Q: Refrigeration performance metric: The coefficient of performance (COP) is defined as useful refrigeration divided by net work. COP is dimensionless. The units of which of the following are the same as COP?

Introduction / Context: Performance indices help compare cycles irrespective of absolute scale. The coefficient of performance (COP) is widely used for refrigerators and heat pumps. Recognizing that COP is a ratio of like units prevents dimensional mistakes in calculations and reporting. Given Data / Assumptions: COP = refrigeration effect / net work. Both numerator and denominator have energy units (e.g., kJ) per cycle or power units (e.g., kW) for steady operation. Therefore, COP is dimensionless. Concept / Approach: Since COP is a ratio of two energy (or power) quantities, the units cancel. None of the listed dimensional quantities (kinematic viscosity, work, temperature, pressure) are unitless; hence, none share the same units as COP. This mirrors thermal efficiency for power cycles, which is also dimensionless. Step-by-Step Solution: Identify units: refrigeration and work both in energy or power.Form the ratio: units cancel → pure number.Conclude that none of the dimensional options match COP. Verification / Alternative check: Handbooks list COP without units (e.g., COP = 3.2), confirming the dimensionless nature. Why Other Options Are Wrong: Kinematic viscosity has units of m^2/s, work has joules, temperature has kelvin, pressure has Pa. These cannot match a dimensionless COP. Common Pitfalls: Reporting COP with energy units attached; confusing COP with EER (which uses Btu/hr per W but is still a ratio convertible to dimensionless via constants). Final Answer: none of these

Q: Jet (ejector) refrigeration: In steam-jet or water-jet refrigerators, the working refrigerant used in the evaporator loop is typically which fluid?

Introduction / Context: Jet (ejector) refrigeration systems exploit high-velocity motive steam or gas to entrain and compress vapor from an evaporator operating at low pressure. The choice of refrigerant in these systems influences achievable temperatures, simplicity, and environmental footprint. A classic configuration uses water as the refrigerant. Given Data / Assumptions: Steam-jet ejector provides suction to the evaporator. Evaporator operates under deep vacuum to boil the refrigerant at low temperature. System targets chilled water production rather than deep cryogenics. Concept / Approach: In water-jet or steam-jet refrigeration, the evaporator contains water as the refrigerant. Under vacuum, water boils at temperatures well below 100°C; at sufficiently low pressure, it can produce chilled water near 5–10°C. The vapor drawn off is compressed by the ejector and condensed, often returning as makeup. This avoids halocarbons and ammonia, simplifying safety and environmental concerns. Step-by-Step Solution: Recognize ejector refrigeration architecture: motive steam + water refrigerant.Identify refrigerant in the evaporator: water under vacuum.Conclude the correct choice is water. Verification / Alternative check: Design texts consistently describe steam-jet refrigeration systems producing chilled water using water as both refrigerant and chilled medium. Why Other Options Are Wrong: Ammonia and freons are used in mechanical vapor-compression systems, not in classic steam-jet water systems. Brine serves as a secondary coolant, not the refrigerant in the evaporator. Common Pitfalls: Confusing the chilled secondary loop (often water/brine) with the primary refrigerant in the ejector-based process. Final Answer: water

Q: Fugacity in mixtures: For a stable binary mixture at constant temperature and pressure, how does the fugacity of a component change as its mole fraction increases?

Introduction / Context: Fugacity generalizes the idea of an effective pressure for real fluids and appears in equilibrium criteria. In mixtures at fixed temperature and pressure, component fugacity is closely tied to composition through activity (liquids) or partial pressure (gases). This question probes the qualitative trend with composition. Given Data / Assumptions: Binary mixture at fixed T and P. No chemical reaction; single phase stable region. Regular behavior without azeotropic anomalies for the qualitative trend. Concept / Approach: For gases, f_i ≈ y_i * φ_i * P; as y_i (the mole fraction in the gas phase) increases at fixed P and T, f_i typically increases. For liquids, f_i ≈ x_i * γ_i * f_i^sat(T); while γ_i can vary with composition, the basic trend for small to moderate nonideality is that increasing x_i raises the product x_i * γ_i, and hence fugacity, unless extreme nonideal effects intervene. Therefore, under ordinary stable conditions, fugacity of a component increases with its mole fraction. Step-by-Step Solution: Relate fugacity to composition: gas phase f_i ∝ y_i; liquid phase f_i ∝ x_i * γ_i.Hold T, P constant; vary composition.Infer that increasing mole fraction increases component fugacity. Verification / Alternative check: Modified Raoult’s law and equations of state lead to monotonic increases of f_i with x_i or y_i in stable single-phase regions away from critical anomalies. Why Other Options Are Wrong: Decrease or constancy contradicts standard thermodynamic relations; oscillation lacks physical basis in stable mixtures. Common Pitfalls: Confusing fugacity with activity coefficient alone; overlooking that fugacity depends on the product with composition (x_i or y_i). Final Answer: increases

Q: Intensive vs. extensive properties – identify the non-intensive quantity Which of the following is not an intensive property (i.e., it does not remain unchanged with system size or subdivision)?

