Question 1

Air-conditioning processes — definition nuance for dehumidification Assess the statement: “The process of removing moisture from the air, without change in its dry-bulb temperature, is called dehumidification.” Choose the best option.

Accepted Answer

Introduction / Context:Dehumidification is the removal of water vapor from moist air. In practice, dehumidification can occur with temperature changes (cooling and reheating) or, in special arrangements, at nearly constant dry-bulb temperature using desiccants. The statement emphasizes a constant dry-bulb scenario.Given Data / Assumptions:Focus on the definition of the process, not a single method.Dry-bulb temperature may be held approximately constant via heat exchange while moisture is removed.Concept / Approach:Dehumidification is defined by a decrease in humidity ratio (specific humidity). Many methods exist: cooling below dew point (then reheating), or passing air over hygroscopic desiccants that absorb moisture. Chemical dehumidification can be arranged so that sensible heat is removed/added to keep dry-bulb nearly constant, satisfying the described condition.Step-by-Step Solution:Identify dehumidification criterion: reduction in w (humidity ratio).Recognize that “without change in dry-bulb temperature” describes a particular implementation (isothermal dehumidification), commonly achievable with desiccant systems and appropriate heat balancing.Therefore, the statement remains correct, albeit describing a specific case of dehumidification.Verification / Alternative check:Psychrometric charts include “isothermal dehumidification” lines showing movement leftward (lower w) at constant T_db, confirming the definition is acceptable.Why Other Options Are Wrong:(b) Incorrect because dehumidification does not require T_db to change; it may or may not change. (c) and (d) restrict the statement to a single method; multiple methods can, with appropriate heat exchange, maintain nearly constant T_db. (e) “Above the saturation line” is nonsensical wording in this context.Common Pitfalls:Assuming all practical dehumidification must cool air; desiccant systems can remove moisture with minimal change in dry-bulb temperature when heat of sorption is managed.Final Answer:Correct

Question 2

Thermal diffusivity — dependence on material properties Thermal diffusivity (alpha) indicates how quickly a material’s temperature field responds to a thermal disturbance. Which combined dependence is correct?

Accepted Answer

Introduction / Context:Thermal diffusivity alpha is a key parameter in transient conduction, dictating the speed of temperature equalization inside solids, liquids, and gases. It combines the effects of how well a material conducts heat and how much energy it stores per unit volume.Given Data / Assumptions:Definition: alpha = k / (rho * c_p).Isotropic, homogeneous material behavior assumed.Concept / Approach:The formula alpha = k / (rho * c_p) shows that materials with high thermal conductivity and low volumetric heat capacity (rho * c_p) respond more quickly to temperature changes. Metals often have high alpha; polymers and water have lower alpha due to higher heat capacity per unit volume and/or lower k.Step-by-Step Solution:Write the definition: alpha = k / (rho * c_p).Direct proportionality: larger k → larger alpha.Inverse proportionalities: larger rho or c_p → smaller alpha.Hence all three component statements are simultaneously true.Verification / Alternative check:Example: Aluminum (high k, moderate rho and c_p) has high alpha; water (low k, high rho*c_p) has low alpha, matching the dependence.Why Other Options Are Wrong:(a), (b), (c) are each partially true alone, but the comprehensive correct choice is the combination (d). (e) is false because alpha is defined entirely by material properties.Common Pitfalls:Confusing thermal diffusivity with thermal conductivity; conductivity alone does not capture thermal inertia effects from rho and c_p.Final Answer:All of the above

Question 3

Heat exchanger design — purpose of a fouling factor In practical heat exchanger calculations, why is a fouling factor included in the overall heat transfer coefficient or area sizing?

Accepted Answer

Introduction / Context:Heat exchangers rarely operate with perfectly clean surfaces. Over time, deposits such as scale, biofilm, corrosion products, and particulates can accumulate, increasing thermal resistance and reducing performance. Designers therefore include a fouling factor.Given Data / Assumptions:Service fluid properties and contamination tendencies are known or estimated.Maintenance/cleaning intervals are finite; continuous perfect cleanliness is unrealistic.Concept / Approach:The overall heat transfer coefficient U_clean is reduced in service due to added thermal resistance R_fouling. The design practice is to specify an overall “dirty” U or to enlarge area so that, with fouling present, the exchanger still meets the required duty. The fouling factor is thus a safety/allowance built into calculations, derived from experience or standards.Step-by-Step Solution:Define total resistance R_total = 1/U = R_inside + R_wall + R_outside + R_fouling.Choose R_fouling based on service (e.g., cooling water, hydrocarbons, dairy).Size A so that Q = U_dirty * A * LMTD still meets duty throughout the run cycle.Verification / Alternative check:Comparing clean vs. dirty performance curves shows the margin provided by fouling allowance, ensuring required heat duty until next cleaning.Why Other Options Are Wrong:(b) Fouling is not specific to Newtonian fluids; it depends on chemistry and particulates. (c) Fouling occurs in liquid–liquid, gas–liquid, and gas–gas services. (d) Ignoring fouling leads to undersized equipment and early failure to meet duty. (e) Radiation losses are typically minor and are not what fouling factor addresses.Common Pitfalls:Underestimating fouling for “clean” services; not aligning fouling allowances with maintenance plans; mixing fouling factor with safety factor on pressure design.Final Answer:As a design safety allowance to account for expected deposit buildup and performance degradation

