Question 1

High-temperature measurement: a radiation pyrometer operates fundamentally according to which physical law relating radiated energy to temperature?

Accepted Answer

Introduction / Context: Radiation pyrometers measure temperature of hot objects without contact by sensing thermal radiation. Understanding the governing radiation laws is vital in furnace control, metallurgy, and materials processing. Given Data / Assumptions: Total (integrating) radiation pyrometers measure emitted energy over a broad band. Emissivity is accounted for or approximated. Objects are sufficiently hot for significant thermal emission. Concept / Approach: The Stefan–Boltzmann law states that total radiated power per unit area is proportional to T^4 (for a blackbody): E = σ T^4; for real surfaces, E = ε σ T^4. Total radiation pyrometers exploit this relationship. Optical (narrow-band) pyrometers often rely on Planck’s law and use approximations such as Wien’s law, but “radiation pyrometer” in general industrial usage most commonly refers to total radiation, hence Stefan–Boltzmann law applies fundamentally. Step-by-Step Solution: Measure radiant flux from target.Account for instrument view factor and emissivity (ε).Relate measured power to temperature via E ∝ T^4. Verification / Alternative check: Two-color/ratio pyrometers minimize emissivity uncertainty but still derive from Planckian emission; in contrast, total radiation units explicitly integrate and back-calculate temperature using T^4 scaling—consistent with Stefan–Boltzmann. Why Other Options Are Wrong: Wien’s law: relates wavelength of peak emission to temperature; used in optical pyrometry but not the basis of total energy measurement. Kirchhoff’s law: links emissivity and absorptivity; supportive, not the direct operative law. Seebeck effect: thermoelectric principle for contact thermocouples, not radiation pyrometers. Common Pitfalls: Ignoring emissivity leads to temperature errors; reflective or oxidized surfaces can change ε significantly. Final Answer: Stefan–Boltzmann law

Question 2

Electromagnetic flow measurement: which statements about a magnetic flowmeter are correct?

Accepted Answer

Introduction / Context: Magnetic flowmeters (magmeters) are common for conductive liquids, including corrosive solutions and slurries. They have no intruding elements, minimizing pressure drop and fouling—key advantages in chemical and wastewater processes. Given Data / Assumptions: Conductive fluid with sufficient conductivity (typically > ~5 μS/cm). Uniform magnetic field applied across the pipe; electrodes sense induced EMF. Flow profile is fully developed or adequately averaged by electrode placement. Concept / Approach: Faraday’s law: E = B * L * v, where E is induced voltage, B magnetic flux density, L electrode spacing (pipe diameter), and v average fluid velocity. Because E ∝ v, volumetric flow rate Q = v * A maps linearly to EMF. Absence of moving parts allows handling slurries/electrolytes. Step-by-Step Solution: Apply magnetic field across conductive fluid.Moving charges in the fluid induce EMF proportional to velocity.Electrodes pick up voltage; transmitter converts to flow signal. Verification / Alternative check: Calibration with known flow (prover or weigh tank) confirms linearity; diagnostics check electrode coating and conductivity thresholds. Why Other Options Are Wrong: Each individual statement is accurate; the comprehensive choice correctly groups them. Common Pitfalls: Using magmeters for non-conductive fluids (e.g., hydrocarbons) yields no signal; electrode coating or air entrainment causes noise. Final Answer: All of (a), (b), and (c)

Question 3

Liquid-level dynamics: for a single well-mixed tank with linear outlet resistance, what is the transfer function from inlet flow rate to liquid level?

Accepted Answer

Introduction / Context: Level control loops often involve a single tank with inflow and a gravity-driven outflow through a valve/orifice exhibiting approximately linear resistance around an operating point. Deriving the transfer function is a fundamental modeling exercise in process control. Given Data / Assumptions: Tank cross-sectional area = A (constant). Outflow qout ≈ h/R (linearized around an operating point, R is resistance). Inflow = qin; state variable = level h. Time constant T = AR. Concept / Approach: Mass balance on the liquid: A dh/dt = qin − qout. With qout = h/R, the linear ODE becomes A dh/dt + (1/R) h = qin. Taking Laplace transforms and rearranging yields a first-order transfer function from Qin(s) to H(s). Step-by-Step Solution: Write dynamic balance: A dh/dt + (1/R) h = qin.Laplace: A s H(s) + (1/R) H(s) = Qin(s).Factor H(s): H(s) [ A s + 1/R ] = Qin(s).Transfer function: H(s)/Qin(s) = 1 / (A s + 1/R) = R / (A R s + 1) = R / (T s + 1). Verification / Alternative check: Step inflow of magnitude Δq causes level to approach a new steady state Δh = RΔq with time constant T = AR. This matches the DC gain (R) and dynamics of the derived transfer function. Why Other Options Are Wrong: 1/(T s) or R/(T s): missing the +1 term; would imply an integrator, not a first-order lag. 1/(T s + 1): incorrect DC gain (should be R). Common Pitfalls: For large deviations, outflow is nonlinear (orifice law q ∝ sqrt(h)); linearization around operating point is required to retain first-order form and constant R. Final Answer: R / (T*s + 1)

