order lag. Given Data / Assumptions: Transfer function form: G(jω) = K / (1 + jωτ). Time constant τ = 1 min; test frequency ω = 1 rad/min. We assume standard steady-state sinusoidal response. Concept / Approach: For G(jω) = K / (1 + jωτ), the phase is φ(ω) = −tan^−1(ωτ). This is independent of K. Substituting τ = 1 and ω = 1 gives φ = −tan^−1(1) = −45°. The negative sign indicates the output lags the input, characteristic of a causal lag element. Step-by-Step Solution: Write the phase formula: φ = −tan^−1(ωτ).Insert values: ωτ = 1 * 1 = 1.Compute: tan^−1(1) = 45°.Attach sign: output lags → φ = −45°. Verification / Alternative check: The magnitude at this frequency is |G(j1)| = K / √(1 + 1^2) = K/√2, confirming a −3 dB point when ω = 1/τ. The corner frequency 1/τ = 1 rad/min also typically corresponds to a −45° phase, consistent with the result. Why Other Options Are Wrong: 45° — sign error; the lag is negative.−90° — would be the asymptotic phase at very high frequency for a first-order lag, not at ω = 1/τ.−180° — never reached by a single first-order lag.0° — only at ω → 0. Common Pitfalls: Forgetting the negative sign (lag), or confusing the break frequency with the high-frequency asymptote. Final Answer: −45°

Q: Stability of a system with a double pole at the origin A linear system has a double pole at s = 0. Which time-domain behaviour explains why such a system is unstable?

Introduction / Context: Pole locations dictate time-domain behaviour. A single pole at the origin gives an integrator; a double pole at the origin corresponds to a double integrator. Such systems cannot return to equilibrium after a disturbance and are considered unstable by BIBO criteria, even if the growth is not exponential. Given Data / Assumptions: Transfer function has a repeated pole at s = 0. Consider response to bounded inputs such as steps and impulses. We use standard LTI system theory. Concept / Approach: An integrator (1/s) converts a step input into a ramp. A double integrator (1/s^2) converts a step into a parabolic growth and an impulse into a ramp. Even the simplest disturbances thus cause outputs that diverge with time, violating bounded-input bounded-output stability. The essential signature is unbounded growth (at least linear), not decay or bounded oscillation. Step-by-Step Solution: Model near the origin: G(s) ≈ K / s^2.Apply a bounded input (e.g., step R(s) = 1/s) → Y(s) = K / s^3.Time domain: y(t) ∝ t^2 (parabolic) for step; for impulse input y(t) ∝ t (ramp).Any of these grow unbounded → instability. Verification / Alternative check: BIBO stability requires all poles strictly in the left half-plane. Poles at the origin violate that requirement; a repeated pole at the origin is worse than a simple integrator and guarantees unbounded growth for common inputs. Why Other Options Are Wrong: Constant or decaying responses imply poles with negative real parts.Exponential growth suggests right-half-plane poles; while still unstable, it is not the correct hallmark for a pole at exactly s = 0.Bounded oscillation needs imaginary-axis conjugate poles without damping, not a double pole at zero. Common Pitfalls: Assuming “unstable” must mean exponential blow-up; integrators are unstable by unbounded growth even at polynomial rates. Final Answer: its response grows linearly with time (ramp)

Q: Anatomy of a pH meter — how many electrochemical cells? A standard laboratory/industrial pH meter uses a measuring (glass) electrode and a reference electrode. Considering their electrochemical arrangement, how many cells are effectively involved?

Introduction / Context: The pH of a solution is determined electrochemically by measuring the potential difference between a pH-sensitive glass electrode and a stable reference electrode (e.g., Ag/AgCl). Understanding the electrode configuration clarifies calibration, junction potentials, and maintenance requirements of pH probes and meters. Given Data / Assumptions: A typical pH measurement uses a glass (indicator) electrode plus a reference electrode. Combination electrodes house both in one body, but internally they remain distinct half-cells. The meter reads the EMF between the two, proportional to pH by the Nernst relation. Concept / Approach: Each electrode constitutes a half-cell. Together, the glass and reference electrodes form one complete electrochemical cell path through the test solution. In conventional teaching/exam wording, this is often described as “two cells” (two half-cells) used by the pH meter, even when combined in a single probe. Hence, the accepted answer aligns with two cells (two half-cells) forming the measurement system. Step-by-Step Solution: Identify components: glass electrode (H+ sensitive) and reference electrode.Note that each is a half-cell, requiring ionic contact via the test solution and a junction.The meter measures EMF between these half-cells → effectively two cells (two half-cells). Verification / Alternative check: Manufacturer schematics label “measuring half-cell” and “reference half-cell,” even in combination electrodes. Calibration with two buffer points verifies the cell potential relation to pH. Why Other Options Are Wrong: One cell — ignores the separate reference and measuring half-cells.Three/four cells — no such requirement for basic pH measurement.No cell — incorrect; pH measurement is an electrochemical cell measurement. Common Pitfalls: Confusing “combination electrode” as a single cell; internally it still embodies two half-cells that the meter compares. Final Answer: two cells

Q: Limits of non-contact thermometry — where can’t radiation thermometers be used? A radiation (optical/infrared) thermometer measures temperature from emitted radiation without touching the target. In which of the following cases is such a thermometer…

Introduction / Context: Radiation thermometers infer temperature from thermal radiation. Their major requirement is an unobstructed optical path between the instrument and the target. If that line of sight is absent, the device cannot sense the target’s radiation, no matter how hot or cold the process is. Given Data / Assumptions: The thermometer is non-intrusive and requires clear optical access. Target emissivity is acceptable or compensated. No specialised windows or viewports are assumed unless stated. Concept / Approach: The only scenario that fundamentally disables a radiation thermometer is the absence of a radiative path. A sealed pressure vessel with no optical window prevents any radiation from reaching the sensor, making measurement impossible. Conversely, measuring moving hot objects, or even cryogenic surfaces (with suitable calibration and emissivity handling), is feasible provided the instrument can “see” the target. Step-by-Step Solution: Check for optical access: inside a pressure vessel implies none.Radiation thermometry works without contact → options (b), (d), (e) are normal applications.Liquid oxygen surface temperature can be measured radiometrically with care (emissivity, windowing) → not inherently impossible. Verification / Alternative check: Industry practice uses sight-glass or sapphire windows to enable radiation measurements into vessels; without such viewports, measurement is not possible, confirming the limitation. Why Other Options Are Wrong: Measuring without contact — this is the defining benefit of radiation thermometry.Liquid oxygen — challenging but feasible with correct spectral band and emissivity corrections.Moving hot objects — a classic use case (steel, glass, kilns).Hot conveyor strip with access — valid scenario. Common Pitfalls: Assuming low temperatures or movement disqualify radiation thermometers. It is the line-of-sight that is truly critical. Final Answer: inside a pressure vessel (no line of sight)

Q: High-temperature thermocouples in oxidising atmospheres (~1600°C) Which thermocouple type is most suitable for measuring about 1600°C in an oxidising environment?