Introduction / Context: Thermodynamic properties are classified as intensive or extensive. Intensive properties are independent of the amount of matter (e.g., temperature, pressure), whereas extensive properties scale with system size (e.g., mass, volume). Correct classification is vital in process modeling and scaling-up operations. Given Data / Assumptions: Chemical potential (μ) is defined per mole; it is intensive. Surface tension (σ) is force per unit length or energy per unit area; it is intensive. Heat capacity can be quoted as total (C) or specific/molar (c, C̄p). Concept / Approach: When the term “heat capacity” appears without the qualifier “specific” or “molar,” it refers to the total heat capacity C of the system. Total heat capacity is proportional to the amount of substance and thus is an extensive property. In contrast, specific heat capacity (per mass) or molar heat capacity (per mole) are intensive because they normalize by the amount of substance. Step-by-Step Solution: Interpret “heat capacity” as total C unless otherwise qualified.Check scaling behavior: doubling the system doubles C → extensive.Chemical potential and surface tension do not scale with amount → intensive.Hence, the non-intensive item asked is total heat capacity. Verification / Alternative check: Process simulators require specific or molar heat capacities as inputs to remain composition- and temperature-dependent but size independent; total heat duty then scales by flowrate. Why Other Options Are Wrong: Chemical potential: Defined per mole; intensive. Surface tension: Defined per unit length/area; intensive. None of these: Incorrect because one item (heat capacity) is indeed non-intensive. Common Pitfalls: Confusing heat capacity (C) with specific heat capacity (c). Always check units to determine whether a property is intensive or extensive. Final Answer: Heat capacity

Q: Third law of thermodynamics – entropy at absolute zero The statement “At absolute zero temperature, the entropy of every perfectly crystalline substance becomes zero” follows from which thermodynamic principle?

Introduction / Context: The low-temperature limit of entropy is fundamental to thermodynamics, materials science, and cryogenics. It provides an absolute reference for entropy and underpins calculations of absolute entropies from calorimetric data. Given Data / Assumptions: A “perfectly crystalline” substance has a single microstate at 0 K (no configurational disorder). Absolute zero is the limit T → 0 K. The quoted statement is Planck’s formulation of the third law. Concept / Approach: The third law of thermodynamics (Planck statement) asserts that the entropy of a perfect crystal approaches zero as temperature approaches zero. Nernst’s heat theorem is closely related, stating that the entropy change for any isothermal process approaches zero as T → 0 K. While the two are connected, the exact wording given corresponds to the third law’s Planck form, not the general second law or the mathematical Maxwell relations. Step-by-Step Solution: Identify the statement as the Planck formulation.Associate it with the third law, which fixes the baseline for absolute entropy.Recognize Nernst’s theorem as a corollary; however, the question seeks the direct source.Select “third law of thermodynamics.” Verification / Alternative check: Entropy tables set S°(0 K) = 0 for perfect crystals, consistent with third-law calorimetry practices. Why Other Options Are Wrong: Second law: Governs entropy increase and reversibility, not the absolute zero limit. Nernst heat theorem: Related but not the exact quoted statement. Maxwell’s relations: Mathematical identities from exact differentials; unrelated to the 0 K entropy axiom. Common Pitfalls: Equating Nernst’s theorem with the entire third law; while related, the wording here is specifically the third law. Final Answer: third law of thermodynamics

Q: Gas laws – precise statement of Boyle’s law Choose the correct form of Boyle’s law for a fixed mass of an ideal gas at constant temperature (isothermal conditions).

Introduction / Context: Boyle’s law is one of the foundational gas laws used to describe the behavior of ideal gases. It underlies isothermal compression/expansion calculations in compressors, syringes, and many laboratory operations. Given Data / Assumptions: Ideal gas behavior assumed. Temperature held constant (isothermal process). Amount of gas (number of moles) held constant. Concept / Approach: For an isothermal change of a fixed mass of an ideal gas, pressure is inversely proportional to volume. Mathematically, P ∝ 1/V, which integrates to P * V = constant. Either expression is a correct statement of Boyle’s law; the most explicit engineering form used for calculations is P1V1 = P2V2 when comparing two states at the same temperature and moles. Step-by-Step Solution: Recognize isothermal, fixed-mass scenario.Use Boyle’s relation: P ∝ 1/V.Write the constant-product form: P * V = constant.Select the explicit constant-product statement as the best answer. Verification / Alternative check: From the ideal gas law PV = nRT, holding n and T constant gives PV = constant, confirming Boyle’s law directly. Why Other Options Are Wrong: P ∝ V: Opposite of Boyle’s law. P/T = constant: That is Gay-Lussac’s relation for fixed V, not Boyle’s law. P ∝ 1/V is conceptually correct, but the most complete engineering statement is the constant-product form selected. Common Pitfalls: Forgetting the “fixed mass and constant temperature” conditions; mixing Boyle’s law with Charles’ or Gay-Lussac’s laws. Final Answer: P * V = constant, at constant temperature and fixed mass of gas

Q: Criteria for spontaneity – behavior of free energy and entropy For a spontaneous process under the usual thermodynamic criteria, how do free energy and entropy behave?

Introduction / Context: Spontaneity indicates the natural direction of a process without external work input. Engineers use Gibbs free energy (for constant temperature and pressure) and Helmholtz free energy (for constant temperature and volume) to assess spontaneity in reactions and phase changes. Given Data / Assumptions: Closed system in thermal contact with a large reservoir at constant temperature (and often constant pressure). Universe entropy criterion: ΔS_universe > 0 for spontaneous change. Gibbs free energy criterion: ΔG < 0 at constant T, P. Concept / Approach: Under constant T, P, the direction of spontaneity corresponds to a decrease in Gibbs free energy. Equivalently, the total entropy of the universe increases. This reconciles the system-level free energy change with the second law applied to system plus surroundings. Therefore, a concise, correct statement is that free energy decreases while entropy increases (considering the universe or, practically, the surroundings absorb heat and increase entropy). Step-by-Step Solution: Apply ΔG criterion: spontaneous → ΔG 0.Relate the two via ΔG = −T * ΔS_universe (for constant T, P).Hence, free energy decreases as entropy of the universe increases. Verification / Alternative check: For a chemical reaction at fixed T, P, tabulated Gibbs energies predict direction; exergonic reactions have negative ΔG and proceed spontaneously toward equilibrium. Why Other Options Are Wrong: Free energy is zero: Only at equilibrium, not for all spontaneous steps. Free energy increases: Opposite of the spontaneity criterion. Both decrease: Violates the second law. Common Pitfalls: Confusing system entropy with total entropy; the system's entropy can decrease if the surroundings’ entropy increases more. Final Answer: decreases whereas the entropy increases

Question 1

Refrigerant selection: Which high property is generally undesirable for a good refrigerant due to increased pumping losses and poorer heat transfer?