Question 4

Thermometry principles: which thermometer operates on volumetric expansion of a liquid?

Accepted Answer

Introduction / Context: Different industrial thermometers rely on distinct physical principles: volumetric expansion, pressure–temperature relations, phase equilibria, or differential solid expansion. Choosing the right device requires understanding the underlying mechanism. Given Data / Assumptions: Mercury-in-glass uses liquid volume expansion. Constant-volume gas thermometer measures pressure change at fixed volume. Vapor-pressure thermometer uses saturation pressure changes. Bimetallic thermometer uses differential linear expansion of two metals. Concept / Approach: Liquids generally expand with temperature. In a mercury-in-glass thermometer, the liquid’s volumetric expansion within a narrow capillary converts small volume changes into easily read length changes along a calibrated scale. The other instruments depend on pressure or bending effects, not direct volume indication within a capillary scale. Step-by-Step Solution: Identify volumetric expansion thermometer: mercury-in-glass.Differentiate from constant-volume gas: measures pressure, not volume change.Differentiate from vapor-pressure: reads pressure of a volatile liquid–vapor system.Differentiate from bimetallic: relies on differential expansion producing curvature. Verification / Alternative check: Calibration curves for mercury-in-glass are based on volumetric expansion coefficient of mercury and glass bulb/capillary geometry; corrections account for glass expansion (emergent stem correction when needed). Why Other Options Are Wrong: Constant-volume gas: pressure-based; not volumetric expansion indication. Vapor-pressure: phase-equilibrium pressure; not capillary volume readout. Bimetallic: mechanical deflection; no liquid volume measurement. Common Pitfalls: Assuming all filled-system thermometers are “volumetric.” Gas and vapor systems primarily measure pressure, even though volume is fixed or phase is present. Final Answer: Mercury-in-glass thermometer

Question 5

Control systems — Nichols chart interpretation In classical frequency-response design, the Nichols chart plots what relationship to help map open-loop data to closed-loop performance?

Accepted Answer

Introduction / Context: The Nichols chart is a cornerstone tool in classical control engineering. It converts frequency-domain information (open-loop gain and phase) into direct insight about closed-loop behavior using families of constant closed-loop magnitude (M-circles) and constant closed-loop phase (N-circles). Designers can judge stability margins and performance straight from the open-loop data. Given Data / Assumptions: We are dealing with linear time-invariant (LTI) feedback systems. Open-loop frequency response is plotted as log magnitude (dB) versus phase angle. Nichols chart overlays closed-loop contours on this open-loop plane. Concept / Approach: The chart maps the point L(jω) = G(jω)H(jω) (open-loop) into the closed-loop transfer T(jω) = L(jω)/(1 + L(jω)). M- and N-circles show how any open-loop point translates into closed-loop magnitude and phase. Thus the chart inherently relates closed-loop values to open-loop data, enabling rapid loop-shaping and robustness assessment. Step-by-Step Solution: Recognize that Nichols axes are open-loop gain (dB) versus open-loop phase (degrees).Identify that the superposed circles correspond to constant closed-loop responses.Therefore the chart relates closed-loop performance to open-loop frequency response. Verification / Alternative check: From T = L/(1 + L), loci of constant |T| and ∠T in the L-plane generate the M and N contours drawn on the Nichols chart. Why Other Options Are Wrong: (a) and (b): Restrict to first- or second-order only; Nichols is general. (d): Not limited to controller curves; it is a system-level mapping tool. Common Pitfalls: Confusing Nichols with Bode or Nyquist; Nichols uniquely uses dB vs phase with closed-loop overlays. Final Answer: Closed-loop performance contours overlaid on open-loop gain (in dB) versus phase

Question 6

Analytical instrumentation — suitable use of mass spectrometry For which sample type is mass spectrometry classically employed to perform detailed compositional (especially isotopic) analysis in process and laboratory settings?

