Question 1

Reference value in steam tables: What value is commonly assigned to the entropy of water at 0°C for the purpose of tabulation and calculations?

Accepted Answer

Introduction / Context: Thermodynamic property tables require a reference state because properties like internal energy and entropy are defined up to an arbitrary constant. For water/steam, a convenient reference is chosen to keep tabulated numbers manageable and consistent across texts and software. Given Data / Assumptions: Water considered at the reference state near 0°C. Consistency with common steam tables used in power-plant calculations. Absolute zero for entropy is not used in engineering tables. Concept / Approach: In many standard steam tables, the entropy of saturated liquid water at 0°C (or sometimes at the triple point) is assigned the reference value s = 0. This convention simplifies relative entropy values at other states. Only differences in entropy matter for most engineering computations, so the specific zero point is a matter of consistent convention rather than physics. Step-by-Step Solution: Recognize that entropy requires a reference: s_reference is arbitrarily set.For water at about 0°C, tables choose s = 0 for convenience.Hence, numerical entropy values elsewhere reflect changes from this baseline. Verification / Alternative check: Comparing different table sets reveals the same convention or clearly stated alternative references; computations of Δs are unaffected as long as a single consistent table is used. Why Other Options Are Wrong: 1, −1, 10: Arbitrary and not standard in steam tables. Common Pitfalls: Mixing tables with different reference states; expecting entropy to be “absolute” like temperature scales—only differences matter in engineering practice. Final Answer: 0

Question 2

First law at constant pressure (closed system): A gas mixture expands from 0.03 m^3 to 0.06 m^3 at a constant pressure of 1 MPa while absorbing 84 kJ of heat. Determine the change in internal energy ΔU.

Accepted Answer

Introduction / Context: For a closed system undergoing a quasi-equilibrium process at constant pressure, the first law of thermodynamics connects heat transfer, boundary work, and the change in internal energy. This problem reinforces correct work calculation and sign convention to obtain ΔU. Given Data / Assumptions: Constant pressure p = 1 MPa throughout the expansion. Initial volume V1 = 0.03 m^3, final volume V2 = 0.06 m^3. Heat added to the system Q = +84 kJ. Closed system; kinetic and potential energy changes are negligible. Concept / Approach: First law for a closed system: Q − W = ΔU, where W is boundary work. For a constant-pressure process, W = p * ΔV. Ensure consistent units (MPa·m^3 = kJ) and correct signs (work done by the system is positive, thus subtracted from Q to get ΔU). Step-by-Step Solution: Compute volume change: ΔV = V2 − V1 = 0.06 − 0.03 = 0.03 m^3.Calculate boundary work: W = p * ΔV = 1 MPa * 0.03 m^3 = 1,000 kPa * 0.03 m^3 = 30 kJ.Apply first law: ΔU = Q − W = 84 − 30 = 54 kJ. Verification / Alternative check: Unit check: 1 MPa·m^3 = 1,000 kPa·m^3 = 1,000 kN/m^2 * m^3 = 1,000 kN·m = 1,000 kJ/m^3 * m^3 → kJ, consistent. The positive ΔU indicates that not all added heat went into boundary work; internal energy increased. Why Other Options Are Wrong: 30 kJ: This is the boundary work, not ΔU. 84 kJ: Ignores work; would be correct only if ΔV = 0. 114 kJ: Sum of Q and W; violates first law sign convention. Common Pitfalls: Mixing sign conventions; forgetting that constant pressure work equals area under the p–V rectangle; unit mismatch between MPa and kJ. Final Answer: 54 kJ

Question 3

Gas laws identification: “The absolute pressure of a fixed mass of a perfect gas varies inversely with its volume at constant temperature.” Does this statement describe Charles’ law?

Accepted Answer

Introduction / Context: Several classical gas laws describe limiting relationships among p, V, and T. Correctly matching statements to their proper names avoids confusion in thermodynamics and fluid mechanics calculations. Given Data / Assumptions: Ideal gas behavior. Temperature held constant (isothermal condition) in the statement. Fixed mass of gas. Concept / Approach: The statement “pressure varies inversely with volume at constant temperature” is Boyle’s law, not Charles’ law. Charles’ law states that for a fixed mass at constant pressure, volume is directly proportional to absolute temperature (V ∝ T). Meanwhile, Gay-Lussac’s law states that at constant volume, pressure is proportional to temperature (p ∝ T). Recognizing which variable is held constant is the key to correct identification. Step-by-Step Solution: Identify condition: T constant ⇒ isothermal relation.Apply ideal gas law pV = nRT ⇒ with T constant, p ∝ 1/V → Boyle’s law.Therefore, the statement does not describe Charles’ law. Verification / Alternative check: Mnemonic: B (Boyle) links p and V; C (Charles) links V and T; G (Gay-Lussac) links p and T—each with the third variable constant. Why Other Options Are Wrong: Yes: Mislabels Boyle’s law as Charles’ law. Other qualifiers: Temperature or gas type limitations are irrelevant to the naming. Common Pitfalls: Swapping Boyle and Charles due to both being simple proportionality laws; forgetting which variable is constant in each statement. Final Answer: No

