Question 1

Polytropic processes – identify the hyperbolic (isothermal) case For a general polytropic process defined by p * v^n = C, the process is called hyperbolic when n equals which value?

Accepted Answer

Introduction / Context: Polytropic processes unify many familiar paths (isothermal, isentropic, isobaric, isochoric) under the relation p * v^n = constant. Recognizing special values of n helps quickly identify process type and apply the right formulas for work and heat. Given Data / Assumptions: Closed system with a simple compressible substance. Quasi-static process enabling state-variable relations. Ideal gas interpretation for the isothermal identification. Concept / Approach: When n = 1, the relation becomes p * v = constant, which plots as a rectangular hyperbola on the P–v plane. For an ideal gas, p * v = R * T, so n = 1 corresponds to constant temperature (isothermal). Other notable cases: n = 0 → isobaric; n → ∞ → isochoric; n = γ → isentropic (ideal gas). The term “hyperbolic” specifically refers to the n = 1 curve shape on P–v axes. Step-by-Step Solution: Start from p * v^n = C.Set n = 1 → p * v = C → rectangular hyperbola.Identify for ideal gas: p * v = R * T ⇒ T constant. Verification / Alternative check: P–v plots of isothermal ideal-gas compression/expansion show hyperbolic curves, matching the n = 1 polytropic case. Why Other Options Are Wrong: n = 0: isobaric; n = γ: isentropic; n → ∞: isochoric; n = −1 does not give the standard hyperbola shape used in this nomenclature. Common Pitfalls: Assuming “hyperbolic” means any curved line; here it specifically denotes p * v = constant. Final Answer: 1

Question 2

Air-standard efficiencies – comparing Otto, Diesel, and Dual cycles For the same compression ratio, where does the thermal efficiency of the Dual-combustion (mixed) cycle lie relative to the Otto and Diesel cycles?

Accepted Answer

Introduction / Context: Otto, Diesel, and Dual cycles differ by how heat is added: constant volume (Otto), constant pressure (Diesel), and a split of both (Dual). For a fixed compression ratio, their ideal thermal efficiencies rank predictably, informing engine design trade-offs and performance expectations. Given Data / Assumptions: Air-standard assumptions (ideal gas with constant properties). Same compression ratio across the compared cycles. No losses other than those intrinsic to the idealized models. Concept / Approach: At a given compression ratio, Otto has the highest efficiency because all heat is added at the smallest volume (highest temperature rise for a given heat input). Diesel has the lowest because heat addition continues while the piston moves, leading to larger mean volumes during heat addition. The Dual cycle splits heat addition; its efficiency therefore lies between those of Otto and Diesel. Hence: Otto > Dual > Diesel for the same compression ratio. Step-by-Step Solution: Fix compression ratio r for all three cycles.Compare heat-addition modes: volume-constant vs pressure-constant vs split.Infer ranking: η_Otto > η_Dual > η_Diesel. Verification / Alternative check: Textbook efficiency formulas confirm this ordering; numerical examples with typical cut-off ratios show Dual efficiencies strictly between Otto and Diesel at the same r. Why Other Options Are Wrong: Any claim placing Dual below Diesel or above Otto contradicts the heat-addition geometry and standard results. Common Pitfalls: Confusing compression ratio with cut-off ratio; changing the cut-off can shift Diesel/Dual efficiencies but not above Otto at the same compression ratio. Final Answer: greater than Diesel cycle and less than Otto cycle

Question 3

Gas turbines – effect of regeneration on performance In a Brayton (gas turbine) cycle equipped with an ideal regenerator of effectiveness greater than zero, which performance metric is primarily improved (for given pressure ratio and turbine/compres…