Accepted Answer

Introduction / Context: Choosing a refrigerant involves balancing thermophysical properties for efficiency, safety, and practicality. Some properties should be high (e.g., latent heat), while others are preferably low (e.g., viscosity) to minimize irreversibilities and parasitic loads in compressors and pumps. Given Data / Assumptions: Focus on property impact on circulation and heat exchange. Comparison is qualitative and broadly valid across common refrigerants. System operates in typical ranges for HVAC/R or process refrigeration. Concept / Approach: High viscosity increases pressure drop in pipes and heat exchangers, raises pumping power, and degrades convective heat transfer coefficients. Conversely, high latent heat reduces mass flow required for a given cooling duty, improving COP. Low specific vapor volume is desirable to reduce compressor size; excessively high specific volume is undesirable for machinery sizing. Between the listed choices, high viscosity is the unambiguously undesirable attribute across most designs. Step-by-Step Solution: Identify which property directly worsens hydraulics and heat transfer when large: viscosity.Relate to pumping power: P_pump ∝ Δp * volumetric flow; Δp ↑ with viscosity.Conclude high viscosity is undesirable. Verification / Alternative check: Empirical correlations for friction factor and Nusselt number show adverse dependence on viscosity, confirming the design penalty. Why Other Options Are Wrong: High latent heat is typically favorable; specific vapor volume is ideally low (but the prompt asks for a single most generally undesirable property—viscosity is the clear choice). Specific heat and thermal conductivity can aid heat transfer in secondary loops. Common Pitfalls: Confusing refrigerant property desirability with secondary coolant properties; misreading 'specific volume' versus 'density' effects. Final Answer: viscosity

Question 2

Joule–Thomson effect: During throttling at approximately ambient conditions, all real gases cool except which of the following?

Accepted Answer

Introduction / Context: The Joule–Thomson (JT) effect describes temperature change during throttling (adiabatic, no shaft work). Whether a gas cools or warms depends on its inversion temperature relative to the operating temperature. This principle is crucial in gas liquefaction and cryogenics. Given Data / Assumptions: Throttling at roughly atmospheric pressure and room temperature. Real-gas behavior; no external heat exchange (adiabatic throttling). We compare common gases CO2, H2, O2, N2. Concept / Approach: If the operating temperature is below the JT inversion temperature of the gas, throttling causes cooling; if above, it causes warming. Most common gases (CO2, O2, N2) have inversion temperatures well above room temperature, so they cool upon throttling. Hydrogen (and helium) have inversion temperatures below room temperature; thus, at ambient conditions, they warm during throttling instead of cooling. Step-by-Step Solution: Identify inversion-temperature relation: cooling occurs when T < T_inversion.At room temperature: CO2, O2, N2 cool; H2 warms.Therefore, the exception is hydrogen. Verification / Alternative check: Cryogenic process design uses pre-cooling or expansion engines for hydrogen/helium before JT valves, reflecting their warming behavior near ambient conditions. Why Other Options Are Wrong: CO2, O2, N2 commonly cool upon throttling at ambient temperatures. Common Pitfalls: Generalizing JT cooling to all gases at all conditions; ignoring the role of inversion temperature. Final Answer: H2

Question 3

Refrigeration performance metric: The coefficient of performance (COP) is defined as useful refrigeration divided by net work. COP is dimensionless. The units of which of the following are the same as COP?

Accepted Answer

Introduction / Context: Performance indices help compare cycles irrespective of absolute scale. The coefficient of performance (COP) is widely used for refrigerators and heat pumps. Recognizing that COP is a ratio of like units prevents dimensional mistakes in calculations and reporting. Given Data / Assumptions: COP = refrigeration effect / net work. Both numerator and denominator have energy units (e.g., kJ) per cycle or power units (e.g., kW) for steady operation. Therefore, COP is dimensionless. Concept / Approach: Since COP is a ratio of two energy (or power) quantities, the units cancel. None of the listed dimensional quantities (kinematic viscosity, work, temperature, pressure) are unitless; hence, none share the same units as COP. This mirrors thermal efficiency for power cycles, which is also dimensionless. Step-by-Step Solution: Identify units: refrigeration and work both in energy or power.Form the ratio: units cancel → pure number.Conclude that none of the dimensional options match COP. Verification / Alternative check: Handbooks list COP without units (e.g., COP = 3.2), confirming the dimensionless nature. Why Other Options Are Wrong: Kinematic viscosity has units of m^2/s, work has joules, temperature has kelvin, pressure has Pa. These cannot match a dimensionless COP. Common Pitfalls: Reporting COP with energy units attached; confusing COP with EER (which uses Btu/hr per W but is still a ratio convertible to dimensionless via constants). Final Answer: none of these

Question 4

Jet (ejector) refrigeration: In steam-jet or water-jet refrigerators, the working refrigerant used in the evaporator loop is typically which fluid?

Accepted Answer

Introduction / Context: Jet (ejector) refrigeration systems exploit high-velocity motive steam or gas to entrain and compress vapor from an evaporator operating at low pressure. The choice of refrigerant in these systems influences achievable temperatures, simplicity, and environmental footprint. A classic configuration uses water as the refrigerant. Given Data / Assumptions: Steam-jet ejector provides suction to the evaporator. Evaporator operates under deep vacuum to boil the refrigerant at low temperature. System targets chilled water production rather than deep cryogenics. Concept / Approach: In water-jet or steam-jet refrigeration, the evaporator contains water as the refrigerant. Under vacuum, water boils at temperatures well below 100°C; at sufficiently low pressure, it can produce chilled water near 5–10°C. The vapor drawn off is compressed by the ejector and condensed, often returning as makeup. This avoids halocarbons and ammonia, simplifying safety and environmental concerns. Step-by-Step Solution: Recognize ejector refrigeration architecture: motive steam + water refrigerant.Identify refrigerant in the evaporator: water under vacuum.Conclude the correct choice is water. Verification / Alternative check: Design texts consistently describe steam-jet refrigeration systems producing chilled water using water as both refrigerant and chilled medium. Why Other Options Are Wrong: Ammonia and freons are used in mechanical vapor-compression systems, not in classic steam-jet water systems. Brine serves as a secondary coolant, not the refrigerant in the evaporator. Common Pitfalls: Confusing the chilled secondary loop (often water/brine) with the primary refrigerant in the ejector-based process. Final Answer: water

Question 5

Fugacity in mixtures: For a stable binary mixture at constant temperature and pressure, how does the fugacity of a component change as its mole fraction increases?