Question 4

Heating at constant volume (closed system gas): For a gas heated at constant volume from T1 to T2, which expression gives the heat supplied? (m = mass, cv = specific heat at constant volume, cp = specific heat at constant pressure, R = gas constant)

Accepted Answer

Introduction / Context: For closed systems undergoing heating with no boundary work, the first law reduces to a direct relation between heat transfer and change in internal energy. At constant volume, boundary work is zero, and the temperature rise translates to internal energy rise determined by cv. Given Data / Assumptions: Ideal or calorically perfect gas approximation. Volume held constant during the process (W = 0). Temperature increases from T1 to T2. Concept / Approach: First law for a closed system: Q − W = ΔU. At constant volume, W = ∫p dV = 0, so Q = ΔU. For an ideal gas, ΔU = m * cv * (T2 − T1). Therefore, the heat supplied equals mcv(T2 − T1). The cp formula applies to constant-pressure processes because enthalpy change ΔH = m * cp * (T2 − T1) equals Q at constant pressure (neglecting kinetic/potential changes). Step-by-Step Solution: Set W = 0 (constant volume).Use ΔU = m * cv * (T2 − T1) for an ideal gas.Therefore Q = ΔU = m * cv * (T2 − T1). Verification / Alternative check: Since enthalpy H = U + pV and pV changes with temperature at constant volume for ideal gases, cp is not the correct proportionality for Q at constant volume; cv is. Why Other Options Are Wrong: mR(T2 − T1): R relates cp and cv (cp − cv = R); not equal to Q at constant volume. mcp(T2 − T1) and mcp(T2 + T1): Apply to constant-pressure heating or are dimensionally or physically incorrect. Common Pitfalls: Confusing cp and cv; forgetting that boundary work vanishes at constant volume so heat equals internal energy change. Final Answer: mcv(T2 - T1)

Question 5

Isothermal process – what remains unchanged? In classical thermodynamics, an isothermal process is defined as a process that proceeds at constant temperature throughout. Which statement is always correct about an isothermal process (for any substanc…

Accepted Answer

Introduction / Context: An isothermal process is one of the classic thermodynamic paths, frequently contrasted with isobaric, isochoric, and adiabatic processes. Many students confuse what exactly must remain constant for isothermal behavior and what may depend on the working substance's equation of state (ideal gas versus real substance). This question clarifies the always-true feature of an isothermal process. Given Data / Assumptions: The term “isothermal” literally means constant temperature. No assumption is made that the working fluid is an ideal gas unless explicitly stated. Other properties like internal energy and enthalpy may or may not vary depending on the substance and path. Concept / Approach: By definition, an isothermal process maintains a constant temperature T from initial to final state. For an ideal gas, internal energy u and enthalpy h depend only on temperature; therefore, in that special case du = 0 and dh = 0 for isothermal changes. However, for real substances (e.g., liquids, vapors near saturation, non-ideal gases), u and h can change even if T is held fixed, because intermolecular effects may alter these properties with pressure or specific volume at constant temperature. Thus, the universally correct statement is the constancy of temperature, not necessarily of u or h. Step-by-Step Solution: Identify definition: isothermal ⇒ ΔT = 0 (this is always true).Consider ideal gas: u = u(T) and h = h(T) ⇒ if ΔT = 0, then Δu = 0 and Δh = 0 (only for ideal gas).Consider real fluids: u and h may vary with pressure and specific volume even when T is constant ⇒ Δu, Δh may not be zero.Therefore, the only statement guaranteed for any substance is “no change in temperature.” Verification / Alternative check: For water at fixed temperature near saturation, changing pressure at the same temperature (e.g., through phase proximity) can alter enthalpy and internal energy significantly, proving that Δh and Δu need not vanish in general isothermal processes. Why Other Options Are Wrong: No change in enthalpy / internal energy: True for ideal gases but not universally valid.All of these: Overgeneralizes ideal-gas behavior to all substances.None of these: Incorrect because temperature is indeed constant by definition. Common Pitfalls: Blindly applying ideal-gas results to real fluids; ignoring property dependence on variables other than temperature. Always check the substance model before asserting constancy of u or h. Final Answer: there is no change in temperature

Question 6

Temperature measurement – which law underpins thermometry? The operational definition and measurement of temperature with thermometers are fundamentally based on which law of thermodynamics?