Question 4

Refrigeration engineering: Among the common refrigerants R-11, R-12, R-22, and ammonia (NH3), which substance has the lowest freezing point (i.e., can remain fluid at the coldest temperature before solidifying)?

Accepted Answer

Introduction / Context:When selecting a refrigerant, one important property is its freezing point. A lower freezing point reduces the risk of the refrigerant solidifying in very low-temperature evaporators, which would block passages and damage equipment.Given Data / Assumptions:Candidates considered: R-11 (CCl3F), R-12 (CCl2F2), R-22 (CHClF2), and ammonia (NH3).We compare typical freezing points reported in standard property tables.No blending effects; pure substances are compared.Concept / Approach:The refrigerant with the most negative (lowest) freezing temperature offers the widest margin against solidification. Halocarbon refrigerants such as R-12 and R-22 have extremely low freezing points, often far below those of common natural refrigerants like ammonia.Step-by-Step Solution:Identify approximate freezing points: Ammonia freezes near −78 °C; R-11 is much higher (warmer) than the others; R-12 is about −158 °C; R-22 is near −160 °C (slightly lower than R-12).Rank from lowest (most negative) to higher: R-22 Therefore, R-22 has the lowest freezing point among the listed options.Verification / Alternative check:Cross-checking multiple handbooks shows R-22’s freezing point a few degrees below R-12 and far below ammonia’s −77.7 °C, confirming the selection.Why Other Options Are Wrong:R-11: Significantly higher freezing point; not suitable for ultra-low evaporators.R-12: Very low, but still a few degrees higher than R-22.Ammonia: Excellent refrigerant but freezes near −78 °C, much higher than halocarbons.Common Pitfalls:Confusing boiling points with freezing points, or assuming ammonia must always be “best” because it is natural and efficient. Property selection must match the temperature range.Final Answer:R-22

Question 5

Heat transfer fundamentals: Natural (free) convection depends on fluid properties and body force. Which of the following quantities influence free convection flow?

Accepted Answer

Introduction / Context:Free (natural) convection is fluid motion driven by buoyancy forces that arise from density variations in a gravitational field. Understanding the parameters that control this motion is key to predicting heat transfer in enclosures, around hot surfaces, and in the atmosphere.Given Data / Assumptions:No external pumping; motion arises solely due to buoyancy.Properties considered: density, viscosity; field variable: gravity.Temperature differences create density gradients through thermal expansion.Concept / Approach:The intensity of free convection is captured by dimensionless groups such as the Grashof number Gr and the Rayleigh number Ra. In simplified form, Ra = Gr * Pr, with Gr proportional to g * beta * ΔT * L^3 / ν^2. Here g (gravitational acceleration), β (thermal expansion), ΔT (temperature difference), L (length scale), and ν (kinematic viscosity) directly influence buoyant flow. Density appears in the definition of buoyancy (via beta and fluid weight), and viscosity appears in ν and in damping of motion.Step-by-Step Solution:Recognize buoyancy: fluid of lower density rises, higher density sinks under gravity.Relate driving force to g and density differences (hence density matters).Relate resistance to viscous effects (hence viscosity matters).Therefore all listed items affect free convection.Verification / Alternative check:Using Ra = g * beta * ΔT * L^3 / (α * ν) shows explicit dependence on gravity g and viscous/thermal diffusivities (which depend on viscosity and density).Why Other Options Are Wrong:Picking only one factor neglects the essential interplay of buoyancy (g, density) and viscous damping (viscosity) that defines the flow regime.Common Pitfalls:Assuming only gravity matters. Without viscosity and density (thus buoyancy contrast), flow intensity and boundary layer development cannot be predicted.Final Answer:All of these

Question 6

Thermal comfort and HVAC: In air-conditioning practice, the term ‘‘air conditioning’’ includes cooling, heating, and moisture control (dehumidifying/humidifying) as required to achieve desired indoor conditions.