Accepted Answer

Introduction / Context: Fugacity generalizes the idea of an effective pressure for real fluids and appears in equilibrium criteria. In mixtures at fixed temperature and pressure, component fugacity is closely tied to composition through activity (liquids) or partial pressure (gases). This question probes the qualitative trend with composition. Given Data / Assumptions: Binary mixture at fixed T and P. No chemical reaction; single phase stable region. Regular behavior without azeotropic anomalies for the qualitative trend. Concept / Approach: For gases, f_i ≈ y_i * φ_i * P; as y_i (the mole fraction in the gas phase) increases at fixed P and T, f_i typically increases. For liquids, f_i ≈ x_i * γ_i * f_i^sat(T); while γ_i can vary with composition, the basic trend for small to moderate nonideality is that increasing x_i raises the product x_i * γ_i, and hence fugacity, unless extreme nonideal effects intervene. Therefore, under ordinary stable conditions, fugacity of a component increases with its mole fraction. Step-by-Step Solution: Relate fugacity to composition: gas phase f_i ∝ y_i; liquid phase f_i ∝ x_i * γ_i.Hold T, P constant; vary composition.Infer that increasing mole fraction increases component fugacity. Verification / Alternative check: Modified Raoult’s law and equations of state lead to monotonic increases of f_i with x_i or y_i in stable single-phase regions away from critical anomalies. Why Other Options Are Wrong: Decrease or constancy contradicts standard thermodynamic relations; oscillation lacks physical basis in stable mixtures. Common Pitfalls: Confusing fugacity with activity coefficient alone; overlooking that fugacity depends on the product with composition (x_i or y_i). Final Answer: increases

Question 6

Thermodynamics of solutions – scope of the Van Laar equation In phase-equilibrium calculations, the Van Laar equation is an empirical model for activity coefficients. For which type of liquid-phase mixtures is it primarily formulated and applied?

Accepted Answer

Introduction / Context: The Van Laar equation is a classic excess-Gibbs-energy model that correlates non-ideality in liquid mixtures. It is frequently taught alongside the Margules and Wilson equations in chemical engineering thermodynamics for predicting activity coefficients required in vapor–liquid equilibrium design and extraction calculations. Given Data / Assumptions: The model uses two adjustable interaction parameters. It targets deviations from Raoult's law in liquid mixtures. Focus is on routine engineering use rather than ab initio prediction. Concept / Approach: Van Laar's two-parameter form is derived for two-component (binary) mixtures. The activity coefficients gamma_1 and gamma_2 are expressed as simple functions of composition and two constants fitted to binary data. While extensions exist, the standard form is not directly parameterized for ternary systems without further assumptions or combination rules. Azeotropes may be described if they occur in the binary being modeled, but the equation is not limited to azeotropic compositions; it covers the entire binary composition range when properly regressed. Step-by-Step Solution: Identify the model's parameter count and dependency: two parameters → two components.Recall that activity coefficients are functions of liquid composition in binary systems.Acknowledge that ternary use generally needs different models or multicomponent extensions.Therefore, the equation primarily deals with binary solutions. Verification / Alternative check: Standard thermodynamics texts tabulate Van Laar parameters for binary pairs (e.g., ethanol–water, acetone–chloroform), confirming its binary focus. Why Other Options Are Wrong: Ternary solutions: Not the native scope without extra mixing rules. Azeotropic mixture only: The model is not restricted to azeotropes. None of these: Incorrect because a correct choice exists. Common Pitfalls: Confusing the Van Laar model with multicomponent-capable models like Wilson or NRTL; assuming a binary model automatically generalizes without re-derivation. Final Answer: binary solutions

Question 7

Intensive vs. extensive properties – identify the non-intensive quantity Which of the following is not an intensive property (i.e., it does not remain unchanged with system size or subdivision)?

Accepted Answer

Introduction / Context: Thermodynamic properties are classified as intensive or extensive. Intensive properties are independent of the amount of matter (e.g., temperature, pressure), whereas extensive properties scale with system size (e.g., mass, volume). Correct classification is vital in process modeling and scaling-up operations. Given Data / Assumptions: Chemical potential (μ) is defined per mole; it is intensive. Surface tension (σ) is force per unit length or energy per unit area; it is intensive. Heat capacity can be quoted as total (C) or specific/molar (c, C̄p). Concept / Approach: When the term “heat capacity” appears without the qualifier “specific” or “molar,” it refers to the total heat capacity C of the system. Total heat capacity is proportional to the amount of substance and thus is an extensive property. In contrast, specific heat capacity (per mass) or molar heat capacity (per mole) are intensive because they normalize by the amount of substance. Step-by-Step Solution: Interpret “heat capacity” as total C unless otherwise qualified.Check scaling behavior: doubling the system doubles C → extensive.Chemical potential and surface tension do not scale with amount → intensive.Hence, the non-intensive item asked is total heat capacity. Verification / Alternative check: Process simulators require specific or molar heat capacities as inputs to remain composition- and temperature-dependent but size independent; total heat duty then scales by flowrate. Why Other Options Are Wrong: Chemical potential: Defined per mole; intensive. Surface tension: Defined per unit length/area; intensive. None of these: Incorrect because one item (heat capacity) is indeed non-intensive. Common Pitfalls: Confusing heat capacity (C) with specific heat capacity (c). Always check units to determine whether a property is intensive or extensive. Final Answer: Heat capacity

Question 8

Third law of thermodynamics – entropy at absolute zero The statement “At absolute zero temperature, the entropy of every perfectly crystalline substance becomes zero” follows from which thermodynamic principle?