Accepted Answer

Introduction / Context: Thermometers work because systems in thermal contact reach a common property that we call temperature. The conceptual foundation for comparing temperatures and building temperature scales is codified in a specific thermodynamic law. Identifying that law is crucial for understanding why “temperature” is a measurable property. Given Data / Assumptions: Three bodies A, B, and C can be placed in thermal contact or isolated. Thermal equilibrium means no net heat exchange when in contact. Practical thermometers rely on a property (e.g., expansion of mercury, resistance of a thermistor) that correlates monotonically with temperature in a calibrated range. Concept / Approach: The Zeroth law states: If A is in thermal equilibrium with B, and B is in thermal equilibrium with C, then A is in thermal equilibrium with C. This transitive property allows us to assign a numerical scale to temperature and to use a thermometer (system B) to compare the temperatures of other systems (A and C). Without the Zeroth law, “temperature” would lack a consistent operational meaning for measurement and comparison. Step-by-Step Solution: Recognize that thermometry requires a transitive equilibrium property.State the Zeroth law and its implication: existence of temperature as a property.Conclude that temperature measurement is based on the Zeroth law. Verification / Alternative check: Calibration procedures (e.g., ice point and steam point) assume transitivity: any thermometer in equilibrium with a standard point has a well-defined reading that transfers to other systems via thermal equilibrium. Why Other Options Are Wrong: First law: Energy conservation; does not define temperature scales.Second law: Direction of processes and entropy; informs absolute temperature but not basic comparability for measurement.Third law: Zero entropy at absolute zero; not the basis of routine thermometry.None of these: Incorrect, because the Zeroth law is precisely the foundation. Common Pitfalls: Confusing the absolute temperature scale (linked to the Second law) with the general measurability of temperature (Zeroth law). Final Answer: Zeroth law of thermodynamics

Question 7

Compression ratio – typical range for Diesel (compression-ignition) engines In automotive and stationary Diesel engines (compression-ignition), which of the following ranges best represents the usual geometric compression ratio?

Accepted Answer

Introduction / Context: Compression ratio strongly influences peak pressure, efficiency, and ignition characteristics of internal combustion engines. Diesel (compression-ignition) engines rely on high compression to raise air temperature sufficiently to auto-ignite injected fuel, so their compression ratios differ markedly from spark-ignition engines. Given Data / Assumptions: Compression ratio r = V_max / V_min in the cylinder. Typical modern Diesel engines operate with much higher r than gasoline Otto-cycle engines. We seek the broadly accepted range rather than a single value. Concept / Approach: Diesel engines commonly use r in the ballpark of 15–20 (sometimes slightly lower for turbocharged engines or as high as ~22 in some designs). Gasoline spark-ignition engines usually have r around 8–12. Extremely low ratios (3–8) are unrealistic for Diesel ignition and efficiency, while 20–30 is higher than standard automotive practice and can impose excessive mechanical and thermal stresses for many designs. Step-by-Step Solution: Recall Diesel ignition requires high compression temperature ⇒ r must be large.Compare candidate ranges with typical design data.Select 15 to 20 as the best-accepted common range. Verification / Alternative check: Manufacturer specifications for many Diesel engines (automotive and generators) list compression ratios in the mid-to-high teens, confirming the selection. Why Other Options Are Wrong: 3–6 or 5–8: Too low for compression ignition; more in line with early low-efficiency engines or not applicable.20–30: Above typical; while possible in special cases, it is not the usual range.8–12: Typical of modern gasoline engines, not Diesel. Common Pitfalls: Confusing boost pressure (turbocharging) with geometric compression ratio; boosting alters effective compression but not the geometric ratio r. Final Answer: 15 to 20

Question 8

Thermodynamic properties – classify intensive vs extensive A thermodynamic property is called intensive if, for a system subdivided into parts, the property value for the whole system __________ the sum of the property values for the individual part…