Accepted Answer

Introduction / Context: A regenerator (recuperator) transfers heat from the hot turbine exhaust to the compressed air before combustion. This internal heat recovery reduces external fuel input for the same turbine inlet temperature, affecting key cycle metrics of Brayton engines and stationary gas turbines. Given Data / Assumptions: Fixed pressure ratio, component efficiencies, and maximum temperature limit. Regenerator with nonzero effectiveness; pressure drops neglected for simplicity. Open or closed Brayton framework treated similarly for efficiency trends. Concept / Approach: By preheating the compressed air using exhaust heat, the required external heat addition in the combustor is reduced, increasing cycle thermal efficiency η_th = W_net / Q_in. The net work per unit mass flow (and thus work ratio) may change only slightly or even decrease when accounting for added pressure drops in real hardware, but the idealized primary benefit is higher thermal efficiency at moderate pressure ratios. Step-by-Step Solution: Recover exhaust heat via the regenerator.Lower fuel heat input Q_in for the same turbine inlet temperature.Since W_net is similar, η_th = W_net / Q_in increases. Verification / Alternative check: Brayton-cycle T–s diagrams with regeneration show a shorter external heat-addition segment; computed η_th rises markedly at low to medium pressure ratios. Why Other Options Are Wrong: Work ratio improvement is not guaranteed and may decline with real pressure drops.Pollution avoidance is not an intrinsic function of regeneration.“None” or “specific thrust only” do not describe the principal thermodynamic effect. Common Pitfalls: Assuming regeneration raises turbine work output; it primarily reduces required heat input, thereby boosting efficiency, not necessarily net work. Final Answer: thermal efficiency

Question 4

Classifying thermodynamic properties – which one is intensive? Select the property that is intensive (independent of the amount of substance) for a thermodynamic system.

Accepted Answer

Introduction / Context: Thermodynamic properties are categorized as intensive or extensive. This classification is fundamental for scaling analyses, mixture calculations, and formulating constitutive relations and equations of state. Given Data / Assumptions: System can be subdivided conceptually into parts. Properties may or may not scale with system size. We identify one property independent of system quantity. Concept / Approach: Intensive properties do not depend on the amount of matter (e.g., temperature, pressure, density). Extensive properties scale with size and are additive over subsystems (e.g., mass, volume, energy, entropy). When combining identical subsystems, intensive properties stay the same; extensive properties add. Step-by-Step Solution: Test each property for additivity when two identical systems are combined.Temperature remains unchanged (assuming equilibrium), hence intensive.Volume, mass, energy, and entropy double, hence extensive. Verification / Alternative check: Specific properties (e.g., specific volume v = V/m) are intensive, formed by the ratio of two extensive properties; temperature behaves similarly as a non-additive, equilibrium property. Why Other Options Are Wrong: Volume, mass, energy, and entropy are additive over parts; they increase with system size and are therefore extensive. Common Pitfalls: Confusing energy per unit mass (specific energy) with total energy; the former is intensive but the latter is extensive. Final Answer: Temperature

Question 5

Reference conditions in thermodynamics and gas laws The conditions of temperature and pressure equal to 0 °C (273 K) and 760 mm Hg are termed as ______ temperature and pressure.

Accepted Answer

Introduction / Context: Engineers and chemists often refer to specific “reference” conditions of temperature and pressure so that gas volumes, densities, and other properties can be compared consistently. In many classical textbooks and exam syllabi, the pair 0 °C (273 K) and 760 mm Hg (1 atm) is given a specific name that you are expected to recall correctly. Given Data / Assumptions: Temperature = 0 °C, i.e., 273 K. Pressure = 760 mm of mercury (approximately 1 atm = 101.325 kPa). Context is foundational thermodynamics and basic gas laws used in engineering education. Concept / Approach: Historically, two labels are used in practice: “NTP” (Normal Temperature and Pressure) and “STP” (Standard Temperature and Pressure). In many engineering and chemistry curricula, NTP corresponds to 0 °C and 1 atm. STP is sometimes defined the same way in older conventions, though modern standards may adopt slightly different pressure values. For this classical MCQ, 0 °C and 760 mm Hg aligns with the term “normal” temperature and pressure. Step-by-Step Solution: Identify temperature: 0 °C = 273 K.Identify pressure: 760 mm Hg ≈ 1 atm.Match with commonly taught term in basic gas-law problems: NTP = Normal Temperature and Pressure.Therefore fill the blank with “normal.” Verification / Alternative check: Typical gas-law examples compute molar volume at NTP using 22.4 L per g-mole at 0 °C and 1 atm, reinforcing the use of the “normal” label for these specific conditions in standard problems. Why Other Options Are Wrong: Standard: may also be used in some references, but within this conventional framing the expected term is “normal.” Reference laboratory / base-line: informal, not the canonical label. Saturated: relates to phase equilibrium (e.g., saturated steam), not ambient reference conditions. Common Pitfalls: Assuming “standard” must always be correct; exam conventions frequently reserve “normal” for 0 °C and 1 atm. Always read the exact pair of numbers and align with the commonly taught terminology for your syllabus. Final Answer: normal

Question 6

Manufacture of coke from coal – identifying the correct industrial process Coke is produced by which of the following methods?