Introduction / Context: Selecting a thermocouple for very high temperatures demands attention to both temperature capability and atmosphere. Oxidising conditions quickly degrade base-metal thermocouples at extreme temperatures. Noble-metal combinations withstand oxidising atmospheres far better and maintain accuracy near 1600°C. Given Data / Assumptions: Target temperature ≈ 1600°C. Atmosphere is oxidising (e.g., furnace air). Conventional industrial thermocouple types considered. Concept / Approach: Platinum–platinum+rhodium (Types S or R) thermocouples are standard for high-temperature measurements in oxidising environments and are commonly used in ceramic kilns and metallurgical furnaces. Base-metal types like Iron–Constantan (Type J) and Copper–Constantan (Type T) have far lower temperature limits. Chromel–Alumel (Type K) handles moderately high temperatures but not reliably around 1600°C in oxidising atmospheres. Tungsten–rhenium requires inert or vacuum conditions; bare use in air is unsuitable due to oxidation. Step-by-Step Solution: Filter by atmosphere: eliminate materials that oxidise rapidly at high T.Check temperature limits: only noble-metal types reliably approach 1600°C in air.Select Platinum–Platinum+Rhodium as the appropriate choice. Verification / Alternative check: Industry standards list Type S/R ranges up to around 1600–1700°C in oxidising atmospheres with proper protection tubes, confirming suitability. Why Other Options Are Wrong: Iron–constantan / Copper–constantan — low maximum temperature limits; unsuitable.Chromel–alumel — not reliable at ~1600°C in oxidising air.Tungsten–rhenium — requires vacuum/inert; oxidises rapidly in air. Common Pitfalls: Choosing on maximum temperature alone without considering the atmospheric compatibility; atmosphere often dictates survivability. Final Answer: Platinum–platinum + rhodium (noble metal type)

Q: Paramagnetism vs diamagnetism in continuous flue-gas analysis A continuous flue-gas analyzer that uses magnetism relies on paramagnetic components moving toward the strongest magnetic field, displacing diamagnetic gases. Which of the following gases…

Introduction / Context: Some continuous emissions monitoring systems (CEMS) measure oxygen by exploiting magnetic properties: oxygen is strongly paramagnetic and is attracted to a magnetic field. In such instruments, diamagnetic components are displaced. To interpret the readings and understand interferences, you should know which common flue-gas constituents are para- or diamagnetic. Given Data / Assumptions: Paramagnetic gases are attracted to magnetic fields. Diamagnetic gases are weakly repelled. Typical stack gases include O2, CO2, NO, NO2, N2, H2O (vapour), etc. Concept / Approach: Molecular oxygen (O2) is a classic paramagnetic gas due to its unpaired electrons. Nitric oxide (NO) and nitrogen dioxide (NO2) also have unpaired electrons and are paramagnetic. Carbon dioxide (CO2), with all electrons paired and a linear, closed-shell electronic configuration, is diamagnetic. Thus, in paramagnetic analyzers, CO2 behaves as the diamagnetic component displaced by O2’s magnetically induced motion. Step-by-Step Solution: Recall magnetic classifications of common gases.Identify O2, NO, NO2 as paramagnetic (unpaired electrons).Recognize CO2 as diamagnetic (all electrons paired).Select CO2 as the diamagnetic gas. Verification / Alternative check: Instrument manuals for paramagnetic O2 analyzers list CO2, N2, and others as diamagnetic, while O2 is the paramagnetic target species. Why Other Options Are Wrong: O2 / NO / NO2: All paramagnetic, not diamagnetic. Common Pitfalls: Assuming all oxides are diamagnetic; many nitrogen oxides are paramagnetic due to odd-electron configurations. Final Answer: CO2

Q: Analytical instrumentation – what does a mass spectrometer analyze best? Mass spectrometry is especially suited for composition analysis and identification of which of the following?

Introduction / Context: Mass spectrometry (MS) separates ions by mass-to-charge ratio and detects their abundances. Because different isotopes of an element have different masses, MS is exceptionally powerful for isotope identification and ratio measurements, widely used in geochemistry, nuclear science, environmental tracing, and quality control of gases and organics. Given Data / Assumptions: MS requires analytes to be converted to gas-phase ions. Ion optics and mass analyzers (quadrupole, TOF, magnetic sector) separate m/z. Detector current is proportional to ion abundance. Concept / Approach: Isotopic variants differ only in neutron number, thus mass. When ionized, their m/z values shift accordingly, producing resolvable peaks that unveil isotopic composition with high sensitivity and precision. While alloys can be studied by MS after appropriate sampling (e.g., spark source, laser ablation), the technique excels most naturally at isotope analysis due to the direct mass distinction. Bulk solids without vaporization/ionization cannot be analyzed directly; sample introduction must create ions first. Step-by-Step Solution: Recognize isotopes differ in mass → ideal for MS separation.Note MS detects m/z, enabling isotope ratio quantification.Eliminate options requiring bulk analysis without ionization. Verification / Alternative check: Applications like isotope ratio MS (IRMS) and accelerator MS are standard for isotopic fingerprints (e.g., C-13/C-12, O-18/O-16). Why Other Options Are Wrong: Alloys: Possible with specialized sampling, but not the quintessential use highlighted in fundamentals. Solids (bulk, without vaporization): Incompatible with MS without ion generation. None of these: Incorrect because isotopes are a prime use-case. Common Pitfalls: Assuming MS directly “weighs” solids; all MS measurements are on ions in vacuum. Final Answer: Isotopes

Q: Flow measurement – identify the device that is not a differential-pressure meter Which of the following is not a differential-pressure (DP) type flow meter?

Introduction / Context: Industrial flow measurement devices come in many forms. Differential-pressure (DP) meters infer flow from a pressure drop created by a restriction. Variable-area meters (rotameters) infer flow from the equilibrium position of a float in a tapered tube. Recognizing the measurement principle is foundational in instrumentation selection and sizing. Given Data / Assumptions: DP meters: pressure drop across a primary element is related to flow (Bernoulli + discharge coefficient). Variable-area meter: float rises until drag force balances weight minus buoyancy. Ideal fluids and standard installation practices are assumed for principle identification. Concept / Approach: Venturimeters, flow nozzles, and orificemeters are textbook DP meters. Each creates a constriction; the static pressure difference between upstream and throat/taps correlates with volumetric or mass flow after calibration. A rotameter, however, uses a tapered transparent tube and a float. The area available to flow increases with float height; the float's position (not a DP reading) is directly indicated and correlated to flow rate. Thus, the rotameter is not a DP meter. Step-by-Step Solution: Group devices by principle: Venturi/nozzle/orifice → DP; rotameter → variable-area.Apply definition: DP meters measure pressure drop; rotameter measures float height.Select the non-DP device: rotameter. Verification / Alternative check: Standards (ISO/ASME) classify Venturi, nozzle, orifice under DP primary devices, while rotameters are listed under variable-area (VA) meters. Why Other Options Are Wrong: Venturimeter / Flow nozzle / Orificemeter: All operate on differential pressure across a constriction. Common Pitfalls: Assuming every meter with a pressure effect is a DP meter; in rotameters the indicated variable is position, not measured pressure drop. Final Answer: Rotameter

Q: Bode plots and excitation signals Bode magnitude and phase plots are generated from a system’s steady-state response to which class of input?