Accepted Answer

Introduction / Context: Mass spectrometry separates ionized species according to mass-to-charge ratio. A key strength is the ability to resolve and quantify isotopes of the same element, which differ only by neutron number but not by chemical behavior. Given Data / Assumptions: Question asks for the sample type most directly associated with compositional analysis by a mass spectrometer. Mass spectrometers measure isotopic abundance with high precision. Concept / Approach: Because isotopes have distinct masses, mass spectrometry is uniquely well-suited to their identification and quantification. While gases, solids, and alloys can also be analyzed after suitable sample preparation and ionization, the canonical, textbook application is isotopic analysis (e.g., deuterium vs protium, C-13 vs C-12). Step-by-Step Solution: Identify the technique’s primary advantage: mass resolution → isotopic separation.Select the choice that explicitly matches this advantage.Therefore, the best answer is “An isotope.” Verification / Alternative check: Radiogenic dating, tracer studies, and isotope ratio mass spectrometry (IRMS) are standard applications confirming this selection. Why Other Options Are Wrong: Natural gas / solids / alloys: analyzable but not uniquely tied to the core capability highlighted by the question; they require specific inlet and prep methods. Common Pitfalls: Assuming “mass spec = any composition.” True in broad terms, but its hallmark is isotopic resolution. Final Answer: An isotope

Question 7

Thermocouple wiring — insulation limits What is the maximum recommended service temperature for fibre-glass insulation on thermocouple extension/compensation wires in typical industrial use?

Accepted Answer

Introduction / Context: Thermocouples often run through hot environments; however, it is usually the insulation and jacket that limit allowable service temperature, not the thermoelements themselves. Fibre-glass sleeves are common for moderate-to-high temperatures. Given Data / Assumptions: Typical E-glass or high-temperature glass braid with appropriate binders is considered. Continuous service temperatures are lower than short-term excursion limits. Concept / Approach: Standard glass fibre insulation for thermocouple leads is widely rated around 500 °C for continuous service. Above this, ceramic fibre or mineral insulation is preferred. Lower options (e.g., 250 °C) are associated with certain polymeric insulations; higher options (750–1000 °C) exceed glass fibre’s binder and softening constraints. Step-by-Step Solution: Identify the commonly published continuous rating for glass fibre insulation.Select the closest matching value from the options → 500 °C. Verification / Alternative check: Manufacturers’ datasheets for glass braid thermocouple wires consistently specify ~500 °C continuous capability. Why Other Options Are Wrong: 250 °C: more consistent with high-temperature polymers, not glass braid. 750–1000 °C: above glass fibre’s practical continuous limits; mineral/ceramic solutions are used instead. Common Pitfalls: Confusing the thermocouple hot junction capability with wire insulation limits. Final Answer: 500 °C

Question 8

Flow measurement — principle of a rotameter A rotameter (variable area flowmeter) indicates flow rate primarily based on which operating principle?

Accepted Answer

Introduction / Context: Among mechanical flowmeters, the rotameter is popular for simplicity and direct visual indication. It is commonly used for gases and liquids in laboratories and process skids. Given Data / Assumptions: The device has a vertical, tapered, transparent tube and a float. Flow is upward; the float reaches an equilibrium position between buoyant, drag, and gravitational forces. Concept / Approach: As flow increases, the float rises to a larger cross-section of the tapered tube, increasing the annular area until the pressure drop and forces balance. Thus, the meter operates on a variable area principle, not on a fixed-area pressure drop or turbine rotation principle. Step-by-Step Solution: Identify unique geometry: tapered tube + moving float.Relate float height to flow via equilibrium of forces and area change.Conclude: measurement principle is variable area. Verification / Alternative check: Calibration marks on the tube correlate float height to standard volumetric flow under specified conditions. Why Other Options Are Wrong: Turbine rotation: describes turbine meters, not rotameters. Nozzle pressure drop: that is an orifice/nozzle/venturi principle with fixed area. Stagnation pressure: used in pitot tubes, not rotameters. Common Pitfalls: Assuming all differential-pressure meters are the same; rotameters vary area, not only measure Δp. Final Answer: Variable flow area created by a float in a tapered tube

Question 9

In applied thermodynamics and HVAC testing, humidity of ambient air is commonly determined using which field instrument that compares dry-bulb and wet-bulb temperatures while being whirled through the air?

