Question 1

In refrigeration system controls, which expansion device maintains a nearly constant degree of superheat at the evaporator outlet?

Accepted Answer

Introduction / Context: Expansion devices meter refrigerant into the evaporator and influence stability, capacity control, and compressor protection. Maintaining superheat at the evaporator outlet prevents liquid refrigerant from reaching the compressor, avoiding damage and ensuring efficient heat transfer. Given Data / Assumptions: Goal: maintain roughly constant superheat at the evaporator exit. System uses a sensing bulb at the evaporator outlet. Evaporating pressure acts on the valve diaphragm via an equalizing line. Concept / Approach: The thermostatic expansion valve (TXV/TEV) compares the bulb pressure (proportional to outlet temperature) with evaporator pressure and spring force. As load increases, outlet temperature and superheat rise; the bulb pressure increases, opening the valve to admit more refrigerant. Conversely, reduced load lowers superheat, prompting the valve to throttle, thus maintaining near-constant superheat. Step-by-Step Solution: 1) Bulb senses outlet temperature → converts to bulb pressure.2) Evaporator pressure opposes bulb pressure across the diaphragm.3) Spring provides reference force for set superheat.4) The valve throttles to keep superheat around the setpoint (e.g., 5–8 K). Verification / Alternative check: Superheat trend can be confirmed by measuring suction line temperature and saturation temperature (from suction pressure). A stable difference indicates proper TXV control. Why Other Options Are Wrong: Automatic expansion valve (a) regulates pressure, not superheat; poor at load variations. Float valves (b, d) control liquid level, not outlet superheat. Capillary tube (e) is a fixed orifice; superheat varies with load and ambient conditions. Common Pitfalls: Misadjusting TXV superheat setting too low, risking floodback; too high wastes evaporator area and reduces capacity. Final Answer: Thermostatic expansion valve

Question 2

For large-tonnage central air-conditioning applications (greater than 200 TR), which compressor type is most commonly recommended and widely used in chillers?

Accepted Answer

Introduction / Context: Selecting a compressor type for high-capacity chillers requires balancing efficiency, reliability, vibration, and maintainability. At very large capacities (200 TR and above), industry practice favors dynamic compressors that can deliver large flow rates smoothly. Given Data / Assumptions: Tonnage > 200 TR for central plant chillers. Continuous-duty commercial/industrial HVAC context. Typical refrigerants compatible with large chillers. Concept / Approach: Centrifugal compressors are dynamic machines that impart kinetic energy to refrigerant, converting it into pressure in the diffuser/volute. They are particularly efficient at large flow rates, deliver low vibration, and integrate well with shell-and-tube heat exchangers. This makes them the dominant choice for very large tonnage applications. While screw compressors can also handle medium-to-large loads (commonly up to several hundred TR), centrifugal units have historically been preferred for the very largest plants due to scalability and efficiency at design points. Step-by-Step Solution (Reasoning): 1) Compare capacity ranges: reciprocating/scroll are suited to small-to-moderate tonnage.2) Screw compressors cover moderate-to-large but may have lower peak efficiencies at very large sizes.3) Centrifugal compressors scale very well, offering high efficiency and smooth operation at >200 TR.4) Hence, for >200 TR, centrifugal is widely recommended. Verification / Alternative check: Survey of chiller catalogs shows centrifugal machines occupying high-tonnage ranges (e.g., several hundred to thousands of TR), confirming the trend. Why Other Options Are Wrong: (a) Reciprocating units have higher vibration and are rarely used at very large capacities. (b) Rotary vane is uncommon in central large-tonnage chillers. (d) Screw is viable but typically selected below the largest centrifugal ranges. (e) Scrolls are for small packaged systems. Common Pitfalls: Assuming screw always replaces centrifugal; application specifics matter, but centrifugal remains dominant above 200 TR in many central plants. Final Answer: Centrifugal compressor

Question 3

Dry-bulb temperature (DBT) is defined as the temperature of air measured by a standard thermometer that is not affected by the moisture present in the air. Which option matches this definition?