Introduction / Context: Bode plots summarize a linear time-invariant (LTI) system’s frequency response by showing gain and phase versus frequency. To obtain these characteristics, we conceptually excite the system with inputs at single frequencies and measure the steady-state output amplitude and phase shift. Identifying the correct excitation class ensures the right mental model for frequency-domain analysis. Given Data / Assumptions: System is LTI and stable for the frequencies of interest. Frequency response G(jω) is defined via sinusoidal steady-state. Magnitude and phase are plotted over a logarithmic frequency axis. Concept / Approach: By definition, the frequency response is the ratio of the steady-state output to input when the input is a sinusoid of frequency ω: u(t) = A sin(ω t). For an LTI system, the steady-state output is also sinusoidal at the same frequency but with different amplitude and a phase lag/lead. Sampling this response across ω yields the data for the Bode magnitude and phase plots. Although other test signals (impulse, step, ramp) can be used to derive frequency response indirectly via transforms, the foundational definition uses sinusoidal input. Step-by-Step Solution: Recall definition: G(jω) = Output(jω)/Input(jω) under sinusoidal steady-state.Vary ω across decades; record gain and phase.Plot magnitude (dB) and phase (degrees or radians) vs frequency. Verification / Alternative check: Experimental frequency response analysis conducts chirp or swept-sine tests; computationally, FFT of sinusoidal steady-state also yields G(jω). Why Other Options Are Wrong: Impulse/Step/Ramp: Useful for time-domain characterisation; frequency response is defined via sinusoidal excitation. Common Pitfalls: Confusing “obtained from” with “related to”: while impulse/step responses can be transformed to frequency domain, the canonical construction of Bode data is sinusoidal steady-state. Final Answer: Sinusoidal

Question 1

Thermal-conductivity-type continuous flue gas analyzer: among common flue gas constituents CO2, N2, O2, and CO, which has the highest thermal conductivity and therefore produces the greatest conductive signal change?

Accepted Answer

Introduction / Context: Thermal-conductivity gas analyzers detect composition changes via heat transfer from a heated element to the surrounding gas. The signal depends on the thermal conductivity k of the gas mixture. Recognizing relative k values of typical flue gas components guides interpretation and instrument selection. Given Data / Assumptions: Operating near ambient pressure and moderate temperature. Constituents considered: CO2, N2, O2, CO (not including H2 or He, which would be much higher). Analyzer element is balanced against a reference cell. Concept / Approach: At room temperature, approximate thermal conductivities are: CO2 ≈ very low (about 0.016 W/m·K), CO ≈ lower mid (≈ 0.024), N2 and O2 ≈ around air (≈ 0.026). Between N2 and O2, oxygen is slightly higher than nitrogen under common conditions. Therefore, among the listed flue gas species, O2 has the highest thermal conductivity and produces the largest conductive signal relative to the others. Step-by-Step Solution: Rank k values: CO2 (lowest) < CO < N2 ≲ O2 (highest of the set).Relate analyzer signal magnitude to k differences.Select O2 as having the highest thermal conductivity. Verification / Alternative check: Property tables show air ≈ 0.026 W/m·K, O2 slightly above N2, validating the ranking for these species. Why Other Options Are Wrong: CO2: lowest k; often used as an example of poor thermal conductor among gases.N2: close to O2 but slightly lower.CO: lower than N2/O2; not the highest. Common Pitfalls: Assuming air’s k equals nitrogen exactly; O2’s slight increase matters when discriminating among listed gases. Final Answer: O2

Question 2

Second-order LTI system — choose the standard canonical transfer function form In classical process control, the standard form of a linear time-invariant second-order system is expressed using the undamped natural frequency (ω_n) and the damping rat…

Accepted Answer

Introduction / Context: Recognising the standard (canonical) transfer function of a second-order linear time-invariant (LTI) system is foundational for predicting overshoot, oscillations, settling time, and stability margins. The canonical form uses two interpretable parameters: the undamped natural frequency (ω_n) and the damping ratio (ζ). This question checks your ability to identify that exact standard expression among look-alike distractors that represent other dynamic elements or non-canonical forms. Given Data / Assumptions: We are looking for the standard second-order LTI form. Symbols: ω_n for natural frequency; ζ for damping ratio; s is the Laplace variable. Unity static form is implied; arbitrary gain factors are not necessary to recognise the canonical structure. Concept / Approach: The canonical second-order transfer function is written as G(s) = ω_n^2 / (s^2 + 2 ζ ω_n s + ω_n^2). From this, step and frequency response features are read directly: underdamped (0 < ζ < 1), critically damped (ζ = 1), overdamped (ζ > 1). Any form that does not match this denominator pattern is not the standard second-order canonical expression, even if it is second-order or dynamic in some other way. Step-by-Step Solution: Recall canonical form: G(s) = ω_n^2 / (s^2 + 2 ζ ω_n s + ω_n^2).Scan the options for an exact match.Identify that option (a) matches the required numerator and denominator pattern.Reject alternatives that represent first-order lags, pure time delay, or non-canonical numerators. Verification / Alternative check: Compare poles: the denominator s^2 + 2 ζ ω_n s + ω_n^2 produces complex poles at −ζ ω_n ± j ω_n sqrt(1 − ζ^2) for ζ < 1, consistent with classical second-order behaviour. Other presented forms do not enforce this pole pattern. Why Other Options Are Wrong: K / (τ s + 1) — a first-order lag, not second-order.K e^(−L s) — pure time delay; magnitude 1 and phase lag only.none of these — invalid because the correct canonical form appears in option (a).K (s + 1) / (s^2 + s + 1) — a second-order with a zero; not the standard canonical form using ω_n and ζ in the numerator/denominator as required. Common Pitfalls: Confusing “any second-order” with the “canonical second-order form.” The presence of a numerator zero changes transient characteristics and is not the template used to define ζ and ω_n. Final Answer: ω_n^2 / (s^2 + 2 ζ ω_n s + ω_n^2)

Question 3

Seebeck effect in thermocouples — what does the generated emf depend on? In practical thermocouple measurements, the electromotive force (emf) is determined by which temperature relationship between the two junctions?