Accepted Answer

Introduction / Context: Humidity measurement is fundamental in air-conditioning design, drying operations, meteorology, and environmental monitoring. Many instruments exist to analyze air composition, but only a few are practical for routine field measurement of moisture content (relative humidity). The classic and widely taught tool is the sling psychrometer, which directly links temperature depression to humidity through psychrometric relationships. Given Data / Assumptions: The task is routine field measurement of atmospheric humidity. Low-cost, portable equipment is implied by “determined by.” We seek the most appropriate, standard instrument from the options given. Concept / Approach: A sling psychrometer has two thermometers: one measures dry-bulb temperature, the other has a wetted wick and measures wet-bulb temperature. Whirling the device promotes evaporation from the wet wick. Evaporation cools the wet-bulb thermometer; the temperature depression (dry-bulb minus wet-bulb) depends on the moisture already in the air. Using psychrometric charts or formulae, operators convert the measured pair into relative humidity, humidity ratio, and dew point. Step-by-Step Solution: Hold the instrument and wet the wick with clean water.Whirl the psychrometer at steady speed for a prescribed time.Read stabilized dry-bulb and wet-bulb temperatures.Use a psychrometric chart/table to compute relative humidity and other properties. Verification / Alternative check: Dew-point hygrometers and electronic capacitive sensors can also measure humidity, but for textbooks and basic labs, the sling psychrometer remains the canonical method due to simplicity, low cost, and traceable calculations. Its readings can be cross-checked against a digital thermo-hygrometer for validation. Why Other Options Are Wrong: Chromatograph / mass spectrometer: Laboratory analyzers, not practical field humidity meters.Polarimeter / refractometer: Optical concentration tools for optically active solutions or refractive index, not atmospheric humidity. Common Pitfalls: Insufficient wetting of the wick, contaminated water, or inadequate air velocity around the wet bulb cause errors. Also, using warm hands to hold bulbs can bias readings. Calibrating thermometers and shielding from radiant heat improves accuracy. Final Answer: Sling psychrometer

Question 10

Analytical methods for sucrose and other optically active sugars: the concentration of a sugar solution is most directly determined using which optical technique that measures the angle of rotation of plane-polarized light?

Accepted Answer

Introduction / Context: Sugar quality control in food, fermentation, and biochemical labs often requires determining concentration quickly and accurately. Many instrumental techniques exist, but for optically active sugars (such as sucrose), the classical and still-relevant method is polarimetry, which exploits their ability to rotate plane-polarized light. Given Data / Assumptions: Analyte is an optically active sugar (e.g., sucrose, glucose). Sample is a clear solution in a suitable cell length. Standard temperature, wavelength (often sodium D-line), and path length are controlled or known. Concept / Approach: According to the polarimetric principle, the observed rotation (alpha) is proportional to concentration (c) and path length (l): alpha = [alpha]_specific * l * c. By measuring the rotation with a polarimeter and knowing the specific rotation (from tables) and cell length, one calculates concentration directly. This method is rapid, non-destructive, and widely standardized for sugar solutions (e.g., International Sugar Scale). Step-by-Step Solution: Prepare a clear, bubble-free sugar solution of known path length.Place it in the polarimeter tube and align the instrument.Measure optical rotation at the specified wavelength and temperature.Compute concentration using the known specific rotation and path length. Verification / Alternative check: Results can be checked by refractometry (Brix) when applicable; however, polarimetry directly targets optical activity and is less confounded by non-optically-active solutes if calibrated correctly. Why Other Options Are Wrong: Flame photometry/emission spectroscopy: Elemental analysis of metals; not for organic sugar concentration.Oscillometry: Measures properties like blood pressure or impedance, not optical rotation.Potentiometric titration: Useful for acids/bases or redox systems, not the standard for sugar concentration. Common Pitfalls: Ignoring temperature control (specific rotation is temperature-dependent), using contaminated cells, or misreading the end-point alignment can introduce bias. Calibrate with certified sucrose solutions for accuracy. Final Answer: Polarimetry

Question 11

Gas constant-volume thermometry with nitrogen: a nitrogen gas constant-volume thermometer is particularly suitable for measuring temperatures in which range relative to 100 °C?