Accepted Answer

Introduction / Context: Dry-bulb temperature is the most familiar temperature measurement and is central to psychrometric analysis. It represents the sensible temperature of air without accounting for the cooling effect of evaporation or the latent moisture content. Given Data / Assumptions: A standard thermometer measures air temperature. No water film influences the reading. Moderate shielding from radiation and adequate airflow yield accurate readings. Concept / Approach: DBT indicates the sensible heat level of air. Moisture affects latent properties and wet-bulb/dew-point temperatures but does not directly affect DBT when measured properly. In contrast, wet-bulb temperature uses a wetted wick and airflow to reflect evaporative cooling; dew-point indicates saturation onset at the current vapour partial pressure. Step-by-Step Clarification: 1) Place a dry (unwetted) thermometer in the airstream.2) Shield from direct radiation and ensure airflow for representative air temperature.3) Reading obtained is the DBT, independent of moisture-driven evaporative effects.4) Compare: wet-bulb uses a wetted wick (lower reading), dew-point is a saturation property, not a direct thermometer reading. Verification / Alternative check: On the psychrometric chart, vertical lines represent constant DBT. Other properties (wet-bulb, humidity ratio, enthalpy) vary independently across the grid. Why Other Options Are Wrong: (b) Describes wet-bulb measurement. (c) Describes dew-point, not DBT. (d) Incorrect because option (a) matches the accepted definition. (e) Radiation shields are good practice outdoors, but DBT does not require “no airflow.” Common Pitfalls: Confusing DBT with operative temperature (which includes radiant effects) or assuming humidity directly alters the DBT reading of a dry thermometer. Final Answer: It is not affected by the moisture present in the air

Question 4

In designing HVAC for hospital operating theatres (OT), what percentage of outdoor (fresh) air should be supplied to the space supply stream?

Accepted Answer

Introduction / Context: Operating theatres require stringent infection control and indoor air quality standards. Ventilation design must minimize contamination risk, control odours and anaesthetic gases, and maintain positive pressure relative to adjacent areas. Given Data / Assumptions: Healthcare OT with aseptic requirements. Supply air is filtered (often HEPA) and pressurized. Air change rates are high, and exhaust is controlled. Concept / Approach: Best practice and many codes require 100% outdoor air (no recirculation into the OT) to prevent build-up of contaminants and to ensure high dilution of any airborne pathogens or anesthetic gases. Positive pressurization is maintained to push clean air outwards, limiting ingress of contaminants from adjacent spaces. Step-by-Step Reasoning: 1) Provide outdoor air in sufficient quantity to meet air changes per hour (ACH) and dilution needs.2) Pass supply air through high-efficiency filtration (often HEPA) to remove particulates and microorganisms.3) Maintain positive pressure in the OT relative to corridors and prep rooms.4) Exhaust air is not recirculated back into the OT supply stream; it is discharged or dedicatedly treated. Verification / Alternative check: Healthcare guidelines and standards (varies by jurisdiction) consistently recommend or mandate 100% outdoor air for OTs to maintain asepsis and to control anaesthetic gas accumulation. Why Other Options Are Wrong: (a) Zero outdoor air undermines IAQ and infection control. (b) and (c) Partial outdoor air still allows contaminant accumulation. (e) Even with HEPA, recirculation into the OT is typically avoided; HEPA is used on the supply, not to justify recirculation. Common Pitfalls: Assuming that high-grade filtration alone permits recirculation. Dilution with 100% outdoor air and proper pressurization are critical. Final Answer: 100% outdoor air

Question 5

Heat transfer from one region of a fluid to another due to actual bulk motion of the fluid induced by mechanical means (fans, pumps, blowers) is called what?