Accepted Answer

Introduction / Context: Coke is a high-carbon, porous solid used in metallurgical operations such as blast furnaces. Understanding how coke is manufactured distinguishes it from other solid fuels and from charcoal or briquetted products. Given Data / Assumptions: Feedstock: bituminous coal (typically), although other ranks can be used. Process environment: absence of air (oxygen) to prevent combustion. Heating duration: approximately 42–48 hours in ovens (by-product or non-recovery types). Concept / Approach: Coking (destructive distillation) removes volatile matter by heating coal in an oxygen-free environment. Volatile by-products (tar, ammonia, gas) are distilled off, leaving a strong, carbon-rich residue called coke. The time and temperature profile are chosen to achieve the desired mechanical strength and porosity for metallurgical use. Step-by-Step Solution: Recognize that true coke production is carbonisation, not simple drying or pressing.Identify key condition: strong heating for many hours without air (destructive distillation).Match with the option specifying 42–48 hours in the absence of air.Select that option as the correct description of coking. Verification / Alternative check: By-product coke ovens (e.g., Otto-Hoffmann) operate with long coking times and recover gases and tars, aligning with the description of extended heating without oxygen. Why Other Options Are Wrong: Drying and pulverising: pre-processing, not coking. Moulding under pressure: produces briquettes; not coke. Heating wood with limited air: that yields charcoal, not coke from coal. Catalytic hydrogenation: relates to coal liquefaction, not solid coke manufacture. Common Pitfalls: Confusing coke (from coal) with charcoal (from wood) or briquettes (pressed fines with binders). The defining feature of coke is destructive distillation of coal in absence of air for extended periods. Final Answer: when coal is strongly heated continuously for 42 to 48 hours in the absence of air in a closed vessel

Question 7

Gas laws – heating a gas at constant pressure (Charles’s law) State whether the following is correct: “The heating of a gas at constant pressure is governed by Charles’s law.”

Accepted Answer

Introduction / Context: Elementary gas laws describe limiting behaviours of ideal gases under conditions where one macroscopic variable is held constant. When pressure is maintained constant, temperature and volume changes follow a specific proportionality known from Charles’s law. Given Data / Assumptions: Gas is modeled as ideal (perfect) in the temperature/pressure range of interest. Pressure remains constant during heating (isobaric process). Amount of gas is fixed (closed mass). Concept / Approach: Charles’s law states that for a fixed mass of an ideal gas at constant pressure, volume is directly proportional to absolute temperature: V ∝ T, or V/T = constant. This is the isobaric gas law and directly governs what happens when you heat a gas without allowing its pressure to change (e.g., a piston that moves freely to keep pressure constant). Step-by-Step Solution: Start with ideal-gas equation: pV = mRT.Hold p and mR constant → V = (mR/p) * T.This yields V/T = constant, which is Charles’s law.Thus, heating at constant pressure increases volume proportionally to temperature. Verification / Alternative check: On a V–T plot at constant pressure, data lie on a straight line. Practical demonstrations include heated air balloons or piston-cylinder experiments where the piston rises as temperature increases while pressure stays near ambient. Why Other Options Are Wrong: False or Boyle’s law: Boyle’s law is for constant temperature (pV = constant), not constant pressure. Restrictions to monatomic gases or near 0 °C: unnecessary within ideal-gas assumptions. Common Pitfalls: Using Celsius instead of kelvin; proportionality is linear only on an absolute temperature scale. Final Answer: True

Question 8

Heating a gas – which properties change? When a gas is heated (and constraints may vary), which of the following quantities can change as a result of the heating?

Accepted Answer

Introduction / Context: The response of a gas to heating depends on the boundary conditions. Gas properties are interrelated by the equation of state; therefore, changing energy content typically alters temperature and, depending on constraints, pressure and/or volume as well. Given Data / Assumptions: Ideal-gas model for clarity. Heating implies net energy input as heat. Different possible constraints: constant volume (isochoric), constant pressure (isobaric), or neither. Concept / Approach: Ideal-gas equation: pV = mRT. Heating raises internal energy and typically raises temperature. If the container volume is fixed, rising temperature increases pressure. If pressure is fixed (e.g., movable piston), rising temperature increases volume. If neither p nor V is constrained, both can change simultaneously under dynamic conditions. Step-by-Step Solution: Case 1 (constant V): Heat in → T increases → p = mRT/V increases.Case 2 (constant p): Heat in → T increases → V = mRT/p increases.Case 3 (general): Heat in → T increases; both p and V may adjust depending on mechanical constraints.Therefore, heating can change temperature, pressure, and volume. Verification / Alternative check: Calorimetry experiments show distinct specific heats: cv for constant-volume heating and cp for constant-pressure heating, confirming that different constraints lead to different property changes (pressure vs. volume). Why Other Options Are Wrong: Choosing only one variable ignores the variety of boundary conditions commonplace in practice. “None” is incorrect; heating necessarily changes at least temperature. Common Pitfalls: Assuming a single “law” covers all heating scenarios; always specify constraints before predicting which state variables change. Final Answer: all of these