Accepted Answer

Introduction / Context: Gas thermometers are primary thermometric standards because gas properties are well described by equations of state. In practice, specific gases are chosen for different temperature regimes. Hydrogen is favored for very low temperatures due to minimal condensation issues, whereas nitrogen is commonly used for higher ranges in constant-volume thermometry. Given Data / Assumptions: Thermometer type: constant-volume gas thermometer. Working gas: nitrogen (chemically inert and readily available). We compare its suitability with respect to 100 °C. Concept / Approach: In a constant-volume gas thermometer, pressure variation tracks temperature at fixed volume (P proportional to T in Kelvin for ideal behavior). Nitrogen is stable and convenient well above ambient and is a traditional choice for temperatures exceeding the boiling point of water. Below 0 °C and at cryogenic temperatures, hydrogen or helium are preferred to avoid liquefaction and to maintain near-ideal behavior. Step-by-Step Solution: Recognize nitrogen’s operating envelope: robust at moderate to high temperatures.Contrast with hydrogen/helium for sub-zero or cryogenic ranges.Conclude that nitrogen constant-volume thermometers are best suited for temperatures greater than 100 °C among the given choices. Verification / Alternative check: Calibration tables and metrological references group nitrogen with mid-to-high temperature service for gas thermometry, while special gases handle extremes. Why Other Options Are Wrong: 0–100 °C: Usable, but nitrogen’s canonical niche in textbooks is above 100 °C.< 0 °C: Risk of non-idealities and condensation; other gases are favored.> 50 °C: Too broad; standard pedagogy specifies above 100 °C.Exactly 100 °C only: Incorrect; a thermometer covers ranges, not single points. Common Pitfalls: Confusing constant-volume with constant-pressure gas thermometers, or assuming all gases are equally suitable across all temperatures. Gas selection impacts measurement uncertainty and practical construction. Final Answer: > 100 °C

Question 12

Electrical resistance strain gauge principle: when a fine conductor in a bonded strain gauge is elastically stretched, its length increases and diameter decreases. The combined dimensional changes result in what net change in electrical resistance?

Accepted Answer

Introduction / Context: Strain gauges convert mechanical deformation into an electrical signal via resistance change. Understanding why resistance changes—and in which direction—is essential for designing Wheatstone bridge circuits, interpreting gauge factors, and avoiding sign errors in instrumentation. Given Data / Assumptions: Elastic tensile strain is applied (no plastic deformation). Conductor length increases while cross-sectional area decreases. Resistivity may change slightly with strain but geometry dominates the sign. Concept / Approach: Resistance R = rho * L / A, where rho is resistivity, L is length, and A is area. Under tensile strain: L increases (raises R) and A decreases (also raises R). The piezoresistive change in rho can contribute but, for metallic gauges, the geometrical effects are primary and lead to a net increase in R under tension. The gauge factor GF approximately equals (ΔR/R)/ε and is typically around 2 for metal foil gauges. Step-by-Step Solution: Apply small tensile strain ε: L → L(1 + ε).Assuming volume constancy for small elastic strain: A decreases roughly by (1 - νε) where ν is Poisson’s ratio.Compute qualitative effect: R = rho * L / A increases because L↑ and A↓.Include minor rho changes: metallic gauges still show net ΔR > 0. Verification / Alternative check: Experimental calibration yields positive ΔR for tensile strain for common constantan or karma alloy gauges; compression yields negative ΔR of similar magnitude per unit strain. Why Other Options Are Wrong: No change: Contradicts R = rho*L/A behavior.Decrease/exponential decrease: Opposite sign; geometry dominates toward increase.Periodic fluctuation: Not characteristic of static elastic strain. Common Pitfalls: Ignoring Poisson effects; miswiring the Wheatstone bridge so that tension appears as a decrease in output; neglecting temperature compensation which can mask true strain signals. Final Answer: Increase

Question 13

Basic density testing: which of the following devices cannot be used to measure the specific gravity (relative density) of a liquid sample in a lab or field setting?

Accepted Answer

Introduction / Context: Specific gravity (SG) is a key property in chemical, petroleum, and food industries. It can be measured by several classical devices, each suited to different sample volumes, viscosities, and accuracy requirements. Identifying which instrument is unrelated to density avoids misapplication in the lab. Given Data / Assumptions: We compare common instruments used in routine SG measurements with one instrument used for something entirely different. Liquids are Newtonian and homogeneous. Room-temperature measurements are implied. Concept / Approach: A pycnometer (specific gravity bottle) determines density by precise mass and known volume. A hydrometer floats to an equilibrium depth tied to density via buoyancy. Digital densitometers use oscillating U-tube methods. By contrast, an anemometer measures air velocity; it is not a density meter for liquids. Step-by-Step Solution: Identify SG-capable tools: specific gravity bottle, pycnometer, hydrometer, digital densitometer.Recognize anemometer’s function: wind speed measurement.Therefore, select anemometer as the device that cannot measure SG. Verification / Alternative check: Laboratory SOPs for SG testing list hydrometers (ASTM D1298), pycnometers/specific gravity bottles (ASTM D4052 equivalents via densitometer). None mention anemometers for density. Why Other Options Are Wrong: Specific gravity bottle/pycnometer: Classical gravimetric density methods.Hydrometer: Float-based quick SG measurement.Digital densitometer: Modern, precise density/SG instrument. Common Pitfalls: Using hydrometers outside their calibrated temperature, ignoring meniscus corrections, or using pycnometers with trapped bubbles can introduce noticeable error. Final Answer: Anemometer