Accepted Answer

Introduction / Context: Understanding the modes of heat transfer—conduction, convection, and radiation—is essential for solving HVAC and thermal engineering problems. Convection specifically involves energy transport by fluid motion and is subdivided into free and forced convection based on the source of fluid motion. Given Data / Assumptions: Fluid motion is driven by mechanical devices like fans, blowers, or pumps. Temperature gradients exist within the fluid and/or at boundaries. Single-phase convection (no boiling/condensation) is assumed for simplicity. Concept / Approach: Convection heat transfer combines energy carried by the moving fluid and diffusion at the boundary layer. When motion is caused by external work (mechanical equipment), the process is termed forced convection. In free convection, motion arises from buoyancy due to density differences from temperature variations; radiation is electromagnetic emission; conduction is molecular energy diffusion without bulk motion. Step-by-Step Reasoning: 1) Identify the cause of fluid motion: mechanical devices → forced convection.2) Recognize that heat flux at a surface in convection is often modeled by q = h * A * (T_surface − T_fluid).3) In forced convection, h is enhanced by higher velocities and turbulence management.4) Therefore, the described process is forced convection. Verification / Alternative check: Dimensionless correlations (e.g., Nusselt vs. Reynolds, Prandtl) are typical of forced convection analyses; buoyancy-based Grashof relations are for free convection. Why Other Options Are Wrong: (a) Conduction involves no bulk motion. (b) Free convection relies on buoyancy alone, not mechanical drives. (d) Radiation does not require a medium and is unrelated to fluid motion. (e) Phase change is not necessary for convection; it can occur without boiling/condensation. Common Pitfalls: Confusing mixed convection (both buoyancy and forced effects) with purely forced convection; in design, the dominant mechanism is often determined by the Richardson number. Final Answer: Forced convection

Question 6

At approximately 20 °C and near-atmospheric pressure, the thermal conductivity of liquid water is about how large? Evaluate the truth of the statement: “It is about 0.51 (W/m·K).”

Accepted Answer

Introduction / Context: Accurate property data for water underpin many HVAC and heat-transfer calculations. Thermal conductivity dictates conductive heat flux through liquids and influences convective heat transfer coefficients through dimensionless groups like Prandtl number. Given Data / Assumptions: Temperature near 20 °C (room temperature). Pressure near 1 atm. Liquid water with typical purity. Concept / Approach: Standard property tables report the thermal conductivity of liquid water at 20–25 °C in the range of roughly 0.58 to 0.60 W/m·K (commonly cited ~0.598 W/m·K at 25 °C and ~0.59 W/m·K at 20 °C). Therefore, a value of 0.51 W/m·K is significantly lower than accepted reference values, making the given statement false for typical conditions. Step-by-Step Reasoning: 1) Identify typical reference: k_water(20–25 °C) ≈ 0.58–0.60 W/m·K.2) Compare proposed value: 0.51 W/m·K is below this range by ~12–15%.3) Conclude: For standard conditions, 0.51 W/m·K understates k; the statement is false.4) Note: k varies modestly with temperature; even then, values near 0.51 W/m·K are not representative at 20 °C. Verification / Alternative check: Consult engineering property tables or reliable databases; they consistently list ~0.6 W/m·K for liquid water around room temperature. Why Other Options Are Wrong: (a) True is incorrect because the value is too low. (c) Pressure effects at near-ambient conditions do not justify 0.51 W/m·K. (d) Ice water (solid–liquid mixture) is a different phase consideration; the liquid’s k remains near published values. (e) Salinity changes k slightly but not enough here. Common Pitfalls: Using an outdated or misprinted table; always check units (W/m·K) and ensure the property is for liquid, not vapor. Final Answer: False

Question 7

By which mode of heat transfer does energy from the sun predominantly reach the Earth's surface through space?

Accepted Answer

Introduction / Context: Understanding solar heat gain is essential in building physics, HVAC load calculations, and climate science. The mechanism by which solar energy travels from the sun to Earth explains why glazing, shading, and surface absorptivity are critical in thermal design. Given Data / Assumptions: Space between the sun and Earth is essentially a vacuum. No material medium is required for electromagnetic wave propagation. Atmosphere modifies the spectrum via absorption and scattering, but the transport through space is primarily wave-based. Concept / Approach: Conduction and convection require a material medium; neither can occur across the vacuum of space. Thermal radiation, the emission of electromagnetic waves (primarily in the shortwave solar spectrum), transfers energy across a vacuum at the speed of light. When these waves strike Earth’s atmosphere and surfaces, a portion is absorbed and converted to internal energy, warming the planet. Step-by-Step Reasoning: 1) Identify available modes: conduction (needs contact), convection (needs fluid motion), radiation (needs no medium).2) Recognize the sun–Earth gap is vacuum → conduction and convection are inapplicable for the transfer through space.3) Electromagnetic radiation travels through space, arrives at the atmosphere and ground.4) Absorption and re-radiation on Earth drive weather, climate, and building loads. Verification / Alternative check: Solar constant (~1361 W/m^2 outside the atmosphere) represents radiant energy flux; building load software explicitly models solar radiation, not conduction or convection from the sun. Why Other Options Are Wrong: (a) and (e) Conduction cannot cross a vacuum. (b) Convection occurs within fluids like air but cannot carry energy from the sun through space. (d) Phase change transport is irrelevant in interplanetary vacuum conditions. Common Pitfalls: Assuming convection dominates because we feel “hot air”; that sensation is terrestrial heat transfer after radiation is absorbed. Final Answer: Thermal radiation (electromagnetic waves)

Question 8

Refrigeration and p-h chart basics Which of the following statements is WRONG for a standard vapour-compression refrigerator?