Accepted Answer

Introduction / Context: Thermocouples operate on the Seebeck effect: when two dissimilar metals are joined to form two junctions held at different temperatures, a voltage is generated. Understanding exactly what this emf depends on is essential for correct cold-junction compensation and accurate temperature measurement in industry and laboratories. Given Data / Assumptions: One junction is commonly called the “measurement” or hot junction. The other is the “reference” or cold junction (often at a known or compensated temperature). Lead materials and calibration tables are standard; parasitic thermal gradients are neglected. Concept / Approach: The thermocouple emf is a function of the temperatures of both junctions, often expressed as E = f(T_hot) − f(T_cold). Hence, it strictly depends on their temperature difference referenced to a standard polynomial relation, not the absolute value of either junction alone. This is why cold-junction compensation (measuring or regulating T_cold) is mandatory for accuracy. Step-by-Step Solution: Recall Seebeck principle: emf arises from a temperature gradient along dissimilar metals.Express emf dependency: E = f(T_hot) − f(T_cold) → depends on temperature difference.Select the option stating “difference between the hot and cold junction temperatures.” Verification / Alternative check: Cold-junction compensation modules add the measured ambient/reference temperature to the indicated emf so the instrument can report the actual hot junction temperature, reinforcing the dependence on ΔT. Why Other Options Are Wrong: Cold only / Hot only — incomplete; emf is not determined by a single junction temperature.Cold vs atmospheric — irrelevant; atmospheric temperature matters only if it sets T_cold.Average temperature — does not describe the Seebeck relation used for calibration tables. Common Pitfalls: Forgetting cold-junction compensation or assuming that holding the cold junction at 0°C is the only valid method; modern instruments measure and compensate T_cold electronically. Final Answer: difference between the hot and cold junction temperatures

Question 4

Frequency response of a first-order system (τ = 1 min) A first-order process with time constant τ = 1 minute is tested at input frequency ω = 1 rad/min. What is the steady-state phase shift (in degrees) between output and sinusoidal input?

Accepted Answer

Introduction / Context: First-order dynamics are ubiquitous in process units (tanks, heat exchangers). Their frequency response is simple yet powerful: knowing the phase shift and attenuation at a given frequency helps in controller tuning and estimating closed-loop behaviour. This question focuses on computing the phase at a specific frequency using the well-known formula for a first-order lag. Given Data / Assumptions: Transfer function form: G(jω) = K / (1 + jωτ). Time constant τ = 1 min; test frequency ω = 1 rad/min. We assume standard steady-state sinusoidal response. Concept / Approach: For G(jω) = K / (1 + jωτ), the phase is φ(ω) = −tan^−1(ωτ). This is independent of K. Substituting τ = 1 and ω = 1 gives φ = −tan^−1(1) = −45°. The negative sign indicates the output lags the input, characteristic of a causal lag element. Step-by-Step Solution: Write the phase formula: φ = −tan^−1(ωτ).Insert values: ωτ = 1 * 1 = 1.Compute: tan^−1(1) = 45°.Attach sign: output lags → φ = −45°. Verification / Alternative check: The magnitude at this frequency is |G(j1)| = K / √(1 + 1^2) = K/√2, confirming a −3 dB point when ω = 1/τ. The corner frequency 1/τ = 1 rad/min also typically corresponds to a −45° phase, consistent with the result. Why Other Options Are Wrong: 45° — sign error; the lag is negative.−90° — would be the asymptotic phase at very high frequency for a first-order lag, not at ω = 1/τ.−180° — never reached by a single first-order lag.0° — only at ω → 0. Common Pitfalls: Forgetting the negative sign (lag), or confusing the break frequency with the high-frequency asymptote. Final Answer: −45°

Question 5

Stability of a system with a double pole at the origin A linear system has a double pole at s = 0. Which time-domain behaviour explains why such a system is unstable?

Accepted Answer

Introduction / Context: Pole locations dictate time-domain behaviour. A single pole at the origin gives an integrator; a double pole at the origin corresponds to a double integrator. Such systems cannot return to equilibrium after a disturbance and are considered unstable by BIBO criteria, even if the growth is not exponential. Given Data / Assumptions: Transfer function has a repeated pole at s = 0. Consider response to bounded inputs such as steps and impulses. We use standard LTI system theory. Concept / Approach: An integrator (1/s) converts a step input into a ramp. A double integrator (1/s^2) converts a step into a parabolic growth and an impulse into a ramp. Even the simplest disturbances thus cause outputs that diverge with time, violating bounded-input bounded-output stability. The essential signature is unbounded growth (at least linear), not decay or bounded oscillation. Step-by-Step Solution: Model near the origin: G(s) ≈ K / s^2.Apply a bounded input (e.g., step R(s) = 1/s) → Y(s) = K / s^3.Time domain: y(t) ∝ t^2 (parabolic) for step; for impulse input y(t) ∝ t (ramp).Any of these grow unbounded → instability. Verification / Alternative check: BIBO stability requires all poles strictly in the left half-plane. Poles at the origin violate that requirement; a repeated pole at the origin is worse than a simple integrator and guarantees unbounded growth for common inputs. Why Other Options Are Wrong: Constant or decaying responses imply poles with negative real parts.Exponential growth suggests right-half-plane poles; while still unstable, it is not the correct hallmark for a pole at exactly s = 0.Bounded oscillation needs imaginary-axis conjugate poles without damping, not a double pole at zero. Common Pitfalls: Assuming “unstable” must mean exponential blow-up; integrators are unstable by unbounded growth even at polynomial rates. Final Answer: its response grows linearly with time (ramp)

Question 6

Photoconductive (photoresistive) transducers — what do they actually sense? A photoelectric device whose resistance varies in direct proportion to incident light is called a photoconductive cell. Photoelectric transducers are therefore used to measu…

Accepted Answer

Introduction / Context: Photoelectric transducers encompass photoconductive cells (LDRs), photovoltaic cells, and photodiodes. In photoconductive cells, the conductivity of a semiconductor film changes with incident light, making them ideal for converting optical variations into electrical resistance changes. This question focuses on the primary physical quantity these devices are intended to sense or track. Given Data / Assumptions: Photoconductive cell resistance R decreases as incident light intensity increases. External circuits translate resistance change into usable voltage or current signals. Operating wavelength and spectral response are appropriate for the source/target. Concept / Approach: The is light intensity (optical power per unit area). Electrical variables (voltage, current) are secondary signals produced by biasing the photoconductive element in a circuit. While flux density can refer to magnetic or radiant flux, in basic instrumentation the natural wording is “light intensity.” Hence the primary parameter measured is light intensity, with the transducer’s resistance serving as the intermediate variable. Step-by-Step Solution: Identify the sensing principle: resistance ∝ incident light intensity.Recognise the role of external circuitry: convert R change to V or I for readout.Select “light intensity” as the primary measured variable. Verification / Alternative check: Data sheets for LDRs map lux (illumination) to resistance; calibration curves are given in terms of light intensity, not inherent current or voltage. Why Other Options Are Wrong: Current/voltage — these are electrical outputs after biasing; not the measured environmental parameter.Flux density — ambiguous and usually refers to magnetic flux; not the intent here.Ambient humidity — unrelated to photoconduction. Common Pitfalls: Confusing “what is sensed” (light) with “what the circuit outputs” (voltage or current). The transducer measures light intensity; electronics translate it. Final Answer: light intensity

Question 7

Anatomy of a pH meter — how many electrochemical cells? A standard laboratory/industrial pH meter uses a measuring (glass) electrode and a reference electrode. Considering their electrochemical arrangement, how many cells are effectively involved?