Question 14

Frequency response of a first-order linear system: the steady-state phase shift between sinusoidal input and output varies between which lower and upper limits (in radians) as excitation frequency goes from very low to very high?

Accepted Answer

Introduction / Context: First-order systems (e.g., thermal elements, RC low-pass circuits, stirred-tank dynamics) exhibit a characteristic frequency response that includes a magnitude roll-off and a phase lag. Knowing the phase limits is crucial for loop stability assessment and Bode plot interpretation in control engineering. Given Data / Assumptions: Standard first-order transfer function: G(s) = K / (1 + τ s). Input is sinusoidal; we consider steady-state sinusoidal response. We analyze the phase shift limit as ω → 0 and ω → ∞. Concept / Approach: The frequency response G(jω) = K / (1 + j ω τ). The phase angle φ(ω) = - arctan(ω τ). As excitation frequency increases, arctan(ω τ) grows from 0 to π/2. Hence, φ(ω) decreases from 0 to -π/2. Therefore the phase shift spans the interval [-π/2, 0], with 0 at low frequency and approaching -π/2 at high frequency. Step-by-Step Solution: Write G(jω) = K / (1 + jωτ).Compute phase: φ = - arctan(ωτ).Evaluate limits: ω→0 ⇒ arctan(0)=0 ⇒ φ→0; ω→∞ ⇒ arctan(∞)=π/2 ⇒ φ→-π/2.Conclude bounds are -π/2 to 0 radians. Verification / Alternative check: Bode plots for first-order low-pass elements universally show -45° at ω=1/τ, 0° at low frequency, and -90° at high frequency, confirming the derived limits. Why Other Options Are Wrong: -∞, π/2: Nonsensical for bounded first-order phase.-π/2, π/2 and 0, π/2: Imply leading phase or positive upper bound not present in lag elements.-π, 0: Too large a lag for first-order; -π is typical of additional dynamics. Common Pitfalls: Mixing up sign conventions or confusing phase of lead/lag compensators. Always check the transfer function form and remember arctan behavior. Final Answer: -π/2, 0

Question 15

High-temperature measurement capability: which of the following instruments cannot measure a temperature as high as about 1600 °C under normal usage?

Accepted Answer

Introduction / Context: Instrument selection depends strongly on the temperature range. Industrial measurements around 1600 °C are encountered in furnaces, kilns, and metallurgical processes. Not all sensors can survive or give reliable readings at such extremes. Given Data / Assumptions: The target temperature is approximately 1600 °C. We compare common sensors: resistance thermometers, thermocouples, and non-contact pyrometers. Normal usage and materials limits apply. Concept / Approach: Platinum resistance thermometers (PRTs) are highly accurate but limited typically to about 650–850 °C for standard designs; specialized versions may extend somewhat higher but far below 1600 °C. Thermocouples (e.g., Type B, R, S, or W-Re) and radiation or photoelectric pyrometers are designed for very high temperatures and can cover 1600 °C and beyond without contacting the process directly (for pyrometers) or with high-temperature thermocouple alloys. Step-by-Step Solution: Identify PRT operating envelope: usually ≤ 850 °C.Identify high-T options: noble-metal thermocouples and non-contact pyrometers.Compare with the target: 1600 °C exceeds PRT capability.Conclude that PRT cannot measure 1600 °C under normal practice. Verification / Alternative check: Manufacturer datasheets and standards (ITS-90 implementation) specify PRT ranges well below 1600 °C, whereas high-temperature thermocouples and pyrometers explicitly cover this domain. Why Other Options Are Wrong: Thermocouple (Type B/R/S or W-Re): Suitable for ≥ 1600 °C.Photo-electric/radiation/two-color pyrometers: Non-contact optical methods designed for high-temperature targets. Common Pitfalls: Assuming PRTs are “best” at all temperatures due to accuracy; accuracy does not imply suitability beyond material limits. Also, confusing emissivity adjustments required for pyrometers with a limitation on maximum temperature. Final Answer: Platinum resistance thermometer

Question 16

Dynamic measurement quality: the degree to which an instrument reproduces changes in the measured variable with no dynamic distortion (i.e., the output waveform is a faithful copy of the input) is called its what?