Accepted Answer

Introduction / Context: Engineers must distinguish universally true principles from convenient rules of thumb. This question checks your understanding of coefficient of performance (C.O.P.), refrigerant state at compressor inlet, and interpretation of the pressure–enthalpy (p–h) diagram for a vapour-compression system. Given Data / Assumptions: Standard single-stage vapour-compression refrigerator. Idealized discussions use dry saturated vapour at compressor inlet; practical systems may use slight superheat. C.O.P. definitions: C.O.P._R = Q_L / W, C.O.P._HP = Q_H / W. Concept / Approach: C.O.P._R can be less than, equal to, or greater than 1 depending on conditions. While good refrigerators normally achieve C.O.P. greater than 1, the statement “always greater than 1” is not a law. Meanwhile, the ideal inlet condition to a compressor is dry saturated vapour (or slightly superheated) to avoid wet compression. On a p–h chart, the space between saturated liquid and saturated vapour lines is indeed the two-phase region. Step-by-Step Solution: Identify the claim that overstates reality: “C.O.P. is always > 1.”Recall definition: C.O.P._R = Q_L / W. With very poor heat exchangers or extreme temperature lifts, W can approach or exceed Q_L, making C.O.P._R ≤ 1.Confirm other statements: dry saturated (or slightly superheated) inlet is standard; the region between saturation lines is the wet-vapour dome.Therefore, the WRONG statement is that C.O.P. is always > 1. Verification / Alternative check: Compare with the Carnot refrigerator: C.O.P._Carnot = T_L / (T_H − T_L). As T_L approaches T_H (favorable), C.O.P. becomes large; for very large temperature lifts, it can be close to or below 1 in real systems. Why Other Options Are Wrong: Option B reflects the ideal inlet condition; Option C correctly describes the two-phase region; Option E is a common practical design choice for reliability. Common Pitfalls: Assuming a performance metric that is “usually > 1” is “always > 1.” Real plants deviate from ideal behavior due to irreversibilities. Final Answer: The value of C.O.P. is always greater than 1.

Question 9

Thermal radiation fundamentals What does Kirchhoff's law of thermal radiation state (at a given temperature and wavelength)?

Accepted Answer

Introduction / Context: Kirchhoff’s law links emission and absorption for bodies in thermal equilibrium and is foundational for understanding gray-body behavior and black-body references used in heat-transfer calculations. Given Data / Assumptions: Thermal equilibrium at a given temperature and wavelength (or narrow band). Definitions: emissive power E_λ and absorptivity a_λ at the same wavelength. Black body has a_λ = 1 and serves as the reference emitter. Concept / Approach: Kirchhoff’s law states E_λ / a_λ is identical for all bodies at the same T and λ and equals E_λ,black. This law underpins the concept of emissivity and guides how real surfaces are compared to an ideal black body. Step-by-Step Solution: Restate the law: E_λ / a_λ = E_λ,black.Interpretation: A good absorber at a given wavelength is a good emitter at that wavelength.Thus, option C is the correct description. Verification / Alternative check: Check limiting case: for a black body, a_λ = 1 ⇒ E_λ = E_λ,black, consistent with definition. Why Other Options Are Wrong: (A) is Stefan–Boltzmann law, not Kirchhoff’s. (B) expresses Wien’s displacement law. (E) is incorrect: a gray body emits a fraction ε of black-body emission. Common Pitfalls: Confusing the different classical radiation laws; remember each addresses a distinct property (E~T^4, λ_max T = constant, or E/α equivalence). Final Answer: For all bodies, the ratio of emissive power to absorptivity is the same and equals the emissive power of a perfect black body.