Accepted Answer

Introduction / Context: Knowing whether a property is intensive or extensive determines how it scales when systems are combined or subdivided. Correct classification is fundamental for material and energy balances and for understanding state equations and constitutive relations. Given Data / Assumptions: System can be partitioned into non-interacting, similar subsystems. Examples: temperature, pressure (intensive); mass, volume (extensive). “Additivity” refers to simple summation over parts. Concept / Approach: Extensive properties are additive: the total equals the sum over parts (e.g., V_total = ΣV_i). Intensive properties do not add upon combining subsystems; instead, they are uniformized by equilibrium (e.g., a common temperature or pressure). Therefore, an intensive property for the whole is not the sum of that property for the parts; it is defined independent of system size or amount of matter. Step-by-Step Solution: Recall definitions: extensive ⇒ additive; intensive ⇒ independent of size.Test examples: T_total ≠ T_1 + T_2; P_total ≠ P_1 + P_2.Conclude wording: an intensive property “is not equal to” the sum over parts. Verification / Alternative check: Specific properties (e.g., specific volume v = V/m) are intensive because ratio of two extensive properties removes size dependence; when two identical systems are combined, v remains the same, not doubled or summed. Why Other Options Are Wrong: Equal to / always twice / additive only for solids: Misstate the non-additive nature of intensive properties.Greater than or equal to: No general inequality of that form applies. Common Pitfalls: Confusing specific properties (intensive) with their corresponding totals (extensive). Remember that “specific,” “molar,” and “per unit mass” properties are typically intensive. Final Answer: is not equal to

Question 9

Fuels – composition of liquid fuels used in engines and burners Liquid fuels (such as gasoline, diesel, kerosene, and fuel oils) primarily consist of which class of chemical compounds?

Accepted Answer

Introduction / Context: Liquid fuels in energy and transportation are largely derived from petroleum. Understanding their chemical makeup is essential for combustion calculations, emissions analysis, and fuel handling. The question asks what class of compounds dominates common liquid fuels. Given Data / Assumptions: Typical fuels: gasoline (petrol), diesel, kerosene, jet fuel, heavy fuel oils. Crude oil refining produces mixtures spanning a range of carbon numbers. Trace additives (e.g., detergents, oxygenates) may be present but do not change the primary class. Concept / Approach: Petroleum-derived liquid fuels are predominantly hydrocarbons—compounds of hydrogen and carbon. Gasoline mainly contains C4–C12 alkanes, cycloalkanes, and aromatics; diesel and kerosene have heavier hydrocarbon fractions (C9–C20+). Oxygenates (e.g., ethanol, MTBE) may be blended, but the fundamental composition remains hydrocarbon-based. Step-by-Step Solution: Identify common fuels and their refinery origin.Recognize predominant molecules: alkanes, cycloalkanes, aromatics.Conclude: liquid fuels are primarily hydrocarbons. Verification / Alternative check: Fuel specifications (ASTM, EN) describe hydrocarbon ranges and properties (e.g., cetane number, octane rating), all premised on hydrocarbon chemistry. Why Other Options Are Wrong: Carbohydrates / metal oxides: Not fuel bases for petroleum liquids.“True/False” without a statement is ill-posed; the clear correct content is that fuels are hydrocarbons. Common Pitfalls: Overemphasizing additives (e.g., ethanol in E10) as the “primary” composition; hydrocarbons remain dominant in most liquid fuel blends. Final Answer: They are primarily hydrocarbons

Question 10

Free expansion (Joule expansion) – reversibility classification A free expansion of a gas (unrestrained expansion into vacuum; non-flow) is best classified as which type of process?

Accepted Answer

Introduction / Context: Free expansion (Joule expansion) is a classic thought experiment where a gas expands into an evacuated space without doing external work. It highlights the difference between energy conservation (First law) and process directionality (Second law), and is a standard example of an irreversible process. Given Data / Assumptions: Gas initially confined; a partition is removed allowing expansion into vacuum. No external pressure opposing the expansion; surroundings do no work. Insulated container → no heat transfer (adiabatic). Concept / Approach: From the First law for a closed, adiabatic system: ΔU = Q − W = 0 − 0 = 0 for an ideal gas (since external work W = 0 and Q = 0). However, the process is highly non-equilibrium and cannot be retraced without external agency, violating reversibility criteria. Entropy increases, so the Second law classifies it as irreversible. For an ideal gas, temperature remains constant (ΔT = 0) because ΔU = 0 and u = u(T); real gases may show slight temperature changes due to Joule effect, but irreversibility remains. Step-by-Step Solution: Set Q = 0 (insulated) and W = 0 (no opposing pressure) → ΔU = 0 (ideal gas).Recognize non-equilibrium path with finite pressure difference across partition.Entropy production > 0 indicates irreversibility.Conclude the correct classification is “irreversible.” Verification / Alternative check: Reversing free expansion would require compressing the gas, doing work on it and removing entropy—impossible without external intervention and compensation, confirming irreversibility. Why Other Options Are Wrong: Reversible / quasi-static: A huge pressure gradient prevents a sequence of equilibrium states.Isentropic, isobaric, polytropic with n = 1: Do not describe free expansion; pressure is undefined during the unrestrained expansion. Common Pitfalls: Assuming ΔU = 0 implies reversibility; energy conservation alone does not guarantee reversibility. Final Answer: irreversible