Accepted Answer

Introduction / Context: The pH of a solution is determined electrochemically by measuring the potential difference between a pH-sensitive glass electrode and a stable reference electrode (e.g., Ag/AgCl). Understanding the electrode configuration clarifies calibration, junction potentials, and maintenance requirements of pH probes and meters. Given Data / Assumptions: A typical pH measurement uses a glass (indicator) electrode plus a reference electrode. Combination electrodes house both in one body, but internally they remain distinct half-cells. The meter reads the EMF between the two, proportional to pH by the Nernst relation. Concept / Approach: Each electrode constitutes a half-cell. Together, the glass and reference electrodes form one complete electrochemical cell path through the test solution. In conventional teaching/exam wording, this is often described as “two cells” (two half-cells) used by the pH meter, even when combined in a single probe. Hence, the accepted answer aligns with two cells (two half-cells) forming the measurement system. Step-by-Step Solution: Identify components: glass electrode (H+ sensitive) and reference electrode.Note that each is a half-cell, requiring ionic contact via the test solution and a junction.The meter measures EMF between these half-cells → effectively two cells (two half-cells). Verification / Alternative check: Manufacturer schematics label “measuring half-cell” and “reference half-cell,” even in combination electrodes. Calibration with two buffer points verifies the cell potential relation to pH. Why Other Options Are Wrong: One cell — ignores the separate reference and measuring half-cells.Three/four cells — no such requirement for basic pH measurement.No cell — incorrect; pH measurement is an electrochemical cell measurement. Common Pitfalls: Confusing “combination electrode” as a single cell; internally it still embodies two half-cells that the meter compares. Final Answer: two cells

Question 8

Limits of non-contact thermometry — where can’t radiation thermometers be used? A radiation (optical/infrared) thermometer measures temperature from emitted radiation without touching the target. In which of the following cases is such a thermometer…

Accepted Answer

Introduction / Context: Radiation thermometers infer temperature from thermal radiation. Their major requirement is an unobstructed optical path between the instrument and the target. If that line of sight is absent, the device cannot sense the target’s radiation, no matter how hot or cold the process is. Given Data / Assumptions: The thermometer is non-intrusive and requires clear optical access. Target emissivity is acceptable or compensated. No specialised windows or viewports are assumed unless stated. Concept / Approach: The only scenario that fundamentally disables a radiation thermometer is the absence of a radiative path. A sealed pressure vessel with no optical window prevents any radiation from reaching the sensor, making measurement impossible. Conversely, measuring moving hot objects, or even cryogenic surfaces (with suitable calibration and emissivity handling), is feasible provided the instrument can “see” the target. Step-by-Step Solution: Check for optical access: inside a pressure vessel implies none.Radiation thermometry works without contact → options (b), (d), (e) are normal applications.Liquid oxygen surface temperature can be measured radiometrically with care (emissivity, windowing) → not inherently impossible. Verification / Alternative check: Industry practice uses sight-glass or sapphire windows to enable radiation measurements into vessels; without such viewports, measurement is not possible, confirming the limitation. Why Other Options Are Wrong: Measuring without contact — this is the defining benefit of radiation thermometry.Liquid oxygen — challenging but feasible with correct spectral band and emissivity corrections.Moving hot objects — a classic use case (steel, glass, kilns).Hot conveyor strip with access — valid scenario. Common Pitfalls: Assuming low temperatures or movement disqualify radiation thermometers. It is the line-of-sight that is truly critical. Final Answer: inside a pressure vessel (no line of sight)

Question 9

Purpose of thermowells in temperature measurement In industrial service, thermowells are installed primarily to achieve which of the following goals when measuring temperature with probes or thermocouples?

Accepted Answer

Introduction / Context: Thermowells are protective housings inserted into process lines and vessels so that temperature sensors can be installed, removed, and protected without breaching the process. Understanding their primary purpose avoids unrealistic expectations about response time or accuracy improvements. Given Data / Assumptions: Thermowells are typically metallic tubes (e.g., stainless steel, alloy steels) immersed in the process. A sensor (thermocouple, RTD) sits inside, isolated from corrosive fluid and pressure. Heat must conduct through the well wall to the sensor. Concept / Approach: The principal function is mechanical and chemical protection: to guard the sensing element from corrosion, erosion, oxidation, pressure, and to permit safe removal. By interposing an extra thermal mass and conduction path, thermowells generally increase lag relative to a bare probe. They do not inherently increase sensitivity or guarantee “perfect fidelity.” Proper design (taper, immersion length) mitigates lag and vibration while preserving acceptable accuracy. Step-by-Step Solution: Identify hazards: corrosion, pressure, erosion, and mechanical removal needs.Map to thermowell role: provide a robust barrier and standardised mounting.Recognise side effects: added thermal mass often slows response (greater lag). Verification / Alternative check: Standards and best practices (e.g., ASME PTC, ISA) emphasise protection and safe maintenance as the key motivations for thermowells; response-time penalties are managed by geometry. Why Other Options Are Wrong: Reduce lag — opposite is typical; wells usually slow response.Increase fidelity or sensitivity — not the thermowell’s purpose; electronics handle sensitivity, not the well.Amplify signal — thermowells are passive mechanical components, not electrical amplifiers. Common Pitfalls: Expecting faster response with a thermowell; in fact, bare sensors are faster but less protected. Final Answer: guard against corrosive and oxidising action on thermocouple materials

Question 10

High-temperature thermocouples in oxidising atmospheres (~1600°C) Which thermocouple type is most suitable for measuring about 1600°C in an oxidising environment?