Question 9

Ideal heat engine benchmark – identifying the four processes of the Carnot cycle Which set of processes correctly describes a complete Carnot cycle?

Accepted Answer

Introduction / Context: The Carnot cycle is the theoretical standard of heat-engine efficiency. It defines the maximum possible efficiency between two thermal reservoirs and serves as a benchmark for real cycles. Given Data / Assumptions: Two heat reservoirs at temperatures Th (hot) and Tc (cold). System (often an ideal gas) undergoing reversible processes. No irreversibilities (quasi-equilibrium, no friction, infinitesimal temperature differences for heat transfer). Concept / Approach: The Carnot cycle comprises four reversible processes: (1) isothermal expansion at Th while absorbing heat, (2) isentropic (adiabatic, reversible) expansion from Th to Tc, (3) isothermal compression at Tc while rejecting heat, and (4) isentropic compression back to the initial state. This combination ensures the highest efficiency possible between Th and Tc. Step-by-Step Solution: Identify heat addition at constant temperature → isothermal at Th.Follow with adiabatic reversible expansion → entropy constant.Compress isothermally at Tc to reject heat.Finish with adiabatic reversible compression to close the cycle. Verification / Alternative check: Efficiency expression η = 1 − Tc/Th derives directly from these steps, relying on the isothermal heat transfers and isentropic links that preserve reversibility and define temperature limits. Why Other Options Are Wrong: Constant-volume or constant-pressure pairs do not produce the Carnot efficiency relation. Mixed CP/CV sequences are characteristic of other idealized cycles (e.g., Otto, Diesel), not Carnot. Common Pitfalls: Equating “adiabatic” with “isentropic” without the reversibility qualifier; Carnot specifically requires reversible adiabats (isentropes). Final Answer: two isothermal and two isentropic processes

Question 10

Molar volume at NTP – volume occupied by 1 g-mole of an ideal gas At normal temperature and pressure (0 °C and 760 mm Hg), the molecular mass expressed in grams (1 g-mole) of an ideal gas occupies a volume of:

Accepted Answer

Introduction / Context: The concept of molar volume connects macroscopic gas volumes to the amount of substance. At widely used reference conditions (NTP/STP in classical teaching), the molar volume of an ideal gas takes a standard value that simplifies quick estimates. Given Data / Assumptions: NTP: T = 273 K, p ≈ 1 atm = 760 mm Hg. Ideal-gas behavior. Amount of substance = 1 g-mole (i.e., 1 mole when molecular mass is expressed in grams). Concept / Approach: From the ideal-gas law, V = nRT/p. Substituting n = 1 mol, R = 0.082057 L·atm/(mol·K), T = 273 K, and p = 1 atm gives V ≈ 22.4 L. This value is used pervasively in stoichiometry and gas-law problems at these reference conditions. Step-by-Step Solution: Write V = nRT/p.Insert n = 1, R = 0.082057 L·atm/(mol·K), T = 273 K, p = 1 atm.Compute V ≈ 0.082057 * 273 / 1 ≈ 22.4 L.Select 22.4 litres as the correct molar volume at NTP. Verification / Alternative check: Using S.I. units: R = 8.314 kJ/(kmol·K), p = 101.325 kPa, T = 273.15 K, yields V ≈ 22.414 m^3/kmol, i.e., 22.414 L/mol, consistent with 22.4 L for 1 mol. Why Other Options Are Wrong: 0.224 L and 2.24 L: off by factors of 100 and 10 respectively. 224 L: off by a factor of 10 too high. 11.2 L: corresponds to half a mole at NTP, not one mole. Common Pitfalls: Confusing updated metrological definitions of STP/NTP with the classical value used in many exam problems; unless otherwise specified, 22.4 L is expected. Final Answer: 22.4 litres

Question 11

Units and dimensions – identifying the S.I. unit of power Evaluate the statement: “The unit of power in S.I. units is kilowatt.”