Question 11

Definition – specific heat at constant volume (cv) Which statement correctly defines the specific heat at constant volume, cv, for a gas?

Accepted Answer

Introduction / Context: Specific heats quantify how much heat is needed to change temperature under specified constraints. Distinguishing between cv and cp is fundamental for analyzing compression/expansion processes and for computing changes in internal energy and enthalpy of ideal gases. Given Data / Assumptions: Unit mass basis is used (per kilogram); molar versions exist but are not implied unless stated. Temperature change is one degree (e.g., 1 K). Constraint is either constant volume (cv) or constant pressure (cp). Concept / Approach: By definition, cv is the heat required per unit mass per degree temperature rise at constant volume, while cp is the analogous quantity at constant pressure. For an ideal gas, increments obey du = cv * dT and dh = cp * dT, and the difference cp − cv = R (per unit mass). The constraint matters because at constant pressure the system does boundary work as it expands, requiring more heat than at constant volume to achieve the same temperature rise (cp > cv for gases). Step-by-Step Solution: Identify that the question asks specifically for constant volume.Select the definition matching “unit mass, one degree, constant volume.”Confirm that other options either refer to cp or are unrelated. Verification / Alternative check: Thermodynamic tables list cv and cp separately; for air at room temperature, cv ≈ 0.718 kJ/kg·K and cp ≈ 1.005 kJ/kg·K, illustrating cp > cv. Why Other Options Are Wrong: Constant pressure and water-specific statements do not define cv on a per-mass-of-gas basis.“Any one of the above” is incorrect because only the constant-volume statement matches. Common Pitfalls: Mixing molar and mass-specific bases (cv,m vs cv); always check the basis and the path constraint. Final Answer: the amount of heat required to raise the temperature of unit mass of gas through one degree, at constant volume

Question 12

Systems vs processes – is “heating and expanding of a gas” a thermodynamic system? Consider the statement: “The heating and expanding of a gas is called a thermodynamic system.” Is this statement correct?

Accepted Answer

Introduction / Context: Thermodynamics distinguishes clearly between a system (the material or region under study) and a process (the transformation of the system from one state to another). This question tests that distinction by presenting a common misconception in wording. Given Data / Assumptions: A thermodynamic system is a specified quantity of matter or a region in space chosen for analysis. A process describes how the system changes state (e.g., heating, expansion, compression). Boundaries may be fixed or movable and may permit heat/work transfer. Concept / Approach: “Heating and expanding” describes actions or path characteristics, i.e., a process. The system would be “the gas within the cylinder” or “the control mass within the control volume.” Therefore, the statement mislabels a process as a system and is incorrect. Proper phrasing: “The gas in the cylinder is the thermodynamic system; it undergoes a heating and expansion process.” Step-by-Step Solution: Define system: specified matter or region (control mass or control volume).Define process: change of state (e.g., heating, expansion) experienced by the system.Identify that the statement uses process wording where system definition is required.Conclude the statement is incorrect. Verification / Alternative check: In PV diagrams, the path represents the process; the state point represents system state. Textbook examples consistently separate the object of study (system) from how it changes (process). Why Other Options Are Wrong: Any “Yes” variants confuse process with system; ideal-gas or isothermal qualifiers do not correct the category error. Common Pitfalls: Describing a device (e.g., “a turbine”) as a process; devices contain systems that undergo processes, but the categories must be kept distinct. Final Answer: No

Question 13

Kinetic theory – name the law for energy sharing among degrees of freedom The statement “The total energy of a molecule is shared equally among the various degrees of freedom it possesses” is known as which law?