Accepted Answer

Introduction / Context: Selecting a thermocouple for very high temperatures demands attention to both temperature capability and atmosphere. Oxidising conditions quickly degrade base-metal thermocouples at extreme temperatures. Noble-metal combinations withstand oxidising atmospheres far better and maintain accuracy near 1600°C. Given Data / Assumptions: Target temperature ≈ 1600°C. Atmosphere is oxidising (e.g., furnace air). Conventional industrial thermocouple types considered. Concept / Approach: Platinum–platinum+rhodium (Types S or R) thermocouples are standard for high-temperature measurements in oxidising environments and are commonly used in ceramic kilns and metallurgical furnaces. Base-metal types like Iron–Constantan (Type J) and Copper–Constantan (Type T) have far lower temperature limits. Chromel–Alumel (Type K) handles moderately high temperatures but not reliably around 1600°C in oxidising atmospheres. Tungsten–rhenium requires inert or vacuum conditions; bare use in air is unsuitable due to oxidation. Step-by-Step Solution: Filter by atmosphere: eliminate materials that oxidise rapidly at high T.Check temperature limits: only noble-metal types reliably approach 1600°C in air.Select Platinum–Platinum+Rhodium as the appropriate choice. Verification / Alternative check: Industry standards list Type S/R ranges up to around 1600–1700°C in oxidising atmospheres with proper protection tubes, confirming suitability. Why Other Options Are Wrong: Iron–constantan / Copper–constantan — low maximum temperature limits; unsuitable.Chromel–alumel — not reliable at ~1600°C in oxidising air.Tungsten–rhenium — requires vacuum/inert; oxidises rapidly in air. Common Pitfalls: Choosing on maximum temperature alone without considering the atmospheric compatibility; atmosphere often dictates survivability. Final Answer: Platinum–platinum + rhodium (noble metal type)

Question 11

Speeding up spring/filled thermometers — what not to put in the well? To improve response speed, the clearance between a pressure spring liquid/gas expansion thermometer bulb and its thermowell is often filled with a good heat-transfer medi…

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Introduction / Context: Spring/filled (bulb) thermometers rely on heat transfer from process fluid to the bulb, then to the working fluid that expands. Any thermal resistance in the conduction path slows the instrument’s response. The small annular gap between the bulb and the thermowell can be improved by filling it with a thermally conductive material — but only if that material enhances heat transfer, not insulates it. Given Data / Assumptions: Gap exists between bulb and well wall. Goal is faster response (lower lag), not long-term drift considerations. Material must have higher thermal conductivity than stagnant air. Concept / Approach: Air is a poor thermal conductor and also allows natural convection pockets, both of which increase thermal resistance and response lag. Conversely, liquids (oils, mercury where permitted), metal powders, graphite, or purpose-made thermal pastes enhance conduction and reduce the dead-space effect. Therefore, to speed response, do not leave the gap filled with air; choose a better heat-transfer medium compatible with the process and safety standards. Step-by-Step Solution: Identify the heat-transfer bottleneck: stagnant air layer in the annulus.Compare conductivities: air (very low) vs oils, metals, or thermal pastes (higher).Conclude that the one material you should not use is air. Verification / Alternative check: Instrument installation guides recommend thermal grease or conductive fills in wells specifically to avoid air gaps and to improve dynamic response time. Why Other Options Are Wrong: Metal powder/graphite — increase effective conductivity; commonly used.Oil — better conductor than trapped air; improves response (check temperature limits).Mercury — excellent thermal conductor (use restricted by safety/environmental rules).Thermal paste — designed to minimise contact resistance; beneficial. Common Pitfalls: Assuming “empty space” is neutral; in fact, trapped air is a significant insulator and degrades response badly. Final Answer: air

Question 12

Routh–Hurwitz stability test in control engineering Which of the following statements correctly describes a limitation or capability of the Routh–Hurwitz criterion applied to a linear time-invariant system?

Accepted Answer

Introduction / Context: The Routh–Hurwitz criterion is a classical analytical tool used to assess closed-loop stability of linear time-invariant (LTI) systems. Instead of computing all roots of the characteristic polynomial, it uses a tabular test (the Routh array) to determine whether any roots lie in the right-half complex plane. This question checks your understanding of what Routh–Hurwitz can and cannot do, especially when time delays appear in the loop. Given Data / Assumptions: System is LTI and described by a characteristic equation in s. “Transportation lag” refers to a pure time delay with factor e^(−L s). Stability is defined by the location of characteristic roots (poles) in the s-plane. Concept / Approach: Routh–Hurwitz applies to characteristic equations that are polynomials in s. It reveals how many roots are in the right half-plane (RHP), on the imaginary axis, or in the left half-plane (LHP) by testing the signs/patterns in the first column of the Routh array. However, it does not return the actual root coordinates; it is a counting test, not a root-solver. When a pure time delay e^(−L s) is present, the characteristic equation is not a polynomial. To use Routh, one must first approximate the delay (for example, with a Pade approximation), thereby recovering a rational approximation suitable for the Routh test. Step-by-Step Solution: Identify what Routh–Hurwitz can do: count RHP roots from a polynomial.Identify what it cannot do: provide exact pole locations.Recognize why pure delay is problematic: e^(−L s) is non-polynomial → needs approximation.Select the statement that captures this limitation regarding time delay. Verification / Alternative check: Standard control texts advise approximating delays before applying Routh or using frequency-domain methods (Nyquist) that handle delays more naturally. Why Other Options Are Wrong: Provides exact locations: False; Routh only counts, it does not locate. Not applicable to polynomials: False; it is specifically for polynomials. Counts RHP roots: True statement in (a), but the question asks for the best single descriptor including the delay limitation; option (b) most directly answers the prompt about transportation lag. Common Pitfalls: Confusing Routh’s counting ability with root-solving; overlooking the special handling required for time delays. Final Answer: It cannot be applied directly when a pure transportation lag is present (e.g., e^(−Ls)) unless the lag is approximated.

Question 13

Paramagnetism vs diamagnetism in continuous flue-gas analysis A continuous flue-gas analyzer that uses magnetism relies on paramagnetic components moving toward the strongest magnetic field, displacing diamagnetic gases. Which of the following gases…

Accepted Answer

Introduction / Context: Some continuous emissions monitoring systems (CEMS) measure oxygen by exploiting magnetic properties: oxygen is strongly paramagnetic and is attracted to a magnetic field. In such instruments, diamagnetic components are displaced. To interpret the readings and understand interferences, you should know which common flue-gas constituents are para- or diamagnetic. Given Data / Assumptions: Paramagnetic gases are attracted to magnetic fields. Diamagnetic gases are weakly repelled. Typical stack gases include O2, CO2, NO, NO2, N2, H2O (vapour), etc. Concept / Approach: Molecular oxygen (O2) is a classic paramagnetic gas due to its unpaired electrons. Nitric oxide (NO) and nitrogen dioxide (NO2) also have unpaired electrons and are paramagnetic. Carbon dioxide (CO2), with all electrons paired and a linear, closed-shell electronic configuration, is diamagnetic. Thus, in paramagnetic analyzers, CO2 behaves as the diamagnetic component displaced by O2’s magnetically induced motion. Step-by-Step Solution: Recall magnetic classifications of common gases.Identify O2, NO, NO2 as paramagnetic (unpaired electrons).Recognize CO2 as diamagnetic (all electrons paired).Select CO2 as the diamagnetic gas. Verification / Alternative check: Instrument manuals for paramagnetic O2 analyzers list CO2, N2, and others as diamagnetic, while O2 is the paramagnetic target species. Why Other Options Are Wrong: O2 / NO / NO2: All paramagnetic, not diamagnetic. Common Pitfalls: Assuming all oxides are diamagnetic; many nitrogen oxides are paramagnetic due to odd-electron configurations. Final Answer: CO2

Question 14

Analytical instrumentation – what does a mass spectrometer analyze best? Mass spectrometry is especially suited for composition analysis and identification of which of the following?