Accepted Answer

Introduction / Context: In instrumentation, terminology distinguishes between how fast, how accurately, and how truthfully an instrument tracks a varying signal. When the concern is whether the output waveform is a faithful replica of the input (scaled and possibly delayed), we speak of fidelity—a critical attribute for dynamic measurements, audio systems, and control loops. Given Data / Assumptions: Measured variable varies with time. We care about waveform integrity, not merely steady-state accuracy. Definitions follow standard measurement and control textbooks. Concept / Approach: Fidelity is the property that an instrument’s output accurately represents the input without dynamic error such as overshoot, lag-induced distortion, or bandwidth limitations. While speed of response concerns how quickly the output settles, and reproducibility concerns consistency of repeated measurements, fidelity emphasizes accurate waveform reproduction across the frequency content of interest. Step-by-Step Solution: Identify required attribute: truthful, undistorted following of input changes.Map attribute to term: fidelity.Confirm other terms do not specifically denote freedom from dynamic distortion. Verification / Alternative check: System identification texts equate high fidelity with flat amplitude response and linear phase within the band of interest, minimizing waveform distortion. Practical tests include sine-sweep and step testing to verify minimal dynamic error. Why Other Options Are Wrong: Speed of response: Addresses time to respond but not distortion.Reproducibility: Repeatability under unchanged conditions; not dynamic accuracy.Static characteristics: Pertains to steady-state sensitivity, offset, linearity.Resolution: Smallest detectable input change, not waveform truthfulness. Common Pitfalls: Confusing high bandwidth (speed) with fidelity; a system can be fast yet distort phases. Conversely, a slower but well-modeled system may have good fidelity within its limited band. Final Answer: Fidelity

Question 17

Controller design basics: for a proportional–derivative (P–D) controller, what is the standard transfer function form in the Laplace domain?

Accepted Answer

Introduction / Context: Classical controllers—P, PI, PD, and PID—are building blocks of feedback control. Recognizing their transfer functions is essential for frequency response design, time-domain tuning, and implementation in analog or digital form. Given Data / Assumptions: P–D controller includes proportional and derivative actions only. Laplace transform conventions are standard. Kc is controller gain; τD is derivative time (seconds). Concept / Approach: The ideal PD controller has transfer function Gc(s) = Kc(1 + τD s). The proportional term Kc sets overall gain. The derivative term Kc τD s anticipates changes by acting on the slope of the error, adding phase lead and improving transient performance. Practical implementations include a small high-frequency roll-off (a filter), but the canonical ideal form remains Kc(1 + τD s). Step-by-Step Solution: Write the ideal PD action: u(t) = Kc[e(t) + τD de/dt].Take Laplace transform: U(s)/E(s) = Kc(1 + τD s).Match to the option list and select Kc(1 + τD s). Verification / Alternative check: Tuning correlations (e.g., Ziegler–Nichols variants) and frequency response analysis use the same PD transfer form; hardware realizations often add a derivative filter term 1/(1 + τf s) to limit noise amplification. Why Other Options Are Wrong: Kc(1 + 1/τD s): Dimensionally inconsistent; additive term should be τD s.Kc τD s: Pure derivative, missing proportional path.Kc/τD s or Kc/(1 + τD s): Resemble integrator or lag forms, not PD. Common Pitfalls: Using an “ideal” derivative without filtering causes noise amplification; always include a small roll-off in practice. Final Answer: Kc(1+τD s)

Question 18

Open-channel discharge measurement: the volumetric flow rate of a river (free-surface flow) is most appropriately measured using which hydraulic structure or device?