Accepted Answer

Introduction / Context: In kinetic theory and statistical thermodynamics, the equipartition theorem links microscopic degrees of freedom to macroscopic thermodynamic quantities like specific heats. Recognizing the name of the law from its statement is a common conceptual check in exams. Given Data / Assumptions: Classical (high-temperature) limit where quantum effects are negligible for accessible modes. Degrees of freedom include translational, rotational, and (at sufficiently high T) vibrational modes. Each quadratic degree of freedom carries an average energy of (1/2) * k_B * T per molecule. Concept / Approach: The equipartition theorem (law of equipartition of energy) states that, at thermal equilibrium, energy is shared equally among all independent quadratic degrees of freedom. This explains, for example, why ideal monatomic gases have cv = (3/2) * R (per mole), while diatomic gases at moderate temperatures exhibit higher specific heats due to active rotational modes. Step-by-Step Solution: Identify the keyword “shared equally among degrees of freedom.”Associate with the equipartition theorem from kinetic theory.Select the named law accordingly. Verification / Alternative check: Measurements of specific heats versus temperature show plateaus corresponding to activation of additional modes (rotational, vibrational), broadly consistent with equipartition in the classical limit. Why Other Options Are Wrong: Conservation/degradation laws describe energy conservation and quality, not equal sharing among modes.Third law relates to entropy behavior near absolute zero, not energy partitioning. Common Pitfalls: Applying equipartition blindly at low temperatures where quantum freezing occurs; some degrees of freedom do not contribute fully to specific heat until sufficiently excited. Final Answer: law of equipartition of energy

Question 14

Air-standard cycles – alternate name for the Otto cycle In air-standard analysis, the Otto cycle (modeling spark-ignition engines) is also referred to as which of the following?

Accepted Answer

Introduction / Context: Air-standard cycles simplify internal combustion engine analysis by modeling heat addition and rejection as idealized processes. The Otto cycle is the canonical model for spark-ignition (SI) engines such as gasoline engines. Knowing its alternate descriptive name helps connect PV-diagram intuition with thermodynamic process labels. Given Data / Assumptions: Air-standard assumptions: working fluid is air with constant properties; combustion and exhaust are replaced by heat addition/removal. Compression and expansion are isentropic (adiabatic and reversible). Heat addition and heat rejection occur as idealized processes at either constant volume or constant pressure depending on the cycle. Concept / Approach: In the Otto cycle, heat addition occurs at constant volume (between the end of isentropic compression and the start of isentropic expansion), and heat rejection also occurs at constant volume. Therefore, the Otto cycle is often called the “constant volume cycle.” By contrast, the Diesel cycle features heat addition at constant pressure (“constant pressure cycle”), and the Brayton cycle has heat addition at (approximately) constant pressure in open systems like gas turbines (with different compression/expansion devices). Step-by-Step Solution: Identify the heat-addition process in the Otto cycle: constant volume.Note that heat rejection is also modeled at constant volume.Conclude that the alternate name is “constant volume cycle.” Verification / Alternative check: PV and TS diagrams for the Otto cycle show vertical heat-addition and heat-rejection lines on the PV diagram (volume fixed), confirming the constant-volume characterization. Why Other Options Are Wrong: Constant pressure cycle: Describes the Diesel cycle, not Otto.Constant temperature or constant enthalpy cycle: Not standard labels for reciprocating-engine cycles.Constant temperature and pressure: Physically inconsistent for finite heat addition in a closed cycle. Common Pitfalls: Confusing Otto and Diesel cycles due to real-engine combustion phasing; in the air-standard idealization, the distinction is strictly about the constraint during heat addition. Final Answer: constant volume cycle

Question 15

Polytropic process – expressing heat transfer in terms of work done For an ideal gas undergoing a polytropic process defined by p * v^n = constant, the heat absorbed (Q) during the process can be related to the work done (W) by which of the followin…