Accepted Answer

Introduction / Context: Mass spectrometry (MS) separates ions by mass-to-charge ratio and detects their abundances. Because different isotopes of an element have different masses, MS is exceptionally powerful for isotope identification and ratio measurements, widely used in geochemistry, nuclear science, environmental tracing, and quality control of gases and organics. Given Data / Assumptions: MS requires analytes to be converted to gas-phase ions. Ion optics and mass analyzers (quadrupole, TOF, magnetic sector) separate m/z. Detector current is proportional to ion abundance. Concept / Approach: Isotopic variants differ only in neutron number, thus mass. When ionized, their m/z values shift accordingly, producing resolvable peaks that unveil isotopic composition with high sensitivity and precision. While alloys can be studied by MS after appropriate sampling (e.g., spark source, laser ablation), the technique excels most naturally at isotope analysis due to the direct mass distinction. Bulk solids without vaporization/ionization cannot be analyzed directly; sample introduction must create ions first. Step-by-Step Solution: Recognize isotopes differ in mass → ideal for MS separation.Note MS detects m/z, enabling isotope ratio quantification.Eliminate options requiring bulk analysis without ionization. Verification / Alternative check: Applications like isotope ratio MS (IRMS) and accelerator MS are standard for isotopic fingerprints (e.g., C-13/C-12, O-18/O-16). Why Other Options Are Wrong: Alloys: Possible with specialized sampling, but not the quintessential use highlighted in fundamentals. Solids (bulk, without vaporization): Incompatible with MS without ion generation. None of these: Incorrect because isotopes are a prime use-case. Common Pitfalls: Assuming MS directly “weighs” solids; all MS measurements are on ions in vacuum. Final Answer: Isotopes

Question 15

Physical systems – example exhibiting underdamped behavior Which of the following is a typical real-world example of an underdamped dynamic system?

Accepted Answer

Introduction / Context: Underdamped systems exhibit oscillatory transients that decay over time. Recognizing such systems in process and instrumentation helps in sensor selection, controller tuning, and interpretation of step tests. This question asks you to pick a canonical underdamped example from common equipment. Given Data / Assumptions: Underdamped response: oscillations with decaying amplitude after a disturbance. Overdamped/first-order response: monotone approach to steady state. Examples span fluid-filled instruments, thermal sensors, and reactors. Concept / Approach: A U-tube manometer behaves like a mass–spring–damper: the oscillating liquid columns (inertia), gravity (restoring force), and viscous/frictional losses (damping). When disturbed by a step in pressure, the liquid level oscillates about the equilibrium and decays depending on damping—an archetypal underdamped response. In contrast, a thermocouple in a thermowell shows a sluggish, non-oscillatory rise (often well-modeled as second-order overdamped or as a sum of first-order lags). A CSTR with a first-order reaction is typically a first-order or overdamped higher-order system with no oscillation. A spring-loaded diaphragm valve in quasi-static use usually exhibits non-oscillatory displacement for small steps (unless actuator dynamics and fluid forces introduce resonance, which is not the typical foundational example). Step-by-Step Solution: Recall the dynamic analog: U-tube ↔ mass–spring–damper.Identify the signature: decaying oscillations following a step input.Compare alternatives: thermal and reactor systems are usually non-oscillatory.Choose the underdamped example: U-tube manometer. Verification / Alternative check: Manometer transient derivations yield a second-order ODE with natural frequency and damping ratio; experiments show classic ring-down behavior. Why Other Options Are Wrong: Thermowell thermocouple: Overdamped (sum of lags), no ringing. CSTR first-order: Monotonic, no oscillation. Spring-loaded diaphragm valve: Typically dominated by static compliance and damping; oscillations are not the fundamental textbook case. Common Pitfalls: Assuming any mechanical device oscillates; damping often suppresses oscillations unless inertia and restoring forces form a clear second-order pair. Final Answer: U-tube manometer

Question 16

Flow measurement – identify the device that is not a differential-pressure meter Which of the following is not a differential-pressure (DP) type flow meter?

Accepted Answer

Introduction / Context: Industrial flow measurement devices come in many forms. Differential-pressure (DP) meters infer flow from a pressure drop created by a restriction. Variable-area meters (rotameters) infer flow from the equilibrium position of a float in a tapered tube. Recognizing the measurement principle is foundational in instrumentation selection and sizing. Given Data / Assumptions: DP meters: pressure drop across a primary element is related to flow (Bernoulli + discharge coefficient). Variable-area meter: float rises until drag force balances weight minus buoyancy. Ideal fluids and standard installation practices are assumed for principle identification. Concept / Approach: Venturimeters, flow nozzles, and orificemeters are textbook DP meters. Each creates a constriction; the static pressure difference between upstream and throat/taps correlates with volumetric or mass flow after calibration. A rotameter, however, uses a tapered transparent tube and a float. The area available to flow increases with float height; the float's position (not a DP reading) is directly indicated and correlated to flow rate. Thus, the rotameter is not a DP meter. Step-by-Step Solution: Group devices by principle: Venturi/nozzle/orifice → DP; rotameter → variable-area.Apply definition: DP meters measure pressure drop; rotameter measures float height.Select the non-DP device: rotameter. Verification / Alternative check: Standards (ISO/ASME) classify Venturi, nozzle, orifice under DP primary devices, while rotameters are listed under variable-area (VA) meters. Why Other Options Are Wrong: Venturimeter / Flow nozzle / Orificemeter: All operate on differential pressure across a constriction. Common Pitfalls: Assuming every meter with a pressure effect is a DP meter; in rotameters the indicated variable is position, not measured pressure drop. Final Answer: Rotameter

Question 17

Bolometer – working principle and purpose In basic instrumentation terms, a bolometer is best described as which of the following?