Accepted Answer

Introduction / Context: The low-temperature limit of entropy is fundamental to thermodynamics, materials science, and cryogenics. It provides an absolute reference for entropy and underpins calculations of absolute entropies from calorimetric data. Given Data / Assumptions: A “perfectly crystalline” substance has a single microstate at 0 K (no configurational disorder). Absolute zero is the limit T → 0 K. The quoted statement is Planck’s formulation of the third law. Concept / Approach: The third law of thermodynamics (Planck statement) asserts that the entropy of a perfect crystal approaches zero as temperature approaches zero. Nernst’s heat theorem is closely related, stating that the entropy change for any isothermal process approaches zero as T → 0 K. While the two are connected, the exact wording given corresponds to the third law’s Planck form, not the general second law or the mathematical Maxwell relations. Step-by-Step Solution: Identify the statement as the Planck formulation.Associate it with the third law, which fixes the baseline for absolute entropy.Recognize Nernst’s theorem as a corollary; however, the question seeks the direct source.Select “third law of thermodynamics.” Verification / Alternative check: Entropy tables set S°(0 K) = 0 for perfect crystals, consistent with third-law calorimetry practices. Why Other Options Are Wrong: Second law: Governs entropy increase and reversibility, not the absolute zero limit. Nernst heat theorem: Related but not the exact quoted statement. Maxwell’s relations: Mathematical identities from exact differentials; unrelated to the 0 K entropy axiom. Common Pitfalls: Equating Nernst’s theorem with the entire third law; while related, the wording here is specifically the third law. Final Answer: third law of thermodynamics

Question 9

Gas laws – precise statement of Boyle’s law Choose the correct form of Boyle’s law for a fixed mass of an ideal gas at constant temperature (isothermal conditions).

Accepted Answer

Introduction / Context: Boyle’s law is one of the foundational gas laws used to describe the behavior of ideal gases. It underlies isothermal compression/expansion calculations in compressors, syringes, and many laboratory operations. Given Data / Assumptions: Ideal gas behavior assumed. Temperature held constant (isothermal process). Amount of gas (number of moles) held constant. Concept / Approach: For an isothermal change of a fixed mass of an ideal gas, pressure is inversely proportional to volume. Mathematically, P ∝ 1/V, which integrates to P * V = constant. Either expression is a correct statement of Boyle’s law; the most explicit engineering form used for calculations is P1V1 = P2V2 when comparing two states at the same temperature and moles. Step-by-Step Solution: Recognize isothermal, fixed-mass scenario.Use Boyle’s relation: P ∝ 1/V.Write the constant-product form: P * V = constant.Select the explicit constant-product statement as the best answer. Verification / Alternative check: From the ideal gas law PV = nRT, holding n and T constant gives PV = constant, confirming Boyle’s law directly. Why Other Options Are Wrong: P ∝ V: Opposite of Boyle’s law. P/T = constant: That is Gay-Lussac’s relation for fixed V, not Boyle’s law. P ∝ 1/V is conceptually correct, but the most complete engineering statement is the constant-product form selected. Common Pitfalls: Forgetting the “fixed mass and constant temperature” conditions; mixing Boyle’s law with Charles’ or Gay-Lussac’s laws. Final Answer: P * V = constant, at constant temperature and fixed mass of gas

Question 10

Criteria for spontaneity – behavior of free energy and entropy For a spontaneous process under the usual thermodynamic criteria, how do free energy and entropy behave?

Accepted Answer

Introduction / Context: Spontaneity indicates the natural direction of a process without external work input. Engineers use Gibbs free energy (for constant temperature and pressure) and Helmholtz free energy (for constant temperature and volume) to assess spontaneity in reactions and phase changes. Given Data / Assumptions: Closed system in thermal contact with a large reservoir at constant temperature (and often constant pressure). Universe entropy criterion: ΔS_universe > 0 for spontaneous change. Gibbs free energy criterion: ΔG < 0 at constant T, P. Concept / Approach: Under constant T, P, the direction of spontaneity corresponds to a decrease in Gibbs free energy. Equivalently, the total entropy of the universe increases. This reconciles the system-level free energy change with the second law applied to system plus surroundings. Therefore, a concise, correct statement is that free energy decreases while entropy increases (considering the universe or, practically, the surroundings absorb heat and increase entropy). Step-by-Step Solution: Apply ΔG criterion: spontaneous → ΔG < 0.Apply ΔS_universe criterion: spontaneous → ΔS_universe > 0.Relate the two via ΔG = −T * ΔS_universe (for constant T, P).Hence, free energy decreases as entropy of the universe increases. Verification / Alternative check: For a chemical reaction at fixed T, P, tabulated Gibbs energies predict direction; exergonic reactions have negative ΔG and proceed spontaneously toward equilibrium. Why Other Options Are Wrong: Free energy is zero: Only at equilibrium, not for all spontaneous steps. Free energy increases: Opposite of the spontaneity criterion. Both decrease: Violates the second law. Common Pitfalls: Confusing system entropy with total entropy; the system's entropy can decrease if the surroundings’ entropy increases more. Final Answer: decreases whereas the entropy increases

Question 11

Gas-phase dissociation equilibrium – effect of added species and pressure For the equilibrium PCl5 ⇌ PCl3 + Cl2 (all gases), identify the incorrect statement about the degree of dissociation of PCl5 under the listed changes.