Accepted Answer

Introduction / Context:Air conditioning is broader than just cooling. The objective is to deliver thermal comfort and acceptable indoor air quality year-round, which requires control of temperature, humidity, cleanliness, and air movement.Given Data / Assumptions:Comfort conditions vary by season and application (residential, commercial, process).Systems may require heating in winter, cooling in summer, and humidity control anytime.Ventilation and filtration are also part of complete air conditioning, though not listed here.Concept / Approach:An HVAC system should maintain dry-bulb temperature within limits and adjust humidity ratio to avoid discomfort such as stickiness (high humidity) or dryness (low humidity). Dehumidification often involves cooling below the dew point to condense moisture, while humidification adds water vapor to the air stream. Heating raises the dry-bulb temperature to maintain thermal balance.Step-by-Step Solution:Define scope: Cooling reduces dry-bulb temperature; heating increases it.Dehumidifying lowers humidity ratio by condensing or adsorbing moisture.Therefore ‘‘air conditioning’’ encompasses all listed functions.Verification / Alternative check:Psychrometric processes plotted on the chart show cooling and dehumidification (down-left toward saturation), heating (horizontal rightward), and humidification (upward toward saturation), all used by HVAC systems.Why Other Options Are Wrong:Choosing only one function ignores the integrated nature of HVAC design aimed at comfort and process control.Common Pitfalls:Equating ‘‘AC’’ strictly with cooling; many systems spend substantial time heating and controlling humidity.Final Answer:All of these

Question 7

Psychrometrics: During a dehumidification process (moisture removal from air at otherwise similar conditions), how does the specific humidity (humidity ratio) change?

Accepted Answer

Introduction / Context:Specific humidity (also called humidity ratio, w) is the mass of water vapor per unit mass of dry air. Dehumidification is a core HVAC process where moisture is removed, typically by cooling air below its dew point so that water condenses out.Given Data / Assumptions:Air stream is contacted with a cold surface (cooling coil) or a desiccant to remove moisture.No external steam or water injection during the dehumidification step.Pressure is near atmospheric and approximately constant.Concept / Approach:On the psychrometric chart, dehumidification at roughly constant pressure moves the state leftward (lower humidity ratio) and, for cooling-coil processes, also downward in dry-bulb temperature until the apparatus dew point is reached. Removing vapor mass per unit dry air necessarily reduces the specific humidity.Step-by-Step Solution:Start with state (T1, w1).Dehumidification removes vapor mass → w decreases to w2 (w2 If via cooling coil, the path moves toward the saturation curve, then along it as condensation occurs.Hence, the specific humidity decreases.Verification / Alternative check:Mass balance on water vapor: m_dot_v,out = m_dot_v,in − m_dot_condensed. With constant dry-air flow, w_out = w_in − (m_dot_condensed / m_dot_dry_air) Why Other Options Are Wrong:Remains constant: Only true for sensible cooling or heating without condensation or moisture addition.Increases: Would require humidification, not dehumidification.Indeterminate: The sign is definite given moisture removal.Common Pitfalls:Confusing sensible-only cooling with cooling plus dehumidification; condensation changes humidity ratio while sensible processes do not.Final Answer:Decreases

Question 8

Cooling and dehumidification on the psychrometric chart: During a typical cooling-and-dehumidifying coil process, what happens to the dry-bulb temperature of the air?

Accepted Answer

Introduction / Context:HVAC cooling coils frequently achieve both sensible cooling and moisture removal. Understanding how dry-bulb temperature (DBT) changes during such a process is essential for coil selection and load calculations.Given Data / Assumptions:Air passes over a cooling coil colder than its dew point.Process pressure is approximately constant (near atmospheric).Condensate is removed, thus humidity ratio decreases.Concept / Approach:A cooling-and-dehumidification process on the psychrometric chart initially moves diagonally down-left (reducing DBT and humidity ratio) toward the saturation curve. Once on the saturation curve, further cooling continues along the curve to the apparatus dew point. The hallmark of the process is a drop in dry-bulb temperature due to heat extraction.Step-by-Step Solution:Entering air at (DBT1, w1) contacts a cold surface; heat and mass transfer occur.Sensible heat removal reduces DBT; latent heat removal condenses moisture.Exit air has lower DBT (DBT2 Therefore, DBT decreases during cooling and dehumidification.Verification / Alternative check:Energy balance shows that coil heat extraction equals sensible plus latent loads; a nonzero sensible component necessarily lowers DBT when the coil is colder than the air.Why Other Options Are Wrong:Remains constant: That describes adiabatic humidification or ideal evaporative cooling lines, not a cold coil below dew point.Increases: Opposite of cooling.Becomes equal to wet-bulb: Not generally; equality occurs only at saturation when DBT equals WBT equals dew point at a specific state.Common Pitfalls:Assuming dehumidification can occur without cooling; with cooling coils, condensation follows reduction below dew point and DBT falls.Final Answer:Decreases

Question 9

Reading the psychrometric chart: The family of curved lines sweeping from the saturation curve across the chart represent which psychrometric property?