Accepted Answer

Introduction / Context: Rivers and canals convey water as free-surface (open-channel) flow. Measuring discharge in such systems uses hydraulic structures that relate upstream water level to flow rate through empirically or theoretically derived equations. Weirs and flumes are the classic choices for field hydrometry. Given Data / Assumptions: The flow is open-channel with a free surface. We seek a practical field method for measuring total river discharge. Steady conditions and calibrated geometry are assumed. Concept / Approach: An open weir (e.g., sharp-crested, broad-crested, or V-notch) creates a controlled overflow. The upstream head over the crest is measured and used in a discharge equation of the form Q = C * b * H^(3/2) (for sharp-crested weirs; variations exist). By surveying water level and applying the correct formula and coefficients, operators determine river flow with good accuracy. In large rivers, current-meter or acoustic Doppler profiling is also used, but among the listed options, only the open weir is an appropriate open-channel device. Step-by-Step Solution: Install or identify a calibrated weir section.Measure upstream head (H) at the proper location to avoid velocity head errors.Apply the correct discharge equation and coefficient C.Compute river discharge Q and record stage–discharge relationship for repeat use. Verification / Alternative check: Portable flumes (Parshall, Palmer–Bowlus) serve similar purposes. Rating curves (stage vs. discharge) validated by current-meter traverses are standard hydrometric practice. Why Other Options Are Wrong: Pitot tube / vane meter / nozzle / Venturi tube: Designed for internal, pressurized pipe flow, not open-channel conditions. Common Pitfalls: Incorrect head measurement location, neglecting approach velocity corrections, or using coefficients for the wrong weir geometry can cause significant error. Final Answer: Open weir

Question 19

In instrumentation and control engineering, the term ‘‘dead zone’’ refers to the input–output insensitivity of an indicating or recording device. Which definition best captures this concept for a measurement instrument (do not confuse with time cons…

Accepted Answer

Introduction / Context: The “dead zone” (also called dead band) is a classic static characteristic in measurement systems. It describes a finite range of input over which the output does not respond. Understanding it helps technicians and engineers diagnose why an indicator shows no movement despite small process changes, and to distinguish it from dynamic behaviors such as time constant or transportation lag. Given Data / Assumptions: We are dealing with an instrument's input–output behavior. Dead zone pertains to a region of no indicated response. Time constant and transportation (dead) time are dynamic, not static, properties. Concept / Approach: Dead zone is a static “insensitivity” band. If the true process variable changes within this band, the pointer, digital display, or recorder remains unchanged. Causes include mechanical friction, backlash, hysteresis, or intentional filtering to prevent flicker. The formal phrasing is “the maximum change in input that produces no output change around a specified operating point.” Step-by-Step Solution: Identify that the question asks for a definition, not a cause.Separate static insensitivity (dead zone) from dynamic lag (time constant, transportation delay).Select the option that directly states the input change producing no reading change. Verification / Alternative check: Calibration procedures often check for dead band by increasing and decreasing input to detect any “no-motion” span around setpoints. Why Other Options Are Wrong: Same as time constant: time constant governs exponential response speed, not insensitivity band.Same as transportation lag: that is a pure time delay, not a static dead band.None of these: incorrect because a correct definition is provided. Common Pitfalls: Confusing dead zone with hysteresis; hysteresis is a loop difference between increasing and decreasing inputs, while dead zone is a flat no-response region. Final Answer: Maximum change in the measured variable that does not change the instrument reading

Question 20

Thermocouple selection for high temperatures: which pair is suitable for measuring about 1400°C in industrial practice, considering stability and usable range?

Accepted Answer

Introduction / Context: Thermocouples are chosen for temperature range, chemical compatibility, and stability. Around 1400°C, only noble-metal or refractory-metal thermocouples reliably operate. The question tests recognition of the appropriate thermocouple family for such high-temperature service. Given Data / Assumptions: Target temperature: approximately 1400°C. Industrial measurement, continuous service implied. Standard thermocouple pairings and their typical ranges are considered. Concept / Approach: Copper–constantan (Type T) is limited roughly to sub-400°C service. Base-metal thermocouples like chromel–alumel (Type K) reach ~1100–1200°C in air but suffer drift at very high temperatures. Noble-metal systems such as platinum–platinum+rhodium (Types S or R) provide stable electromotive force and excellent oxidation resistance up to ~1600°C with appropriate protection. Thus, they are the preferred choice near 1400°C. Step-by-Step Solution: Match the temperature requirement (~1400°C) to thermocouple families.Eliminate low- and mid-range base-metal pairs due to drift and limits.Select the platinum–platinum+rhodium pair as suitable and widely used. Verification / Alternative check: Standards and vendor datasheets specify Types S/R for continuous use to ~1600°C in oxidizing environments, validating the selection. Why Other Options Are Wrong: Copper–constantan: low-temperature instrumentation; unsuitable at 1400°C.Aluminium–chromel: not a standard industrial pair; the common pair is chromel–alumel (Type K), whose range is lower.None of these: incorrect because a correct high-temperature pair is given. Common Pitfalls: Confusing Type K capability in inert environments with long-term stability at 1400°C; noble metals are preferred. Final Answer: Platinum–platinum+rhodium

Process Control and Instrumentation Questions