Accepted Answer

Introduction / Context: This question tests your understanding of energy transfer in a general polytropic process for an ideal gas. The goal is to connect the heat transfer Q to the mechanical work W using the polytropic index n and the specific-heat ratio gamma = cp/cv. Given Data / Assumptions: Ideal gas behavior with constant specific heats (cp, cv) and gamma = cp/cv. Process follows p * v^n = constant. Sign convention: positive W is work done by the system; Q is heat added to the system. Concept / Approach: Apply the first law of thermodynamics: Q = ΔU + W. For an ideal gas, ΔU = m * cv * (T2 - T1). In a polytropic process, the work can be written in temperature form, which allows elimination of temperature change and writing Q directly as a multiple of W. Step-by-Step Solution: Start with W = m * R * (T2 - T1) / (1 - n).Compute ΔU = m * cv * (T2 - T1) = m * R * (T2 - T1) / (gamma - 1).Use first law: Q = ΔU + W.Factor m * R * (T2 - T1) and combine: Q = m * R * (T2 - T1) * [1/(gamma - 1) + 1/(1 - n)].Relate to W: since W = m * R * (T2 - T1) / (1 - n), then Q = [(gamma - n) / (gamma - 1)] * W. Verification / Alternative check: Special cases: for n = 1 (isothermal), Q = (gamma - 1)/(gamma - 1) * W = W, which matches the isothermal ideal-gas result where ΔU = 0. For n = gamma (adiabatic), Q = 0 as expected. For n < gamma, Q is positive if W is positive (expansion with heat input). Why Other Options Are Wrong: [(gamma - 1)/(gamma - n)] * W: reciprocal of the correct factor; contradicts the first-law derivation. [(n - 1)/(gamma - 1)] * W: does not reduce correctly for isothermal or adiabatic limits. Independent of W: false; Q is proportional to W with a factor set by n and gamma. Q = 0 for any n ≠ 1: incorrect; only the adiabatic index n = gamma yields Q = 0. Common Pitfalls: Mixing sign conventions or using variable specific heats without noting that the closed-form factor assumes constant cp and cv. Final Answer: [(gamma - n) / (gamma - 1)] * W

Question 16

Thermodynamic process naming – constant-temperature transformation A process in which the temperature of the working substance remains strictly constant during expansion or compression is called:

Accepted Answer

Introduction / Context: Naming thermodynamic processes by the variable held constant is foundational. Here, the temperature remains constant while the system expands or compresses. Given Data / Assumptions: Temperature is maintained constant for the entire process. Working substance may be ideal gas for simple relations. Quasi-equilibrium path is implied for clear property relations. Concept / Approach: Isothermal means constant temperature. For an ideal gas, the equation of state gives p * v = constant at fixed T, which traces a rectangular hyperbola on a p–v diagram (hence sometimes termed a hyperbolic curve). Step-by-Step Solution: Identify the controlled variable: temperature remains constant.Relate to ideal-gas law: p * v = m * R * T = constant for fixed m and T.Conclude: the correct name is isothermal process. Verification / Alternative check: Work for an ideal-gas isothermal process: W = m * R * T * ln(V2/V1), consistent with constant T behavior. Why Other Options Are Wrong: Hyperbolic process: describes the p–v curve shape but does not explicitly state temperature constancy for non-ideal substances. Adiabatic: no heat transfer, temperature generally changes. Polytropic: general law p * v^n = constant; does not enforce constant T unless n = 1 for ideal gases. Isobaric: constant pressure, not constant temperature. Common Pitfalls: Assuming “hyperbolic” always means isothermal—even though many non-ideal behaviors deviate. Final Answer: isothermal process

Question 17

Fuel gas technology – correct method of producing producer gas Producer gas is obtained by which process among the following options?

Accepted Answer

Introduction / Context: Producer gas is a low-calorific-value fuel gas used historically for industrial heating and early engines. It is important to distinguish it from related gases such as water gas, Mond gas, and coke oven gas. Given Data / Assumptions: Solid carbonaceous fuel bed in a gas producer. Air (oxygen source) and steam as the gasifying agents. Operating bed at red-hot temperatures to drive endothermic/exothermic reactions. Concept / Approach: Producer gas results from partial oxidation and gasification: carbon reacts with limited oxygen to form CO and with steam to form CO and H2. The mixed air–steam blast moderates temperature and increases H2 content while maintaining a combustible CO–H2 mixture with N2 dilution. Step-by-Step Solution: Key reactions: C + 1/2 O2 → CO (exothermic); C + H2O → CO + H2 (endothermic).Air supplies O2 and contributes N2 (diluent), while steam boosts H2.The balanced operating point yields producer gas composition roughly rich in CO and H2 with significant N2.Hence, the correct production route is partial combustion with an air–steam blast. Verification / Alternative check: Contrast with water gas (steam only) and Mond gas (air plus large steam at lower temperature for ammonia recovery), and coke oven gas (from destructive distillation of bituminous coal). Why Other Options Are Wrong: Carbonisation makes coke oven gas, not producer gas. Steam over coke only makes water gas (CO + H2) without the characteristic N2 dilution. Mond process yields Mond gas with higher H2 and lower calorific value due to high N2 and added steam. Electrolysis/methanation is unrelated to producer gas. Common Pitfalls: Confusing names because all are CO–H2 mixtures; the oxidant (air vs steam) and operating temperature distinguish them. Final Answer: partial combustion of coal, coke, anthracite coal, or charcoal in a mixed air–steam blast

Question 18

Thermodynamic systems – definition of a closed system A closed system is one in which heat and work may cross the boundary, but the mass of the working substance does not cross the system boundary. Is this statement correct?