Accepted Answer

Introduction / Context:Interpreting a psychrometric chart quickly is vital in HVAC design and troubleshooting. Each set of lines corresponds to a specific property of moist air.Given Data / Assumptions:Standard chart with dry-bulb temperature on the horizontal axis and humidity ratio on the vertical axis.Saturation curve forms the 100% relative humidity boundary.Concept / Approach:On a typical chart: vertical lines are constant humidity ratio; horizontal lines are constant dry-bulb temperature; lines slanted downward to the right are constant wet-bulb temperature; and the smoothly curved family of lines running from the saturation curve toward the dry region are constant relative humidity (RH) lines.Step-by-Step Solution:Locate the saturation curve (100% RH) at the left/top boundary.Observe the family of curves labeled, for example, 90%, 70%, 50%, etc., bowing between saturation and dry regions.These curves, by definition, represent relative humidity values.Therefore, the curved lines are constant RH lines.Verification / Alternative check:Cross-referencing the chart legend confirms the property families and their geometric orientation, including constant wet-bulb lines being nearly straight and slanted, not smoothly curved like RH lines.Why Other Options Are Wrong:Dry-bulb temperature: Shown as horizontal straight lines.Wet-bulb temperature: Generally straight or slightly curved slanted lines, not the family in question.Dew point temperature: Read horizontally from saturation; not a family of curved lines across the field.Common Pitfalls:Confusing wet-bulb lines with RH lines; always check line labels and orientation.Final Answer:Relative humidity

Question 10

Materials compatibility in refrigeration: For systems using ammonia (NH3) as the refrigerant, should copper piping be used for refrigerant lines?

Accepted Answer

Introduction / Context:Material compatibility is critical in refrigeration system design. Ammonia is a widely used industrial refrigerant, but it reacts with certain metals and alloys, influencing the choice of piping materials.Given Data / Assumptions:Refrigerant: anhydrous ammonia (R-717).Common piping options: copper, steel, and certain stainless steels.Desire to avoid corrosion, contamination, and safety hazards.Concept / Approach:Ammonia attacks copper and copper-based alloys (brass, bronze), leading to stress corrosion cracking and the formation of copper ammine complexes. This weakens components and can result in leaks or failures. Carbon steel and suitable stainless steels are preferred for NH3 service.Step-by-Step Solution:Identify chemical compatibility: NH3 is incompatible with copper alloys.Assess risk: corrosion can cause embrittlement and perforation of copper lines.Specify alternative: use steel (e.g., schedule-rated carbon steel) or appropriate stainless grades instead of copper.Conclusion: Copper should not be used for ammonia refrigerant piping.Verification / Alternative check:Industry standards and manufacturer guidelines list carbon steel as the standard material for ammonia refrigeration systems, with explicit prohibition of copper tubing.Why Other Options Are Wrong:Yes / low-pressure only: Incompatibility is chemical, not only pressure-related; damage can occur across the system.Internally tin-lined: Not a standard or reliable mitigation for ammonia–copper incompatibility.Common Pitfalls:Assuming copper is universally acceptable because it is common with halocarbon refrigerants; ammonia is an exception due to its chemistry.Final Answer:No

Question 11

Vapour absorption refrigeration (ammonia–water system): Which working fluid acts as the refrigerant in a typical absorption refrigerator?

Accepted Answer

Introduction / Context:In the ammonia–water absorption cycle, a refrigerant is absorbed in a liquid absorbent, pumped, desorbed in the generator, condensed, expanded, and evaporated to provide cooling. Knowing which fluid is the refrigerant clarifies the roles of each component.Given Data / Assumptions:Working pair: ammonia (NH3) and water (H2O).Typical small to industrial absorption systems.Cycle uses heat (not mechanical work) to drive refrigeration.Concept / Approach:The refrigerant is the fluid that evaporates at low temperature in the evaporator, absorbing heat from the cooled space, and then condenses in the condenser at higher pressure. In the NH3–H2O system, ammonia plays this role; water is the absorbent that dissolves ammonia in the absorber and releases it in the generator.Step-by-Step Solution:Identify evaporator function: low-pressure ammonia evaporates, providing cooling.In the absorber, water absorbs ammonia vapor, forming strong solution.The solution is pumped to the generator, heated to release (desorb) ammonia vapor.Ammonia condenses, is expanded, and repeats the cycle—confirming ammonia as the refrigerant.Verification / Alternative check:Component naming (absorber, generator, analyzer, rectifier) in NH3–H2O systems is consistent with ammonia being the volatile refrigerant requiring rectification to remove water carryover.Why Other Options Are Wrong:Water: Acts as absorbent, not the refrigerant, in NH3–H2O systems.Freon: Used in vapor-compression systems, not in the classic ammonia–water absorption cycle.Aqua-ammonia: This is the solution (ammonia dissolved in water), not the pure refrigerant fluid.Common Pitfalls:Confusing the solution name (aqua-ammonia) with the refrigerant; the refrigerant must be the vapor that circulates through condenser and evaporator.Final Answer:Ammonia

Question 12

Thermal radiation law identification: “The wavelength corresponding to maximum emissive power is inversely proportional to absolute temperature.” Does this statement describe Planck’s law?