Accepted Answer

Introduction / Context: Le Châtelier’s principle predicts how an equilibrium shifts when conditions change. For the dissociation PCl5 ⇌ PCl3 + Cl2, the product side has more moles of gas than the reactant side. Pressure changes and additions of reacting or inert gases can shift the equilibrium and hence the degree of dissociation α. Given Data / Assumptions: Stoichiometry: 1 mole ⇌ 2 moles (increase in gaseous moles on dissociation). Ideal gas behavior approximation. Comparisons at the same temperature. Concept / Approach: Adding a product (Cl2) increases its partial pressure and shifts equilibrium to the left, reducing dissociation. Increasing total pressure favors the side with fewer moles (left), again reducing dissociation. Adding an inert gas at constant pressure allows volume to increase to keep pressure fixed; this expansion favors the side with more moles (right), increasing dissociation. Thus, each specific statement (a), (b), and (c) is correct; therefore, the prompt asking for the “wrong” statement has answer “none of these.” Step-by-Step Solution: Consider mole count: left 1, right 2.Add Cl2 → shift left → α decreases.Add inert gas at constant pressure → effective expansion → shift right → α increases.Increase pressure → shift left → α decreases. Verification / Alternative check: Equilibrium constant in terms of partial pressures Kp is unchanged at fixed T; qualitative shifts follow from how partial pressures adjust to maintain Kp under constraints. Why Other Options Are Wrong: Each of (a), (b), (c) correctly describes the shift; none is wrong. Common Pitfalls: Confusing constant-pressure vs. constant-volume addition of inert gas; at constant volume, adding inert gas does not change partial pressures and has no effect on equilibrium. Final Answer: none of these

Question 12

Work and heat in thermodynamic processes – select the correct statement Which of the following statements is correct regarding reversible/irreversible work and the nature of thermodynamic quantities?

Accepted Answer

Introduction / Context: Comparing different processes for ideal gases (isothermal vs. adiabatic) and understanding state vs. path functions are foundational for cycle analysis and equipment design (compressors, expanders, engines). Given Data / Assumptions: Ideal gas behavior for qualitative comparisons. Same initial state and same final volume are considered for work comparison. Reversible paths maximize work magnitude for a given change. Concept / Approach: For a reversible expansion from the same initial state to the same final volume, the isothermal path has higher pressures at any intermediate volume than the adiabatic path; thus the area under the P–V curve (work by the gas) is larger for the isothermal case. Therefore, reversible adiabatic work (by the gas) is less than reversible isothermal work to the same V2. Also, reversible work magnitude exceeds irreversible work for the same endpoints. Finally, heat and work are path functions, whereas enthalpy and entropy are state functions. Step-by-Step Solution: Compare P–V curves: P_iso > P_adiabatic for V between initial and final.Conclude W_rev,adiabatic < W_rev,isothermal (expansion work by gas).Note: Irreversible work is less in magnitude than reversible for the same endpoints.Classify functions: heat/work = path; enthalpy/entropy = state. Verification / Alternative check: Using ideal-gas formulas, W_rev,isothermal = nRT ln(V2/V1), whereas W_rev,adiabatic = (P1V1 − P2V2)/(γ − 1). For the same V2/V1, the isothermal work is larger. Why Other Options Are Wrong: Irreversible work more than reversible: False; reversible is maximum (for work output). All four are state functions: False; heat and work are not state functions. Closed system cannot exchange energy: False; it exchanges energy (heat/work) but not matter. Common Pitfalls: Comparing to the same final pressure instead of the same final volume; mixing up sign conventions for work. Final Answer: Under reversible conditions, the adiabatic work is less than isothermal work.

Question 13

Refrigeration cycles – COP ranking for a fixed refrigeration effect A refrigeration cycle is a reversed heat engine. For the same refrigeration effect, which cycle offers the maximum theoretical coefficient of performance (COP)?

Accepted Answer

Introduction / Context: The COP is a key metric for comparing refrigeration cycles. It measures cooling provided per unit of work input. Theoretical limits help benchmark real systems such as vapor compression units and gas cycles. Given Data / Assumptions: Same cold and hot reservoir temperatures for all cycles compared. Ideal, reversible operation defines the theoretical upper bound. Air and vapor compression cycles have practical irreversibilities. Concept / Approach: The Carnot refrigeration cycle is the ideal reversible cycle operating between two temperature reservoirs. Its COP for refrigeration is COP_Carnot = Tc / (Th − Tc), which is the maximum achievable for any cycle between the same reservoir temperatures. Real vapor compression systems that use an expansion valve suffer throttling losses; using an expansion (work-recovering) turbine improves COP but still falls short of the Carnot limit. Air cycles (reverse Brayton) typically have lower COPs at common refrigeration temperatures and pressures. Step-by-Step Solution: Identify the ideal reversible benchmark: Carnot cycle.Recall COP_Carnot depends only on reservoir temperatures.Recognize practical cycles include irreversibilities, lowering COP below Carnot.Therefore select “Carnot refrigeration cycle”. Verification / Alternative check: Any real cycle must satisfy COP_real ≤ COP_Carnot. Textbook comparisons show Carnot > vapor compression with expander > vapor compression with valve > air cycle (typical conditions). Why Other Options Are Wrong: Expansion valve: Irreversible throttling reduces COP. Air cycle: Generally lowest COP for given temperature lift. Expansion engine improves COP but cannot surpass Carnot. Common Pitfalls: Comparing COPs at different temperature lifts; always compare at identical Tc and Th. Final Answer: Carnot refrigeration cycle

Question 14

Acentric factor (ω) – typical magnitude and definition insight The acentric factor ω is defined by ω = −log10(Pr_sat) at Tr = 0.7. What is the usual magnitude range of ω for real substances?