Accepted Answer

Introduction / Context: Identifying the correct type of thermodynamic system is essential for applying conservation laws. Systems are classified as closed, open, or isolated based on mass and energy exchange across the boundary. Given Data / Assumptions: System boundary is well defined. Energy can be transferred as heat and/or work. No mass transfer occurs across the boundary. Concept / Approach: A closed system (control mass) keeps its mass fixed, but energy exchange is allowed. An open system (control volume) allows mass, heat, and work to cross. An isolated system allows neither mass nor energy to cross. Step-by-Step Solution: State the definition of a closed system: mass is constant, heat and work may cross.Check boundary conditions: whether rigid or deformable, the classification depends on mass transfer, not on mechanical flexibility.Therefore the statement given is correct. Verification / Alternative check: Examples include a sealed piston–cylinder with moving piston (work crosses) and heated walls (heat crosses) but no mass leaves or enters. Why Other Options Are Wrong: “No”: contradicts the standard definition. Restrictions to ideal gases or rigid boundaries are unnecessary for the definition. “Heat cannot cross a closed boundary” describes an isolated system, not a closed one. Common Pitfalls: Confusing closed with isolated; the latter forbids energy transfer as well. Final Answer: Yes

Question 19

Free expansion (Joule experiment) – is it a constant enthalpy process? Assess the statement: “The free expansion process is a constant enthalpy (isenthalpic) process.”

Accepted Answer

Introduction / Context: Free expansion (Joule experiment) involves a gas expanding into a vacuum from an insulated container with no external work. It is often contrasted with throttling, which is an isenthalpic process. Given Data / Assumptions: Insulated system (adiabatic). No shaft work and no boundary work (expansion into vacuum). Real or ideal gas as working substance. Concept / Approach: First law for a closed, adiabatic system: ΔU = Q − W = 0 − 0 = 0, so internal energy remains constant. Enthalpy H = U + pV generally changes in free expansion because pV changes and there is no constraint keeping H constant. By contrast, throttling (flow through a restriction at steady state) satisfies h_in = h_out (constant specific enthalpy). Step-by-Step Solution: Identify process: free expansion into vacuum → Q = 0, W = 0.Apply first law (closed system): ΔU = 0.Conclude: U is constant, but H = U + pV need not be constant since p and V change.Therefore, the statement “constant enthalpy” is incorrect for free expansion (it is constant internal energy). Verification / Alternative check: For an ideal gas, U depends only on temperature, so ΔU = 0 implies ΔT = 0; hence ΔH = 0 as well. However, this special case does not make free expansion generally isenthalpic for real gases; the standard isenthalpic process is throttling. Why Other Options Are Wrong: “Correct”: conflates free expansion with throttling. “Correct only for throttling” (option d) actually describes a different process. Heat transfer is not present in free expansion; adding heat changes the process class. Common Pitfalls: Generalizing ideal-gas behavior to real-gas free expansions; real gases may change temperature even when ΔU = 0 due to intermolecular effects. Final Answer: Incorrect

Question 20

Process identification – law p * v^n = constant When expansion or compression follows the law p * v^n = C, the process is known as a:

Accepted Answer

Introduction / Context: Many real processes lie between isothermal and adiabatic extremes. The polytropic relation p * v^n = constant provides a flexible model with index n capturing heat transfer and non-idealities. Given Data / Assumptions: Quasi-equilibrium path for a compressible substance. n is constant during the process. Ideal-gas approximations often used for closed-form results. Concept / Approach: Special cases of the polytropic family include n = 1 (isothermal for ideal gases), n = gamma (adiabatic for ideal gases), and n → ∞ (isochoric). Thus, the general name for p * v^n = C is the polytropic process. Step-by-Step Solution: Recognize the given law p * v^n = C.Map n to special cases to confirm understanding.Select the general term: polytropic process. Verification / Alternative check: Work and heat expressions reduce correctly to isothermal and adiabatic forms when n takes the corresponding values. Why Other Options Are Wrong: Isothermal and adiabatic are specific cases within the polytropic family. Hyperbolic describes the curve shape for n = 1, not the general family. Isochoric keeps v constant, which is not the given law unless n → ∞. Common Pitfalls: Assuming a single value of n applies universally; n depends on heat transfer and process details. Final Answer: polytropic process

Thermodynamics Questions