Question 10

Convective “film” coefficient concept The film coefficient (convective heat-transfer coefficient, h) can be interpreted as the ratio of:

Accepted Answer

Introduction / Context: In many correlations and simple resistive analogies, convection is modeled as if a thin, stagnant “film” of fluid were conducting heat. This leads to an intuitive definition of the convective coefficient. Given Data / Assumptions: Equivalent conductive film model adjacent to a surface. Uniform properties within the film: thermal conductivity k and notional thickness δ. Linear temperature drop across the film. Concept / Approach: Using the analogy q″ = k (ΔT/δ) and q″ = h (ΔT), the two forms give h = k/δ. While real convection involves velocity and temperature fields, this equivalence provides a useful way to visualize h and connect with thermal resistance R_conv = 1/(hA). Step-by-Step Solution: Write conductive form for a thin layer: q″ = k * (T_s − T_∞) / δ.Write Newton’s law of cooling: q″ = h * (T_s − T_∞).Equate and solve: h = k / δ → option A. Verification / Alternative check: Dimensional check: k has W/m·K, dividing by δ (m) gives W/m^2·K, which matches units of h. Why Other Options Are Wrong: (B), (C), and (D) mix ratios but do not yield the correct units for h; (E) is unrelated to convection. Common Pitfalls: Taking the film model too literally; δ is not a physical constant but a conceptual parameter that varies with flow conditions. Final Answer: thermal conductivity to the equivalent thickness of the fluid film (h = k/δ).

Question 11

Heat pump vs. refrigerator relationship For the same device viewed as a heat pump and as a refrigerator, the coefficients of performance satisfy:

Accepted Answer

Introduction / Context: The same vapour-compression machine can be interpreted either as a refrigerator (cooling device) or as a heat pump (heating device). Their C.O.P.s are closely linked. Given Data / Assumptions: Q_L = cooling effect, Q_H = heating effect, W = compressor work. (C.O.P.)_R = Q_L / W; (C.O.P.)_HP = Q_H / W. First law for the cycle: Q_H = Q_L + W. Concept / Approach: Substitute the energy balance into the definitions to relate the performance ratios directly. Step-by-Step Solution: Start: Q_H = Q_L + W.Divide by W: Q_H/W = Q_L/W + 1.Therefore, (C.O.P.)_HP = (C.O.P.)_R + 1. Verification / Alternative check: Check a numerical example: if (C.O.P.)_R = 3, then (C.O.P.)_HP = 4. This matches the formula. Why Other Options Are Wrong: Options A and C add or subtract the wrong constant; D ignores the energy balance; E is not generally true. Common Pitfalls: Forgetting that a heat pump’s useful output includes both the cooling effect and the work input converted to heat at the hot side. Final Answer: (C.O.P.)_HP = (C.O.P.)_R + 1

Question 12

Air-cycle (reversed Brayton) refrigeration In a reversed Brayton (air) refrigeration cycle, heat is absorbed from the cold space during the:

Accepted Answer

Introduction / Context: The reversed Brayton (also called reversed Joule) cycle is the basis of air-cycle refrigeration used in aircraft environmental control systems. Understanding which process provides the cooling effect is crucial. Given Data / Assumptions: Cycle steps: isentropic compression → constant-pressure heat rejection → isentropic expansion → constant-pressure heat absorption. Working fluid: air, treated as an ideal gas. Concept / Approach: After the turbine, the air is at low temperature and low pressure. It then absorbs heat from the refrigerated space at essentially constant low pressure, producing the refrigeration effect before returning to the compressor inlet. Step-by-Step Solution: 1–2: Isentropic compression raises T and p; no external heat absorbed.2–3: Constant-pressure cooling rejects heat to ambient.3–4: Isentropic expansion through the turbine drops T greatly.4–1: Constant-pressure heat absorption in the low-pressure heat exchanger → refrigeration effect. Verification / Alternative check: On a T–s diagram, the horizontal (constant-pressure) segment at low pressure corresponds to heat addition to the cycle, i.e., cooling the space. Why Other Options Are Wrong: (A) and (B) are on the high-pressure (hot) side; (C) is an internal work-producing expansion with negligible external heat transfer; (E) does not exist in the ideal air cycle. Common Pitfalls: Confusing the isentropic turbine expansion (which lowers temperature) with the actual heat absorption step that follows at low pressure. Final Answer: constant-pressure expansion (low-pressure heat absorption) process

Question 13

Where is refrigerant temperature highest in a mechanical refrigeration system? Identify the line location with the maximum refrigerant temperature.