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Introduction / Context: The acentric factor (ω) is a shape- and polarity-related parameter introduced by Pitzer to improve corresponding-states correlations for vapor pressures and compressibility. It is widely used with cubic equations of state (e.g., Soave–Redlich–Kwong, Peng–Robinson). Given Data / Assumptions: Definition: ω = −log10(Pr_sat) at Tr = 0.7. Pr_sat = Psat / Pc and Tr = T / Tc. Simple spherical molecules (e.g., argon, methane) have small ω; complex/polar molecules have larger ω. Concept / Approach: By construction, ω measures the deviation of a substance from the simple spherical model. For many common fluids, ω falls between roughly 0 and 1. Light gases like methane have ω near 0.01, while heavier or more polar substances like water are around 0.34, and aromatics may approach ~0.6–0.9. Values greater than 1 are unusual and reserved for highly non-ideal species under specific definitions; thus the safe, general statement is ω < 1 for typical substances. Step-by-Step Solution: Recall definition point Tr = 0.7 used to evaluate Pr_sat.Recognize typical ω values from data tables (0 ≲ ω ≲ 1).Conclude the best universal choice among options is “< 1”. Verification / Alternative check: Databanks list ω(CH4) ≈ 0.011, ω(N2) ≈ 0.037, ω(H2O) ≈ 0.344, ω(benzene) ≈ 0.212, all less than 1. Why Other Options Are Wrong: > 2 or > 1: Not representative of typical fluids. < 3: Trivially true but uninformative; the conventional characterization is ω well below 1. Common Pitfalls: Assuming ω relates directly to critical compressibility factor; although correlated, ω specifically parameterizes vapor-pressure behavior at a reduced temperature. Final Answer: < 1

Question 15

Statistical interpretation – entropy as a system property In thermodynamics and statistical mechanics, entropy is fundamentally a measure of the system’s __________.

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Introduction / Context: Entropy connects macroscopic thermodynamics with microscopic statistics. It quantifies how many microscopic arrangements (microstates) correspond to a macroscopic state, and thereby captures the degree of randomness or disorder in the system. Given Data / Assumptions: Boltzmann relation: S ∝ ln W, where W is the number of accessible microstates. Greater multiplicity implies higher entropy. Thermal interactions and mixing generally increase W. Concept / Approach: While “disorder” is an informal term, it succinctly conveys that higher entropy corresponds to more ways of arranging components without changing macroscopic constraints. Heating a system, mixing different species, or allowing expansion into a vacuum increases the number of microstates, thus raising entropy. Conversely, ordering (e.g., crystallization) reduces the number of accessible configurations and lowers entropy for the system, though the total entropy of the universe increases in a spontaneous process due to heat release to the surroundings. Step-by-Step Solution: Relate entropy to microstate count: S increases with W.Map physical processes (heating, mixing, expansion) to increases in W.Conclude that entropy measures the degree of disorder/randomness.Select “disorder”. Verification / Alternative check: Statistical ensembles (microcanonical, canonical) show that maximizing entropy corresponds to equilibrium distributions, reinforcing the disorder interpretation. Why Other Options Are Wrong: Orderly behaviour: Opposite concept; increasing order usually decreases system entropy. Temperature changes only: Temperature affects entropy but is not its sole meaning. None: Incorrect, as a widely accepted interpretation exists. Common Pitfalls: Over-literalizing “disorder”; remember entropy is precisely defined via state variables and statistical counting, not just qualitative messiness. Final Answer: disorder

Question 16

Anomalous expansion of water in basic thermodynamics: When liquid water is gently heated from 1°C up to 4°C (with no phase change and at approximately atmospheric pressure), what happens to its volume?

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Introduction: Water exhibits an unusual behavior near its density maximum. Unlike most liquids, which expand on heating, water between about 0°C and 4°C becomes denser as temperature increases. Appreciating this “anomalous expansion” is fundamental to thermodynamics and environmental engineering because it influences lake stratification, ice formation, and heat transfer calculations. Given Data / Assumptions: Pure liquid water, atmospheric pressure, no impurities. Temperature range considered: 1°C to 4°C. No phase change; water remains liquid. Concept / Approach: Density ρ is inversely related to volume V for a fixed mass (ρ = m / V). Water has a well-known density maximum at approximately 4°C. Therefore, as temperature increases from 1°C to 4°C, its density increases and its specific volume decreases. For a fixed mass, decreasing specific volume means the bulk volume contracts. Step-by-Step Solution: Identify the unique property: water's maximum density occurs at around 4°C.Consider a fixed mass of water in the 1–4°C range.As temperature rises toward 4°C, density increases ⇒ volume must decrease.Hence, water contracts when heated from 1°C to 4°C. Verification / Alternative check: Reference density tables show ρ(1°C) < ρ(4°C). Because m is constant, V must be smaller at 4°C than at 1°C, confirming contraction. Why Other Options Are Wrong: Expands/has same volume: Opposite to observed behavior within this interval. May contract or expand: Not ambiguous in this specific range; it contracts. “Becomes less dense but keeps the same mass”: Mass is constant, but density does not decrease here; it increases. Common Pitfalls: Assuming all liquids expand on heating at all temperatures. Water is an important exception near 0–4°C due to hydrogen-bond network rearrangements. Final Answer: contracts

Question 17

Foundation of refrigeration cycles: The fundamental principle that makes refrigeration (heat pumping from cold to hot) possible is based on which law of thermodynamics?

Accepted Answer

Introduction: Refrigeration and heat pump systems move heat from a lower-temperature reservoir to a higher-temperature reservoir by doing external work. Understanding which thermodynamic law underpins this possibility is crucial for analyzing vapor-compression, absorption, and gas refrigeration cycles used in HVAC and process industries. Given Data / Assumptions: Idealized cyclic operation of a refrigerator/heat pump. Work input is available from an external source (compressor, pump, etc.). No violation of thermodynamic laws. Concept / Approach: The second law of thermodynamics states that heat does not spontaneously flow from cold to hot. However, it can be forced to do so when external work is supplied. Refrigeration cycles exploit this by using a working fluid that absorbs heat at low temperature (evaporator) and rejects it at higher temperature (condenser), with a compressor providing the necessary work to overcome the natural direction of heat flow. Step-by-Step Solution: Identify the task: transfer heat from cold to hot reservoir.Invoke the second law: spontaneous transfer is impossible; work input is required.Conclude that refrigeration is governed by the second law, not merely energy conservation (first law). Verification / Alternative check: Coefficient of performance (COP) definitions and Carnot refrigerator analysis come directly from second-law statements and entropy balances. Why Other Options Are Wrong: Zeroth law: Defines temperature and thermal equilibrium, enabling thermometry. First law: Energy conservation; necessary but not sufficient to enable cold-to-hot heat flow. Third law: Concerns entropy at absolute zero. Equipartition: A statistical concept, not the governing thermodynamic law here. Common Pitfalls: Confusing “possible with work input” (second law compliant) with “forbidden without work input.” Final Answer: second

Question 18

Effect of pressure on phase-change points: Which of the following quantities increases when the external pressure on a pure substance is increased?