Accepted Answer

Introduction / Context: Power, the rate of doing work or transferring energy, has a well-defined S.I. unit. While multiples such as kilowatt are in widespread use, the base S.I. unit must be identified correctly in examinations to avoid conceptual errors. Given Data / Assumptions: S.I. base and derived units are used. 1 watt = 1 joule per second. Multiples like kilowatt (kW) are allowed but are not the base unit. Concept / Approach: The S.I. derived unit of power is the watt (W). Kilowatt is a decimal multiple (1 kW = 1000 W). Statements that equate the S.I. unit itself to kilowatt are therefore inaccurate; the correct phrasing is “the S.I. unit is the watt.” Step-by-Step Solution: Recall definition: power P = dW/dt with unit J/s.1 W = 1 J/s = 1 N·m/s = 1 kg·m^2/s^3.Kilowatt is a multiple: 1 kW = 10^3 W.Hence the statement “unit is kilowatt” is false. Verification / Alternative check: Electrical nameplate ratings often list kW or MW for convenience, but standards (ISO, IEC) define the S.I. unit of power as the watt. Why Other Options Are Wrong: “True only for electrical systems” or “only for large machines”: the unit does not depend on application or magnitude. Option (e) contains the correct information but (a/b) asks truth value; the correct truth value is “False.” Common Pitfalls: Assuming commonly used multiples are the fundamental units. Always distinguish base/derived units from their decimal multiples. Final Answer: False

Question 12

Second law (Clausius statement) – heat transfer from cold to hot with external aid Identify the scientist associated with the statement: “Heat can flow from a colder body to a hotter body, but only with the aid of an external agency (input).”

Accepted Answer

Introduction / Context: The second law of thermodynamics has several equivalent formulations. The Clausius statement focuses on the direction of spontaneous heat transfer and the need for external work to move heat from cold to hot. Given Data / Assumptions: Macroscopic thermodynamics framework. Understanding of “external agency” as work input (e.g., refrigeration cycles). Equivalence between Clausius and Kelvin–Planck statements. Concept / Approach: The Clausius statement asserts: “It is impossible for a self-acting machine, unaided by any external agency, to transfer heat from a cooler body to a hotter body.” With external work input, such transfer is possible (as in refrigerators and heat pumps). Hence the attribution is to Rudolf Clausius. Step-by-Step Solution: Recognize the quoted idea: cold-to-hot requires external aid.Associate this with the Clausius formulation of the second law.Select “Clausius” as the correct scientist.Note: Kelvin–Planck version instead prohibits 100% conversion of heat to work in a cyclic heat engine. Verification / Alternative check: All refrigeration devices (vapour compression, absorption) consume work or high-grade energy specifically to move heat from a low-temperature region to a higher-temperature region, exemplifying the Clausius statement. Why Other Options Are Wrong: Kelvin: authored the Kelvin–Planck statement (heat engines), not the cold-to-hot transfer statement. Joule: established the mechanical equivalent of heat (first law), not directionality. Gay-Lussac: known for gas laws, not the second law statements. Carnot: analyzed ideal engine efficiency; did not state this form. Common Pitfalls: Mixing the two second-law statements; remember Clausius → refrigerators/heat pumps, Kelvin–Planck → heat engines. Final Answer: Clausius

Question 13

Boyle’s law – verifying the classical statement “The absolute pressure of a given mass of a perfect gas varies inversely as its volume when the temperature remains constant.” Is this the correct statement of Boyle’s law?

Accepted Answer

Introduction / Context: Boyle’s law is one of the foundational gas laws, describing how pressure and volume relate during isothermal (constant-temperature) transformations of a fixed mass of ideal gas. Given Data / Assumptions: Fixed amount of a perfect (ideal) gas. Temperature held constant. Quasi-equilibrium changes so the state equation applies continuously. Concept / Approach: For an ideal gas, pV = mRT. Holding T and m constant makes the right-hand side constant, so pV = constant. Therefore p ∝ 1/V (inverse proportionality), which is exactly the statement given. Step-by-Step Solution: Write ideal gas law: pV = mRT.Hold T constant and m fixed → pV = constant.Rearrange: p = constant / V → p varies inversely with V.Conclude: the statement given is the classical wording of Boyle’s law. Verification / Alternative check: p–V isotherms for ideal gases are rectangular hyperbolas. Experimental data for many gases at modest pressures approximate this behaviour, validating Boyle’s law as a limiting relation. Why Other Options Are Wrong: “No” and conditional variants contradict the ideal-gas model where the law holds regardless of gas type at low to moderate pressures. Referencing Charles’s law is incorrect; that pertains to V ∝ T at constant pressure. Common Pitfalls: Using gauge pressure instead of absolute; gas laws require absolute pressure and temperature for correct proportionalities. Final Answer: Yes