Accepted Answer

Introduction / Context: Locating peak temperatures in a vapour-compression system helps in material selection, oil life assessment, and safety (e.g., avoiding decomposition of certain refrigerants). Given Data / Assumptions: Single-stage compressor without inter-cooling. Negligible pressure losses in lines for conceptual answer. Condensation occurs downstream at higher pressure. Concept / Approach: Compression raises both pressure and temperature. The hottest point occurs at the compressor discharge, before the refrigerant rejects heat in the condenser. Step-by-Step Solution: Compressor inlet: low-pressure vapour at low temperature.Compression: temperature rises sharply due to work input.Discharge line: peak temperature exists here before any heat rejection.Condenser: gas cools and condenses, reducing temperature thereafter. Verification / Alternative check: T–s or p–h diagrams show the highest temperature at the end of the compression stroke for both ideal and real cycles. Why Other Options Are Wrong: (A) Evaporator outlet is cool; (B) liquid before throttling is at saturation or sub-cooled, not the hottest; (D) liquid line is cooler; (E) receiver contains saturated or sub-cooled liquid at condenser pressure, cooler than discharge gas. Common Pitfalls: Confusing “highest pressure” with “highest temperature”: while both occur at discharge, the key is the state before heat rejection starts. Final Answer: Between the compressor discharge and the condenser inlet (discharge line)

Question 14

Why must moisture be removed from refrigerants? Select all key reasons relevant to system reliability and performance.

Accepted Answer

Introduction / Context: Moisture is a critical contaminant in refrigeration and air-conditioning systems. Even tiny amounts can create blockages, degrade materials, and shorten compressor life. Given Data / Assumptions: System includes an expansion device (TXV/capillary), compressor, condenser, and evaporator. Refrigerant oil may react with acids formed in the presence of moisture. Low-temperature throttling points risk freezing water into ice. Concept / Approach: At the expansion device, temperatures can drop below 0°C. Any dissolved water can precipitate as ice, causing blockage. Moisture also participates in hydrolysis reactions forming acids (especially with halocarbon refrigerants), leading to corrosion and insulation breakdown in hermetic motors. Desiccant driers are therefore standard. Step-by-Step Solution: Identify freezing risk: water → ice at throttling → blockage.Recognize flow restriction: intermittent icing produces erratic pressures and poor cooling.Consider materials: acids from moisture cause corrosion and oil degradation.Conclusion: all listed reasons apply. Verification / Alternative check: Service practices mandate evacuation (vacuum) and filter-driers to control moisture levels to a few ppm. Why Other Options Are Wrong: (E) focuses only on the condenser and ignores major risks at the expansion device and compressor. Common Pitfalls: Assuming sight-glass “no bubbles” implies no moisture; proper indicators or laboratory tests are needed. Final Answer: All of these

Question 15

Aircraft refrigeration using air as the working fluid Which thermodynamic cycle best represents air-cycle refrigeration used on aircraft?

Accepted Answer

Introduction / Context: Environmental control systems in many aircraft rely on air-cycle refrigeration. Knowing the representative cycle clarifies why turbines and heat exchangers, rather than evaporators and expansion valves, dominate these systems. Given Data / Assumptions: Working fluid: air (treated as an ideal gas). Key components: compressor, heat exchangers, turbine. Primary processes: isentropic compression/expansion and constant-pressure heat exchange. Concept / Approach: The reversed Brayton cycle (also called the reversed Joule cycle) consists of two isentropic and two constant-pressure processes. It is the standard model for air-cycle machines such as bootstrap or regenerative systems on aircraft. Step-by-Step Solution: Identify air as refrigerant → no phase change equipment.Map processes: compress, reject heat at pressure, expand in turbine, absorb heat at pressure.This sequence is the reversed Brayton cycle. Verification / Alternative check: System schematics for aircraft ECS show exactly these components and processes. Why Other Options Are Wrong: (A) Carnot is an ideal limit, not the actual cycle; (D) Otto is for spark-ignition engines; (E) absorption is a different technology using phase-change pairs. Option B is synonymous with C, but the standard name in refrigeration texts is “reversed Brayton.” Common Pitfalls: Thinking only vapour-compression cycles exist; air-cycle systems are common where bleed air and turbines are available. Final Answer: Reversed Brayton cycle