Accepted Answer

Introduction: Designers frequently need to predict how melting and boiling points shift with pressure in separations and materials processing. These dependencies arise from equilibrium thermodynamics and are captured by the Clapeyron and Clausius–Clapeyron relations for phase boundaries. Given Data / Assumptions: Pure, typical substances with positive solid–liquid volume change (most solids are denser than their melts). Boiling refers to liquid–vapor equilibrium. Wax behaves like a typical solid (melting point increases with pressure). Concept / Approach: Boiling point increases with pressure because a higher external pressure requires a higher saturation temperature for the vapor pressure to match it. For melting, most substances contract upon solidification (solid is denser), so increasing pressure favors the solid phase and raises the melting point. Wax follows this normal trend. (Water is a notable exception: it expands upon freezing, hence its melting point decreases with pressure.) Step-by-Step Solution: Use Clausius–Clapeyron: ln P_sat increases with 1/T; higher P → higher T for boiling.For melting: dT/dP = T * ΔV / ΔH_fus; with ΔV < 0 (solid denser), dT/dP > 0.Therefore, both melting point (for wax) and boiling point increase with pressure. Verification / Alternative check: Phase diagrams for typical organics show positive slopes for solid–liquid lines and rising boiling curves with pressure. Why Other Options Are Wrong: Neither: Contradicted by basic phase-equilibrium relations. Only triple-point temperature: Pressure affects the entire coexistence curves, not a single point only. Common Pitfalls: Overgeneralizing water’s anomalous behavior to all materials; most behave like wax, not water. Final Answer: both (a) and (b)

Question 19

Pressure dependence of freezing point: The freezing point of a liquid decreases when pressure is increased if, during solidification, the liquid __________.

Accepted Answer

Introduction: Engineers must predict how phase-change temperatures shift with pressure, especially for materials with anomalous solid–liquid behavior. Water is the classic example where increasing pressure lowers the freezing point, allowing ice skating and pressure melting at the blade contact. Given Data / Assumptions: Liquid undergoing freezing (liquid → solid). External pressure is increased slightly. We consider the sign of volume change on freezing. Concept / Approach: From the Clapeyron relation for solid–liquid equilibrium: dT/dP = T * ΔV / ΔH_fus, where ΔV = V_solid − V_liquid. If the liquid expands on freezing, the solid has a larger specific volume (ΔV > 0). Then dT/dP is positive; however, note that for water the conventional observation is that increasing pressure lowers the freezing point. Interpreting carefully: when the solid is less dense (volume larger) than the liquid, applying pressure favors the denser phase (liquid), so to maintain equilibrium the freezing temperature must decrease—thus the freezing point drops as pressure rises. Step-by-Step Solution: Identify volume change: liquid expands on freezing ⇒ solid less dense.Pressure favors the phase with lower volume (the liquid here).To freeze under higher pressure, the system needs a lower temperature.Therefore, freezing point decreases when pressure is increased. Verification / Alternative check: Water expands upon freezing; experimentally, higher pressure lowers its melting/freezing point—consistent with the reasoning above. Why Other Options Are Wrong: Contracts or no volume change: Then pressure would not lower the freezing point; it would raise it or leave it almost unchanged. “Either”: The direction is specific; expansion on freezing is required for the decrease. Common Pitfalls: Confusing sign conventions in ΔV; always ask which phase is denser to infer the pressure effect. Final Answer: expands

Question 20

Equilibrium shifts and inert gases in reversible reactions: Given Δx = (moles of gaseous products) − (moles of gaseous reactants), identify the correct statements about adding an inert gas and about pressure effects on equilibrium.

Accepted Answer

Introduction: Chemical reaction equilibria depend on temperature, pressure, and composition. The effect of adding an inert gas (a diluent that does not participate in the reaction) depends critically on whether the addition occurs at constant pressure or constant volume, as well as on the change in total moles (Δx) between products and reactants. Given Data / Assumptions: Reversible gas-phase reaction at fixed temperature. Δx = moles of gaseous products − moles of gaseous reactants. Inert gas does not react and has no direct role in the equilibrium constant K(T). Concept / Approach: At constant pressure, adding inert gas increases the total volume to maintain P, thereby decreasing partial pressures. If Δx > 0 (more moles on the product side), the system shifts toward products to counter the dilution (Le Châtelier principle). If Δx < 0, it shifts toward reactants. At constant volume, adding inert gas does not change the partial pressures of reacting species (mole fractions change, but total pressure rises correspondingly), so the equilibrium composition is unaltered. The equilibrium constant K depends only on temperature, not on the presence of inert species or total pressure, hence remains unchanged. Step-by-Step Solution: Evaluate (a): Constant-pressure dilution favors the side with higher moles when Δx > 0 → true.Evaluate (b): When Δx = 0, changing pressure does not shift equilibrium → true.Evaluate (c): At constant volume, adding inert gas does not alter equilibrium composition; K(T) unchanged → true.Therefore, all three statements are correct. Verification / Alternative check: Deriving equilibrium from minimizing Gibbs free energy under appropriate constraints reproduces these conclusions. Why Other Options Are Wrong: Option (e) asserts a universal decrease in conversion, which is false; the direction depends on Δx and constraints. Common Pitfalls: Forgetting to specify whether the system is at constant pressure or constant volume; the effect of inert gas differs drastically. Final Answer: all 'a', 'b' & 'c'.

Chemical Engineering Thermodynamics Questions