Accepted Answer

Introduction / Context:Several named laws describe blackbody radiation. Correctly identifying which statement corresponds to which law helps avoid conceptual errors in heat transfer.Given Data / Assumptions:The quoted statement links peak wavelength and absolute temperature via an inverse relationship.We compare with well-known radiation laws.Concept / Approach:Wien’s displacement law states: lambda_max * T = constant, meaning the wavelength at peak emission (lambda_max) is inversely proportional to temperature. Planck’s law, by contrast, gives the full spectral distribution of blackbody radiation intensity as a function of wavelength and temperature—not merely the location of the peak.Step-by-Step Solution:Identify the statement: “wavelength of maximum energy is inversely proportional to absolute temperature.”Recall Wien’s relation: lambda_max * T = b (constant) → lambda_max ∝ 1/T.Planck’s law provides E_lambda(T) using fundamental constants and exponential dependence; it does not simplify to the above proportionality.Therefore, the statement is Wien’s displacement law, not Planck’s law.Verification / Alternative check:Plotting blackbody spectra using Planck’s law shows peaks shifting with T such that lambda_max * T is constant, which is Wien’s result derived from Planck’s distribution.Why Other Options Are Wrong:Yes: Misattributes Wien’s law to Planck.Only at very high temperatures / only for black surfaces: Wien’s law applies to ideal blackbodies across temperatures; emissive peaks for real surfaces follow similar trends but with emissivity effects.Common Pitfalls:Confusing names: Stefan–Boltzmann (total emission proportional to T^4), Wien (peak wavelength shift), Planck (full spectral law).Final Answer:No

Question 13

Automobile radiator as a heat exchanger In automotive engineering, the engine's radiator transfers heat from hot coolant to ambient air by forcing air across finned tubes. Which broad heat-exchanger flow arrangement best describes a typical automobi…

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Introduction / Context:Automobile radiators are compact heat exchangers that remove waste heat from circulating engine coolant. They are built with many small tubes and fins to maximize heat transfer area while keeping pressure drop and mass low. Correctly identifying the flow arrangement helps predict performance, temperature profiles, and effectiveness.Given Data / Assumptions:Hot liquid coolant flows through narrow tubes from inlet tank to outlet tank.Ambient air passes through the finned core due to vehicle motion and/or a fan.Air and coolant flow directions are essentially perpendicular in the core.Concept / Approach:Heat-exchanger arrangements are commonly described as parallel flow (both fluids move in the same main direction), counter flow (fluids move in opposite directions along the same axis), cross flow (fluids move approximately perpendicular), or regenerative (hot and cold streams alternately occupy the same matrix). Radiators are designed with a tube-fin core where the air stream passes across the tubes. The coolant flows longitudinally inside the tubes, while the air stream is driven through the fin passages nearly orthogonal to tube flow. This is a classic cross-flow configuration.Step-by-Step Solution:Identify flow path of coolant: along tubes from top/bottom tank to the other.Identify flow path of air: through fins, generally normal to the tube axis.Compare with standard definitions: perpendicular main directions indicate cross flow.Conclude: the best descriptor for an automobile radiator is a cross-flow heat exchanger.Verification / Alternative check:Photographs and cutaways of radiators show a tube bundle with louvered fins. The fan or vehicle motion drives air through the core face, not along the tubes. That geometric relationship verifies cross flow. Some designs use multi-pass coolant routing, but the primary relationship remains cross flow.Why Other Options Are Wrong:Parallel flow: would require air and coolant to move in the same direction along a shared axis, which is not the case.Counter flow: would require opposite, colinear directions; radiators do not route air that way.Regenerator type: involves periodic storage and release of heat in a matrix, not used in typical radiators.Mixed-flow shell-and-tube: a different construction; automobile radiators are plate-fin/tube-fin cross-flow cores.Common Pitfalls:Confusing “crossflow radiator” (a plumbing term about tank positions) with heat-exchanger “cross flow.” Regardless of tank placement, the air path is perpendicular to coolant flow within the core, so the thermodynamic arrangement is cross flow.Final Answer:Cross flow type

Question 14

LMTD comparison for evaporators/condensers For the same terminal temperatures and capacity duty, how does the logarithmic mean temperature difference (LMTD) for parallel flow compare with that for counter flow?