Question 16

Critical insulation thickness for spheres For a spherical insulation on a hot or cold body, the critical radius (or thickness) is:

Accepted Answer

Introduction / Context: Adding insulation does not always reduce heat loss immediately for cylindrical and spherical geometries. The concept of a critical radius explains why heat loss can first increase before decreasing as insulation thickness increases. Given Data / Assumptions: External convection with heat-transfer coefficient h0 at the insulation outer surface. Insulation thermal conductivity k is uniform. Steady, radial heat transfer; contact resistances neglected. Concept / Approach: For spheres, the critical outer radius r_crit is 2k/h0. If the actual outer radius is below r_crit, adding insulation can increase heat loss because the increase in outer area (boosting convection) outweighs the added conduction resistance. Beyond r_crit, further insulation reduces heat loss. Step-by-Step Solution: Write total thermal resistance R_total(r_o) = R_cond,insulation + R_conv,outer.Differentiate heat loss Q with respect to r_o and set dQ/dr_o = 0 for extremum.Solve condition to obtain r_crit = 2k / h0 for a sphere (compare with k / h0 for a long cylinder). Verification / Alternative check: Dimensional check: k (W/m·K) divided by h0 (W/m^2·K) gives metres; multiplying by 2 gives a length, as required. Why Other Options Are Wrong: (A) is the cylindrical result, not spherical; (C) and (D) invert units; (E) has incorrect dimensions. Common Pitfalls: Forgetting geometry matters: cylinder → k/h0; sphere → 2k/h0. Also, “critical thickness” is often described via the outer radius, not the material thickness alone. Final Answer: 2k / h0

Question 17

Dimensionless groups in transient conduction The ratio of surface convection resistance to internal conduction resistance is termed as:

Accepted Answer

Introduction / Context: Dimensionless numbers compare competing physical mechanisms. In transient conduction and lumped-capacitance analysis, the Biot number assesses the relative importance of internal conduction versus external convection. Given Data / Assumptions: Internal characteristic length L_c (typically volume/surface area for bodies). Convection coefficient h at the surface and thermal conductivity k within the solid. Thermal resistances: R_conv = 1/(hA) and R_cond ≈ L_c/(kA). Concept / Approach: Biot number Bi is defined as h L_c / k. It can be interpreted as the ratio of internal conduction resistance to surface convection resistance (R_cond / R_conv). Small Bi (≪ 1) implies negligible internal temperature gradients (justifying lumped analysis); large Bi indicates significant internal gradients. Step-by-Step Solution: R_cond / R_conv = (L_c/(kA)) / (1/(hA)) = h L_c / k = Bi.Hence Bi compares internal conduction to surface convection effects.Although some texts phrase the ratio oppositely (R_conv/R_cond), the conventional named number associated with these resistances is the Biot number. Verification / Alternative check: Lumped capacitance criterion uses Bi < 0.1 to justify spatially uniform temperature within the solid. Why Other Options Are Wrong: Grashof relates buoyancy to viscous forces in free convection; Stanton concerns convective heat transfer in boundary layers; Prandtl links momentum and thermal diffusivities; Nusselt is a dimensionless temperature gradient or hL/k, not a resistance ratio as posed. Common Pitfalls: Mixing up Biot and Nusselt; remember Bi uses a solid's L_c while Nu uses a fluid's flow length scale. Final Answer: Biot number

Question 18

Psychrometrics fundamentals: The wet-bulb temperature (WBT) is the temperature indicated by a thermometer whose bulb is covered with a wetted wick and exposed to moving air, reflecting cooling by evaporation.