Accepted Answer

Introduction / Context: Bolometers are widely used in infrared (IR) thermography, astrophysics, and thermal imaging. They translate incident electromagnetic radiation, typically in the IR, into a measurable change in temperature and therefore resistance. Understanding what a bolometer actually measures and how it signals is essential to distinguish it from photonic detectors or general thermometers. Given Data / Assumptions: Incident radiation is absorbed by a sensing element. Absorption raises the element's temperature slightly. Electrical resistance of the element changes with temperature and is read out. Concept / Approach: A bolometer measures radiant power by calorimetric means: optical energy → heat in the absorber → temperature rise → resistance change. The output is electrical (change in resistance or related bridge voltage), not a “thermal output” delivered to the process. This sets bolometers apart from photodiodes/phototransistors (which generate photocurrent via photon–electron interactions) and from gas thermometers or mechanical gauges (which work on expansion or elastic deformation, not radiation absorption). Step-by-Step Solution: Identify the measured quantity: radiant power in IR/optical bands.Recognize the mechanism: absorption → heating → resistance change.Choose the description that mentions measuring thermal radiation via temperature-dependent resistance. Verification / Alternative check: IR camera datasheets describe microbolometer arrays where each pixel is a tiny bolometer, read out electrically to form images of thermal radiation. Why Other Options Are Wrong: Optical input with thermal output: Misleading; the useful output is electrical. Photodiode-like visible detector: Different detection physics. Gas expansion thermometer: Unrelated to bolometric detection. Common Pitfalls: Thinking a bolometer “measures temperature” directly; it measures absorbed radiant power that causes a temperature change in the detector. Final Answer: A sensor used for measuring thermal radiation power via temperature-dependent resistance.

Question 18

Bode plots and excitation signals Bode magnitude and phase plots are generated from a system’s steady-state response to which class of input?

Accepted Answer

Introduction / Context: Bode plots summarize a linear time-invariant (LTI) system’s frequency response by showing gain and phase versus frequency. To obtain these characteristics, we conceptually excite the system with inputs at single frequencies and measure the steady-state output amplitude and phase shift. Identifying the correct excitation class ensures the right mental model for frequency-domain analysis. Given Data / Assumptions: System is LTI and stable for the frequencies of interest. Frequency response G(jω) is defined via sinusoidal steady-state. Magnitude and phase are plotted over a logarithmic frequency axis. Concept / Approach: By definition, the frequency response is the ratio of the steady-state output to input when the input is a sinusoid of frequency ω: u(t) = A sin(ω t). For an LTI system, the steady-state output is also sinusoidal at the same frequency but with different amplitude and a phase lag/lead. Sampling this response across ω yields the data for the Bode magnitude and phase plots. Although other test signals (impulse, step, ramp) can be used to derive frequency response indirectly via transforms, the foundational definition uses sinusoidal input. Step-by-Step Solution: Recall definition: G(jω) = Output(jω)/Input(jω) under sinusoidal steady-state.Vary ω across decades; record gain and phase.Plot magnitude (dB) and phase (degrees or radians) vs frequency. Verification / Alternative check: Experimental frequency response analysis conducts chirp or swept-sine tests; computationally, FFT of sinusoidal steady-state also yields G(jω). Why Other Options Are Wrong: Impulse/Step/Ramp: Useful for time-domain characterisation; frequency response is defined via sinusoidal excitation. Common Pitfalls: Confusing “obtained from” with “related to”: while impulse/step responses can be transformed to frequency domain, the canonical construction of Bode data is sinusoidal steady-state. Final Answer: Sinusoidal

Question 19

Control systems with dead time (transportation lag): For a feedback system that contains a significant pure time delay (transportation lag), which analysis approach is generally the most reliable for assessing closed-loop stability and margins?

Accepted Answer

Introduction / Context: Transport delays (also called dead time or transportation lag) appear in chemical processes due to material and energy holdup, sample lines, analyzer delays, and long pipelines. Such delays complicate stability analysis because they introduce a non-rational factor exp(−θs) in the open-loop transfer function. This question asks which technique best handles these non-polynomial dynamics when deciding if the closed loop will be stable and with what safety margins. Given Data / Assumptions: A linear time-invariant single-loop system with a significant pure time delay. Standard negative feedback architecture. Objective: determine stability and quantify gain/phase margins. Concept / Approach: Frequency response methods (Bode and Nyquist) naturally accommodate dead time because exp(−θs) becomes a multiplicative term with magnitude 1 and phase −ωθ at jω. Thus, delay simply adds frequency-dependent phase lag without altering magnitude. Stability can be assessed from the loop’s gain and phase at the crossover frequencies, enabling direct reading of phase/gain margins despite the delay. Step-by-Step Solution: Represent the open loop as L(s) = G(s) * exp(−θs).Evaluate L(jω): |exp(−jωθ)| = 1, ∠exp(−jωθ) = −ωθ (pure phase lag).Plot Bode/Nyquist; read gain crossover and phase margin to judge stability.Conclude: frequency response is the preferred tool for dead-time systems. Verification / Alternative check: Bode plots immediately show how increasing θ reduces phase margin. Nyquist explicitly reveals encirclements of −1 as delay grows. Smith Predictor design also starts from frequency-domain insight. Why Other Options Are Wrong: Routh test: Requires a polynomial characteristic equation; exact dead time is non-polynomial, so approximations are needed. Root locus: Also built on rational transfer functions; dead time forces Padé approximations and may mislead if order is too low. None/state-space-only: Not the standard or most convenient path for routine stability/margin checks with delay. Common Pitfalls: Relying on low-order Padé approximations can over- or under-estimate margins. Always validate with frequency response if delay is substantial. Final Answer: Frequency response methods

Question 20

Industrial thermocouples and protection wells: When a bare thermocouple junction is enclosed in a protective sheath (thermowell), how does the dynamic response typically change?

Accepted Answer

Introduction / Context: Thermocouples are common in process plants for temperature indication and control. To protect the sensor from corrosion, erosion, or high velocity streams, the bare junction is often inserted in a metallic thermowell (protective sheath). This modification affects dynamics. Understanding that change helps tune controllers and pick the right measurement lag model. Given Data / Assumptions: Bare junction replaced by a protected junction inside a thermowell. Same process fluid and flow conditions. We focus on qualitative dynamic behavior: speed and tendency to oscillate. Concept / Approach: Adding a sheath increases the thermal mass between the fluid and the hot junction and adds a conductive path through metal plus a convective film. The equivalent first-order time constant τ increases (more capacitance and resistance), so the measured signal reacts more slowly. At the same time, extra damping reduces susceptibility to noise-driven wiggles; the response remains non-oscillatory for standard sensor/thermowell designs. Step-by-Step Solution: Model the sensor as first-order lag: G(s) = 1 / (1 + τs).Add thermowell → higher thermal resistance/capacitance → larger τ.Larger τ means slower rise time; well-damped behavior remains non-oscillatory. Verification / Alternative check: Step tests in plants consistently show bare junctions respond faster than sheathed ones; datasheets list greater time constants for thermowell assemblies. Why Other Options Are Wrong: “Faster…”: Contradicts added thermal mass and resistance. “…oscillatory”: Sensor dynamics are dominantly first-order; oscillation typically arises from loop tuning, not the sensor alone. “Unchanged”: Practically never true; the hardware change is significant. Common Pitfalls: Blaming oscillations on the sensor when the root cause is aggressive controller tuning; the thermowell usually smooths noise rather than causing oscillation. Final Answer: Slower and non-oscillatory

Process Control and Instrumentation Questions