Accepted Answer

Introduction / Context:The logarithmic mean temperature difference (LMTD) is the primary temperature driving force used in sizing heat exchangers. For a fixed set of inlet and outlet temperatures, the LMTD depends on how the two fluids are arranged. Understanding which arrangement yields a larger LMTD helps designers choose more compact or efficient exchangers.Given Data / Assumptions:Two-stream heat exchanger (evaporator or condenser) with specified terminal temperatures.Steady-state heat transfer with negligible heat loss to surroundings.Comparison strictly between parallel flow and counter flow arrangements.Concept / Approach:For the same terminal temperatures, counter flow consistently provides a larger LMTD than parallel flow. This is because counter flow maintains a more uniform temperature driving force along the length of the exchanger. Parallel flow suffers from a high initial driving force that rapidly diminishes, reducing the logarithmic mean overall.Step-by-Step Solution:Define LMTD = (ΔT1 - ΔT2) / ln(ΔT1 / ΔT2).For a given set of terminal temperatures, compute ΔT1 and ΔT2 according to the arrangement.In counter flow, the hot outlet approaches the cold inlet, increasing the smaller terminal difference and boosting LMTD.Therefore, LMTD_parallel Verification / Alternative check:Plotting temperature profiles along length shows a steeper drop in parallel flow with a small tailing driving force, versus a more even counter-flow profile. Integrating the local driving force along the length reproduces the LMTD inequality.Why Other Options Are Wrong:Greater or equal: contradicts textbook results for two-stream exchangers under the same terminal temperatures.“Unrelated to flow arrangement” is incorrect; flow arrangement directly affects ΔT1 and ΔT2.Fouling alters required area but does not overturn the fundamental LMTD ordering.Common Pitfalls:Mixing up effectiveness and LMTD. Effectiveness accounts for capacity rates; LMTD is set by terminal temperatures and arrangement. Also, ensure temperatures are absolute values when evaluating differences.Final Answer:Less than for counter flow

Question 15

Radiative properties of a “white body” Evaluate the statement: For a white body, absorptivity α = 0, reflectivity ρ = 1, and transmissivity τ = 0.

Accepted Answer

Introduction / Context:Radiative heat transfer uses three basic surface interaction parameters: absorptivity (fraction absorbed), reflectivity (fraction reflected), and transmissivity (fraction transmitted). Idealized surface types like black, white, and grey bodies help students reason about limits.Given Data / Assumptions:A “white body” is an idealization that perfectly reflects all incident radiation.Opaque assumption is applied, consistent with τ = 0 for many engineering surfaces.Energy conservation requires α + ρ + τ = 1 for any surface at a given wavelength/direction.Concept / Approach:By definition, a white body reflects all incident radiation across the spectrum of interest, implying ρ = 1. With no transmission (τ = 0 for an opaque white body), the balance α + ρ + τ = 1 forces α = 0. Thus the statement α = 0, ρ = 1, τ = 0 is correct for the idealized, opaque white body model used in thermal engineering.Step-by-Step Solution:Apply energy conservation: α + ρ + τ = 1.Ideal white body: ρ = 1.Opaque surface: τ = 0.Therefore α = 1 - ρ - τ = 0 → the given statement is consistent.Verification / Alternative check:Real materials are “nearly white” over limited wavelength bands (e.g., polished aluminum in infrared or titanium dioxide paints in visible). Their ρ is high, α low, τ near zero if opaque. The ideal white body is the limiting case.Why Other Options Are Wrong:“Incorrect” conflicts with the ideal definition.Confining correctness to visible wavelengths or incidence angles introduces dependence not specified in the ideal.Diffuse versus specular reflection changes angular distribution, not the integrated value of ρ = 1 for an ideal white body.Common Pitfalls:Equating “white” only with human visual perception; in heat transfer, the relevant spectrum is often infrared and the definition is spectral-band dependent. Here, the idealized definition holds for the band considered.Final Answer:Correct

Question 16

Applications of heat exchangers Identify where heat exchangers are commonly used in thermal engineering practice.