Accepted Answer

Introduction / Context: Wet-bulb temperature (WBT) is a key psychrometric property used in HVAC, meteorology, and cooling tower analysis. It reflects the combined effect of temperature and humidity through evaporative cooling at the thermometer bulb. Given Data / Assumptions: Thermometer bulb is wrapped with a wetted wick (usually clean water). Air moves past the bulb (natural or forced draft) to enable evaporation. Evaporation rate depends on air humidity and velocity. Concept / Approach: When water evaporates from the wick, it absorbs latent heat from the bulb. The thermometer cools below the ambient dry-bulb temperature until an energy balance is reached between latent heat needed for evaporation and sensible heat supplied from the air to the bulb. The stabilized reading is the wet-bulb temperature. Step-by-Step Solution: Define WBT as the temperature achieved by a wetted-bulb thermometer in a moving airstream.Recognize that evaporation draws heat: q_latent = m_evap * h_fg.Sensible heat from air to bulb equals latent heat for evaporation at equilibrium.Therefore, the correct measuring method uses a wet wick and ventilation. Verification / Alternative check: On a psychrometric chart, lines of constant wet-bulb temperature are close to lines of constant enthalpy for unsaturated air. Sling psychrometers and aspirated psychrometers exploit the same principle. Why Other Options Are Wrong: “Not affected by moisture” is incorrect; WBT explicitly depends on humidity. “Begins to condense” describes dew-point conditions, not WBT. “Dry cotton” prevents evaporation and measures dry-bulb temperature. Common Pitfalls: Poor ventilation around the bulb, dirty water, or a dry wick will lead to inaccurate WBT readings. Final Answer: Its bulb is covered by a wet cloth (wick) and exposed to air flow

Question 19

Psychrometrics application: Adding water vapour to the air in an enclosed space causes a gain primarily in which component of heat content?

Accepted Answer

Introduction / Context: In HVAC processes such as humidification, we often distinguish between sensible heat (associated with temperature change) and latent heat (associated with moisture phase change). Understanding which component changes helps size coils, humidifiers, and energy requirements. Given Data / Assumptions: Closed or controlled air volume is considered. Water vapour is added (e.g., steam injection or evaporative humidifier). No chemical reactions occur in the air. Concept / Approach: When moisture is added, the air’s humidity ratio increases. The energy tied to vaporizing water is latent heat. Even if the dry-bulb temperature changes slightly during humidification, the defining energy gain is latent in nature because it accompanies the phase change of water to vapour. Step-by-Step Solution: Identify the process: moisture addition to air.Associate evaporation or steam mixing with latent heat input.Conclude that the predominant gain is latent heat, while sensible heat change may be small or application-dependent.Therefore, the correct choice is latent heat. Verification / Alternative check: On a psychrometric chart, humidification typically moves the state toward higher humidity ratio; enthalpy rises largely due to latent component unless steam is superheated and also adds sensible heat. Why Other Options Are Wrong: Sensible heat dominates when only temperature changes without phase change. Chemical, nuclear, and electrical terms are unrelated to simple humidification of air. Common Pitfalls: Confusing relative humidity (a ratio) with humidity ratio; and assuming any temperature rise means “sensible heat only.” In steam injection, both sensible and latent may rise, but the defining component is latent. Final Answer: Latent heat

Question 20

Critical temperature concept check: “The temperature below which a gas is always liquefied is known as the critical temperature.” Evaluate the statement.

Accepted Answer

Introduction / Context: Critical temperature (T_c) is a fundamental thermodynamic property on phase diagrams. Misunderstanding its definition leads to errors in liquefaction and refrigeration applications. Given Data / Assumptions: No specific gas; general definition is required. Standard thermodynamic definitions apply. Concept / Approach: The correct definition is: the critical temperature is the temperature above which a substance cannot be liquefied by pressure alone. Below T_c, the gas can be liquefied if sufficient pressure is applied; at or above T_c, no amount of pressure yields a separate liquid phase. Step-by-Step Solution: State the correct definition: T_c is an upper limit for liquefaction by pressure.Compare with the given claim (“below which a gas is always liquefied”).Note the error: being below T_c allows the possibility, not the certainty, of liquefaction (pressure must still be applied).Therefore, the statement is incorrect. Verification / Alternative check: Phase diagrams show that liquid–vapour coexistence exists only below T_c; however, attaining liquid still requires appropriate pressure conditions. Why Other Options Are Wrong: “Correct only for ideal gases/1 atm/below triple point” misrepresent T_c; the correct definition is universal and not limited to those conditions. Common Pitfalls: Assuming temperature alone guarantees condensation; both temperature and pressure determine phase state below T_c. Final Answer: Incorrect

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