Question 14

Basic chemical terminology – smallest independently existing, chemically recognizable unit The smallest quantity of a substance that can exist by itself in a chemically recognizable form is called a:

Accepted Answer

Introduction / Context: Precise terminology in chemistry underpins stoichiometry and material characterization. The question asks for the smallest amount of a substance that, by itself, preserves the substance’s chemical identity in composition and properties. Given Data / Assumptions: The unit must “exist by itself,” i.e., as a discrete entity. It must be “chemically recognizable,” meaning it exhibits the substance’s characteristic composition and bonding. Applies to covalently bonded substances and also to diatomic elements in their natural form. Concept / Approach: A molecule is a discrete aggregate of atoms held together by chemical bonds that represents the smallest particle of a pure substance (elemental or compound) capable of independent existence while retaining its chemical properties. An atom by itself may or may not represent the substance’s standard form (e.g., oxygen exists as O2 molecules in nature). Elements/compounds are bulk classifications, not smallest units. Step-by-Step Solution: Identify the requirement of independent existence: points to a bonded unit rather than an abstract formula unit.Ensure chemical recognizability: composition and structure correspond to the substance (e.g., H2O molecule for water).Therefore, “molecule” fits the definition best.Note: for ionic solids, the basic repeating unit is a formula unit in a lattice, but as a discrete “by itself” entity, we still refer to molecules for molecular substances. Verification / Alternative check: Diatomic elemental gases (H2, N2, O2, Cl2) demonstrate that the recognizable chemical form is molecular, not atomic, under standard conditions. Why Other Options Are Wrong: Element: a class of atoms with the same atomic number; not a discrete smallest particle. Compound: a substance composed of two or more elements; again not the smallest particle. Atom: for many substances this does not represent the stable independently existing form (e.g., O atoms do not persist as free entities at STP). Radical: a reactive group; not generally stable by itself nor representative of the complete substance. Common Pitfalls: Equating “atom” with smallest unit universally; while true in a physical sense, the question emphasizes chemically recognizable and independently existing form, which is a molecule for molecular substances. Final Answer: molecule

Question 15

Air-Standard Otto Cycle – Process Composition and Idealization The ideal Otto cycle (spark-ignition engine model) consists of four internally reversible processes: two constant-volume heat-transfer processes (isochoric heat addition and isochoric he…

Accepted Answer

Introduction / Context: The Otto cycle is the standard air-standard model for spark-ignition (SI) engines. Knowing the exact sequence of idealized processes helps in deriving thermal efficiency, mean effective pressure, and the effects of compression ratio on performance. Given Data / Assumptions: Air-standard assumptions (ideal gas with constant specific heats). Internally reversible processes (no friction or pressure losses). Heat addition and rejection are idealized to occur at constant volume. Concept / Approach: The four processes are: isentropic compression, constant-volume heat addition, isentropic expansion, and constant-volume heat rejection. This pairing (CV + isentropic) is distinctive and differentiates Otto from Diesel (which has constant-pressure addition) and from Dual cycles (mixed CP and CV addition). Step-by-Step Solution: List processes: 1–2 isentropic compression; 2–3 constant-volume heat addition; 3–4 isentropic expansion; 4–1 constant-volume heat rejection.Confirm there are exactly two isentropic and two constant-volume steps.Recognize no isothermal or constant-pressure segments exist in the ideal Otto model.Hence, the correct description is 'two constant volume and two isentropic processes'. Verification / Alternative check: Typical p-v and T-s diagrams show vertical lines (CV) and adiabatic curves (isentropic) for the Otto cycle. Thermal efficiency derived from this sequence depends only on compression ratio and gamma, matching textbook results. Why Other Options Are Wrong: Constant-pressure segments belong to Diesel/Ericsson/Brayton; isothermal segments belong to Carnot/Stirling, not Otto. Mixed CP/CV with two isentropics describes the Dual cycle, not Otto. Common Pitfalls: Confusing real engine valve events with idealized heat-transfer steps; thinking isothermal appears in SI cycle models (it does not in Otto). Final Answer: two constant volume and two isentropic processes