Accepted Answer

Introduction / Context:Heat exchangers enable energy transfer between two fluids at different temperatures without direct mixing. They are foundational components across power, process, automotive, and HVAC industries. Recognizing their ubiquitous applications helps connect theory with real systems.Given Data / Assumptions:Two-stream heat exchangers with metal walls separating fluids.Steady operation and typical industrial configurations.Focus on application domains rather than specific designs.Concept / Approach:In automobiles, the engine radiator rejects heat from coolant to air. In steam plants, boilers transfer heat from combustion gases to water/steam, and condensers remove latent heat from exhaust steam to cooling water. In refrigeration and air conditioning, evaporators absorb heat from the conditioned space while condensers reject heat to ambient. Each is a heat exchanger performing sensible or latent heat transfer (or both).Step-by-Step Solution:Automotive: radiator = cross-flow exchanger rejecting engine heat.Steam plants: boilers and condensers exchange heat between gas/steam/water circuits.HVAC/R: evaporators and condensers move heat between indoor air and outdoor environment via a refrigerant.Conclusion: heat exchangers are integral in all listed applications.Verification / Alternative check:System schematics across these industries prominently display heat exchangers labeled as radiators, condensers, boilers, economizers, intercoolers, and aftercoolers—substantiating the wide applicability.Why Other Options Are Wrong:Choosing any single application ignores the prevalence of heat exchangers elsewhere.“Only in power plants” is clearly false due to automotive and HVAC usage.Common Pitfalls:Assuming the term “boiler” is separate from heat exchangers; a boiler is a specialized heat exchanger producing phase change on the water side with combustion products on the hot side.Final Answer:All of the above

Question 17

Boundary-layer thickness ratio and Prandtl number The ratio of thermal boundary-layer thickness to hydrodynamic boundary-layer thickness over a surface scales approximately as (Prandtl number)^n. What is the typical value of the exponent n (engineer…

Accepted Answer

Introduction / Context:When a fluid flows over a surface, two boundary layers develop: a hydrodynamic boundary layer where velocity transitions from zero at the wall to free-stream, and a thermal boundary layer where temperature transitions from wall temperature to free-stream. The relative growth of these layers depends on the Prandtl number, Pr = ν/α, where ν is kinematic viscosity and α is thermal diffusivity.Given Data / Assumptions:External flow over a flat plate (laminar regime reference) or correlations adapted for engineering estimates.Prandtl number greater than about 0.6 for common liquids and gases in many applications.Interest in scaling of δ_t / δ.Concept / Approach:Analyses and empirical correlations show that for Pr > 0.6, the thermal boundary layer is thinner than the velocity boundary layer when Pr > 1, and thicker when Pr Step-by-Step Solution:Define Pr = ν / α.Relate boundary-layer thicknesses: δ_t / δ ∝ Pr^n.Use engineering correlation: n ≈ −1/3 → δ_t / δ ≈ Pr^(−1/3).Interpretation: for water (Pr ~ 7), δ_t / δ ≈ 7^(−1/3) 1.Verification / Alternative check:More detailed similarity solutions (Pohlhausen, Leveque approximations) yield exponents around −1/3 for many practical ranges. Turbulent-flow analogies also retain a −1/3 exponent in simplified forms for Prandtl numbers not far from unity.Why Other Options Are Wrong:−2/3 or −1: exaggerate the sensitivity to Pr and do not match standard correlations.1 or 0: would imply the thermal layer is equal to or independent of velocity layer thickness, which is not generally correct.Common Pitfalls:Assuming the correlation is exact for all flows. The exponent can change for extreme Pr or different geometries, but −1/3 is a widely taught engineering rule-of-thumb for external laminar flow and often used in turbulent analogies.Final Answer:-1/3

Question 18

Sensible Heat Factor (SHF) during heating and humidification Given h1 = enthalpy of air entering the heating coil, h2 = enthalpy of air leaving the heating coil, and hA = enthalpy of air at the end of the humidification process, the sensible heat fa…

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Introduction / Context:In air-conditioning psychrometrics, the sensible heat factor (SHF) quantifies how much of the total heat added or removed is sensible (temperature change) versus latent (moisture change). For a heating and humidification process, air is first heated (sensible addition) and then moisture is added (latent addition). Correctly formulating SHF ensures accurate coil sizing and process line plotting on the psychrometric chart.Given Data / Assumptions:h1: enthalpy at the coil inlet (state 1).h2: enthalpy at the coil outlet after sensible heating (state 2).hA: final air state after humidification (state A).Steady flow and negligible heat losses to surroundings.Concept / Approach:By definition, SHF = sensible heat / total heat for the process of interest. In this sequence, sensible heat is represented by the change from h1 to h2, while total heat added is from h1 to hA. Therefore SHF = (h2 - h1) / (hA - h1). This ratio lies between 0 and 1, with smaller values indicating larger latent components.Step-by-Step Solution:Identify sensible portion: heating at essentially constant humidity ratio from state 1 to 2 → enthalpy change = h2 - h1.Identify total heat added: overall change from state 1 to final state A → enthalpy change = hA - h1.Form ratio: SHF = (h2 - h1) / (hA - h1).Check bounds: if no humidification (hA = h2), SHF = 1; if only latent addition (h2 = h1), SHF = 0.Verification / Alternative check:On the psychrometric chart, the process 1→2 is a nearly horizontal line (constant humidity ratio), and 2→A is a roughly vertical/up-right move (moisture addition). The slope of the overall process line relates to SHF, and the above formula matches the geometry.Why Other Options Are Wrong:(hA - h2) / (hA - h1): represents the latent share, not the sensible share.(hA - h1) / (h2 - h1): reciprocal of SHF.(h2 - h1) / hA or (h1 - h2) / (hA - h2): not dimensionally or conceptually aligned with sensible-to-total heat.Common Pitfalls:Confusing SHF for cooling with SHF for heating-humidification; always identify the sensible leg and total leg for the specific process path under consideration.Final Answer:SHF = (h2 - h1) / (hA - h1)