Question 16

Gas Heating at Constant Volume – Identify the Governing Law When a fixed mass of gas is heated in a rigid container (volume held constant), the pressure varies directly with absolute temperature according to Gay-Lussac's law (also called Amontons' l…

Accepted Answer

Introduction / Context: Classical gas laws describe limiting cases of the ideal-gas equation. For safety and design of rigid vessels, we need the law that links pressure and temperature at constant volume. Given Data / Assumptions: Fixed mass of gas. Constant volume (rigid container). Ideal-gas behavior near the operating state. Concept / Approach: The ideal-gas equation pV = m R T reduces to p ∝ T when V and m are constant. This direct proportionality is historically named Gay-Lussac's (or Amontons') law, whereas Boyle's law applies at constant temperature (p ∝ 1/V) and Charles' law at constant pressure (V ∝ T). Step-by-Step Solution: Start from pV = m R T.At constant V and m, rearrange to p/T = constant.Hence pressure changes linearly with absolute temperature: p2/p1 = T2/T1.Identify this as Gay-Lussac's law (Amontons' law). Verification / Alternative check: Manometer or transducer readings in a heated rigid tank follow p ∝ T_K, confirming this law for gases near ideal behavior. Why Other Options Are Wrong: Boyle: constant temperature case; Charles: constant pressure case; Avogadro: equal volumes have equal moles at same p and T; Dalton: total pressure is sum of partial pressures in mixtures. Common Pitfalls: Using Celsius instead of Kelvin; mislabeling Charles and Gay-Lussac; assuming non-ideal effects negate the linear trend over small ranges (they typically do not). Final Answer: Gay-Lussac law

Question 17

Closed-Cycle Gas Turbine – Cooling in the Cooler (Heat Rejection) In a closed Brayton (closed-cycle gas turbine), the working fluid is cooled at essentially constant pressure in the cooler/heat exchanger before returning to the compressor.

Accepted Answer

Introduction / Context: Closed-cycle gas turbines recirculate a working fluid (often helium, nitrogen, or air). Understanding where heat is added and rejected and under what idealized conditions is crucial for modeling performance and sizing heat exchangers. Given Data / Assumptions: Closed Brayton loop with compressor, heater, turbine, and cooler. Pressure drops in heat exchangers are neglected in the ideal model. Steady-state, steady-flow operation. Concept / Approach: The ideal Brayton (open or closed) has two constant-pressure heat-transfer processes: heat addition in the heater/combustor and heat rejection in the cooler. The other two processes (across compressor and turbine) are ideally isentropic. Therefore, the cooler removes heat at nearly constant pressure, returning the fluid to the compressor inlet state along the low-pressure line of the p-v or T-s diagram. Step-by-Step Solution: Identify components: compressor → heater → turbine → cooler → compressor.Idealize heat exchangers as isobaric: dp ≈ 0, so p ≈ constant.Conclude that cooling occurs at constant pressure in the cooler.Use this to compute Q_out via m * Cp * (T_out − T_in) on the low-pressure side. Verification / Alternative check: T-s diagrams of the Brayton cycle show horizontal lines (isobars) during heat addition and rejection. Small real pressure losses do not change the fundamental classification. Why Other Options Are Wrong: Constant volume applies to Otto/Stirling isochores; constant temperature is for Carnot/Stirling isotherms; 'none' is incorrect given the standard Brayton idealization. Common Pitfalls: Confusing open vs. closed cycles; assuming exhaust to atmosphere implies open cycle (closed cycles reject heat in a cooler, not to free atmosphere directly). Final Answer: constant pressure

Question 18

Perpetual Motion of the First Kind (PMM-1) – First-Law Feasibility A machine that produces net work without any energy input (violates energy conservation) is called a PMM-1 and is impossible according to the First Law of Thermodynamics.

Accepted Answer

Introduction / Context: Thermodynamics classifies hypothetical perpetual-motion machines by which law they violate. PMM-1 devices claim to create energy from nothing. Identifying their impossibility strengthens understanding of energy conservation. Given Data / Assumptions: Closed system or cycle allegedly delivering net work output. No heat or other energy input from surroundings. Classical macroscopic thermodynamics. Concept / Approach: The First Law states ΔE = Q − W for a cycle, where ΔE = 0. Therefore, for a device producing work W > 0 in a cycle, a compensating heat input Q = W must be supplied. A PMM-1 claims W > 0 while Q = 0, which contradicts ΔE = 0 and violates energy conservation. Step-by-Step Solution: For a cycle, set ΔE = 0.Apply the First Law: 0 = Q − W → Q = W.If Q = 0 but W > 0, the equality is broken.Hence, PMM-1 cannot exist; it is impossible. Verification / Alternative check: No experimental evidence has ever demonstrated PMM-1; all verified engines obey Q_in ≥ W_out over a cycle with residual losses. Why Other Options Are Wrong: Superconductivity or zero friction reduce losses but do not create energy. Ambient temperature does not circumvent conservation of energy. Common Pitfalls: Confusing PMM-1 with PMM-2 (which violates the Second Law). Believing lossless components alone enable perpetual work output. Final Answer: impossible

Question 19

Meaning of Entropy Increase – What Does It Signify? An increase in the entropy of a system (or universe) represents degradation of energy quality and a reduction in the maximum useful work (availability/exergy) obtainable.

Accepted Answer

Introduction / Context: Entropy is a measure of energy dispersion and irreversibility. When entropy increases, less of the system's energy can be converted into useful work. Understanding this connection is vital in power-plant, refrigeration, and process design. Given Data / Assumptions: Second-law framework with system and surroundings. Availability/exergy defined relative to an environment state. Irreversibilities generate entropy and destroy exergy. Concept / Approach: Entropy generation S_gen > 0 accompanies friction, mixing, unrestrained expansion, finite-ΔT heat transfer, and chemical irreversibility. Exergy destruction is T0 * S_gen (per unit time or process), where T0 is ambient temperature. Thus, higher entropy implies lower capacity to do work, i.e., degraded energy quality. Step-by-Step Solution: State second law: ΔS_universe = S_gen ≥ 0.Relate exergy loss to entropy generation: X_dest = T0 * S_gen.Interpret physically: more disorder/dispersion → less extractable work.Conclude: entropy increase represents energy degradation (lower availability). Verification / Alternative check: Turbine with high irreversibility yields larger S_gen and lower actual work versus isentropic ideal; heat exchanger with large temperature differences generates entropy and reduces potential to do work. Why Other Options Are Wrong: Availability does not increase with entropy; temperature/pressure changes are not direct indicators of entropy sign; potential energy is unrelated to entropy definition. Common Pitfalls: Equating entropy strictly with 'disorder' without linking to work potential; assuming any temperature rise means entropy rise (not necessarily true). Final Answer: degradation of energy

Question 20

Stoichiometry of Carbon Combustion – Mass Ratios for Complete Oxidation One kilogram of carbon requires 8/3 kg of oxygen for complete combustion and produces 11/3 kg of carbon dioxide: C + O2 → CO2.

Accepted Answer

Introduction / Context: Accurate stoichiometric ratios are essential for combustion calculations, flue-gas analysis, and sizing of air-fuel systems. The carbon–oxygen reaction to form carbon dioxide is a fundamental example. Given Data / Assumptions: Chemical reaction: C + O2 → CO2 (complete combustion, no CO formation). Molar masses: M_C = 12 kg/kmol, M_O2 = 32 kg/kmol, M_CO2 = 44 kg/kmol. Idealized, complete oxidation with no side reactions. Concept / Approach: Mass conservation across the balanced equation yields fixed mass ratios. For each 12 kg of C, 32 kg of O2 are required, and 44 kg of CO2 are produced. Scaling to 1 kg of C gives oxygen requirement 32/12 = 8/3 kg and CO2 produced 44/12 = 11/3 kg. Step-by-Step Solution: Write balanced reaction: C + O2 → CO2.Use molar masses: 12 kg C reacts with 32 kg O2 → 44 kg CO2.Scale per kg of C: O2 needed = 32/12 = 8/3 kg.CO2 formed = 44/12 = 11/3 kg. Verification / Alternative check: Elemental balance on C and O confirms stoichiometry. Flue-gas analyzers would measure CO2 consistent with these ratios under ideal complete combustion. Why Other Options Are Wrong: Pressure, oxygen purity, or air humidity do not change the stoichiometric mass ratios; they affect kinetics or dilution, not the balanced-equation proportions. Common Pitfalls: Confusing air requirement with oxygen requirement; neglecting possible CO formation under oxygen-deficient conditions (not considered here). Final Answer: Agree

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