Question 19

Psychrometric chart basics Do the horizontal and uniformly spaced lines on a standard psychrometric chart represent relative humidity?

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Introduction / Context:Interpreting a psychrometric chart correctly is essential for HVAC calculations. Each family of lines—dry-bulb temperature, humidity ratio, relative humidity, wet-bulb temperature, enthalpy, and specific volume—has a distinct orientation. Misreading these lines leads to wrong loads, coil duties, and comfort predictions.Given Data / Assumptions:Standard psychrometric chart at a fixed barometric pressure (often 1.013 bar).Axes: horizontal axis for dry-bulb temperature, vertical axis for humidity ratio (kg/kg of dry air).Concept / Approach:On the standard chart, horizontal lines correspond to constant humidity ratio (also called specific humidity). Relative humidity lines are curved lines that connect points of equal RH, sweeping from 100% at the saturation curve to lower values inside the chart. Therefore, the statement that “horizontal and uniformly spaced lines indicate relative humidity” is incorrect.Step-by-Step Solution:Identify the axes: x-axis is dry-bulb temperature, y-axis is humidity ratio.Horizontal lines: constant humidity ratio.Curved lines: constant relative humidity (0–100%).Diagonal/oblique lines: near-straight wet-bulb and enthalpy lines (chart dependent).Verification / Alternative check:Any standard chart legend confirms line families: constant RH curves are not horizontal except at 100% along the saturation boundary, which itself is a curve, not a straight horizontal line.Why Other Options Are Wrong:“Correct” contradicts the defined geometry of the chart.Pressure or low RH caveats do not turn the RH curves into horizontal lines; only the scales might shift slightly with altitude.Common Pitfalls:Confusing humidity ratio with relative humidity. Humidity ratio is a mass ratio, while RH is a percentage measure of saturation at a given temperature. On the chart they are represented by different line families.Final Answer:Incorrect

Question 20

Identify the Bell–Coleman refrigeration cycle The Bell–Coleman air refrigeration cycle is thermodynamically equivalent to which reversed power cycle?

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Introduction / Context:The Bell–Coleman cycle (air cycle refrigeration) is used in applications like aircraft cooling and some specialized cryogenic systems. It employs air as the working fluid and standard turbomachinery components rather than phase-change refrigerants.Given Data / Assumptions:Working fluid: air modeled as an ideal gas.Basic components: compressor, heat exchanger (aftercooler), expander (turbine), and heat exchanger (refrigerator).Idealized processes: adiabatic compression/expansion and constant-pressure heat exchange.Concept / Approach:The sequence of processes in Bell–Coleman exactly mirrors the Joule (Brayton) gas-turbine power cycle but operated in reverse: instead of producing net work from heat addition, it consumes work to move heat from cold space to a warm sink. Therefore, the Bell–Coleman cycle is the reversed Joule (Brayton) cycle.Step-by-Step Solution:Compare power Brayton: 1→2 adiabatic compression, 2→3 constant-pressure heat addition, 3→4 adiabatic expansion, 4→1 constant-pressure heat rejection.Reverse the arrows for refrigeration: compressor work input, reject heat at high pressure, turbine expansion to create low temperature, absorb heat at low pressure.Conclude equivalence: Bell–Coleman = reversed Joule (Brayton).Verification / Alternative check:Temperature–entropy and pressure–volume diagrams of the air cycle refrigeration align with the reversed Brayton sequence; the device COP expressions also correspond to Brayton relations.Why Other Options Are Wrong:Reversed Rankine: involves phase change of a condensable refrigerant, not ideal-gas air.Reversed Otto/Carnot/Diesel: do not match the constant-pressure heat exchange and adiabatic legs of the air cycle used here.Common Pitfalls:Assuming all refrigeration cycles are reversed Rankine because most domestic systems use vapor-compression; air cycle is a different family.Final Answer:Reversed Joule (Brayton) cycle

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