Question 1

Relative mass comparison – O2 molecule vs. H atom By what factor is the mass of one molecule of oxygen (O2) greater than the mass of a single hydrogen atom (H)?

Accepted Answer

Introduction / Context: Quick mass ratios are handy in reaction stoichiometry and gas property calculations. Comparing molecular and atomic masses by simple factors builds intuition for molar mass and mixture behavior in thermodynamics and chemistry problems. Given Data / Assumptions: Atomic mass of hydrogen (H) ≈ 1 u (relative atomic mass scale). Atomic mass of oxygen (O) ≈ 16 u. Molecule considered: O2 (diatomic oxygen), so molecular mass ≈ 32 u. Concept / Approach: Since an O2 molecule consists of two oxygen atoms, its mass is roughly 2 * 16 u = 32 u. Dividing by the mass of a hydrogen atom (≈ 1 u) gives a factor of ≈ 32. This ratio is independent of unit system because it uses relative masses (dimensionless on the atomic scale). Step-by-Step Solution: Compute M_O2 = 2 * 16 = 32 u.Compute ratio r = M_O2 / M_H = 32 / 1.Hence r ≈ 32 → the O2 molecule is 32 times heavier than a hydrogen atom. Verification / Alternative check: Molar masses confirm the same ratio: 32 g/mol for O2 versus 1 g per mol of H atoms (or 2 g/mol for H2). The dimensionless factor remains 32 for O2 against H. Why Other Options Are Wrong: 12, 14, 16 confuse the atomic mass of oxygen or nitrogen with the diatomic molecular comparison; 2 would compare H2 to H, not O2 to H. Common Pitfalls: Mixing up atoms and molecules (e.g., comparing O atom to H atom would give 16, not 32). Always check whether the comparison is per atom or per molecule. Final Answer: 32

Question 2

Excess air in combustion – purpose and rationale To achieve complete and rapid combustion in practical burners and engines, should some air in excess of the theoretical (stoichiometric) requirement be supplied?

Accepted Answer

Introduction / Context: Stoichiometric air ensures exact oxygen for complete reaction with fuel. In real equipment, mixing limitations and diffusion constraints mean that theoretical air is often insufficient to guarantee complete burnout and acceptable emissions. This question addresses the engineering practice of providing excess air. Given Data / Assumptions: Practical combustors (boilers, furnaces, IC engines, burners). Finite mixing rates and non-uniformity of local fuel–air ratios. Desire for complete combustion (minimal CO, unburned hydrocarbons, soot). Concept / Approach: Excess air increases the availability of oxygen in regions where mixing is imperfect, promoting the final oxidation steps from CO to CO2 and from H2/HC to H2O and CO2. While too much excess air lowers flame temperature and thermal efficiency (due to nitrogen ballast and stack losses), a moderate percentage is standard practice to balance efficiency, stability, and emissions. Typical ranges vary by fuel and device (e.g., 5–10% for gas burners, higher for oil/solid fuels). Step-by-Step Solution: Determine theoretical air from stoichiometry.Account for mixing and residence time limitations in real flames.Add controlled excess air to ensure complete oxidation and stable operation. Verification / Alternative check: Flue-gas oxygen analyzers show residual O2 when excess air is used; CO and unburned HC drop as excess air rises from zero to an optimal value before efficiency penalties dominate. Why Other Options Are Wrong: “No” disregards real mixing constraints; categorical statements for specific fuels are incorrect since most systems benefit from some excess air.Claiming excess air reduces flame speed to zero is physically false; it modestly reduces temperature and speed but does not extinguish combustion unless extremely high. Common Pitfalls: Assuming more excess air is always better; too much raises stack losses and may cause instability. Optimal excess air is a controlled compromise. Final Answer: Yes

Question 3

Kelvin–Planck statement of the Second law According to the Kelvin–Planck statement, a perpetual motion machine of which kind is impossible?

Accepted Answer

Introduction / Context: The Second law of thermodynamics has several equivalent statements, including those of Kelvin–Planck and Clausius. Each rules out a class of perpetual motion machines (PMMs). Identifying which “kind” is prohibited by Kelvin–Planck clarifies what is fundamentally impossible for heat engines. Given Data / Assumptions: Heat engines exchange heat with reservoirs and produce work cyclically. Thermal reservoirs are at fixed temperatures. Perpetual motion refers to devices violating energy or entropy principles. Concept / Approach: The Kelvin–Planck statement: It is impossible to construct a device that operates in a cycle and produces no effect other than the extraction of heat from a single reservoir and the performance of an equivalent amount of work. This forbids a PMM of the second kind (PMM2). A PMM of the first kind violates the First law by creating energy from nothing; Kelvin–Planck addresses the Second law (directionality and quality of energy), not the First. Step-by-Step Solution: Define PMM2: engine claiming 100% conversion of heat from one reservoir to work.Link to Kelvin–Planck: explicitly rules out such a single-reservoir engine.Therefore, the impossible device per Kelvin–Planck is PMM of the second kind. Verification / Alternative check: Equivalence with the Clausius statement can be shown by contradiction: if either were violated, one could violate the other, confirming both prohibit PMM2 and spontaneous heat flow from cold to hot without compensation. Why Other Options Are Wrong: PMM1 pertains to First law violation; not the Kelvin–Planck formulation.Other “kinds” are nonstandard or irrelevant nomenclature. Common Pitfalls: Thinking “100% efficient heat engine” is allowed if perfectly designed; the Second law forbids it regardless of ingenuity. Final Answer: second kind

Question 4

Petroleum fractions – typical distillation range for kerosene In crude-oil fractional distillation, kerosene (paraffin) is generally drawn off within which approximate temperature range (cut points vary by crude and refinery practice)?

Accepted Answer

Introduction / Context: Refinery fractionation separates crude oil into products by boiling range. Knowing the approximate temperature windows helps map products to process units and end uses (e.g., gasoline, kerosene/jet, diesel/gasoil, vacuum gas oil, residue). This question asks for the typical kerosene cut range. Given Data / Assumptions: Simple atmospheric distillation column without deep conversion. Cut points depend on crude type and specifications (smoke point, freezing point, flash point, sulfur). Ranges are approximate and overlapping. Concept / Approach: Industry texts commonly place kerosene (jet/lighting kerosene) between the heavier end of naphtha and the lighter end of diesel/gasoil. While many refineries target ~150–300°C, a widely taught educational bracket places kerosene around 220–345°C in simplified question banks, distinguishing it clearly from lighter naphtha (below ~200°C) and heavier diesel (often starting ~250–350°C). Given the provided options, 220–345°C is the best match for the kerosene cut. Step-by-Step Solution: Identify lighter fraction (naphtha/gasoline) typically below ~200°C.Identify kerosene range between naphtha and diesel.Among the given brackets, select 220–345°C to represent kerosene. Verification / Alternative check: Jet fuel specifications (e.g., Jet A/kerosene-type) align with mid-distillate ranges overlapping ~150–300+°C; many curricula adopt a broader 220–345°C window to separate from gasoline and gasoils in MCQ contexts. Why Other Options Are Wrong: 65–220°C corresponds more to light naphtha through light kerosene transition and is commonly associated with gasoline and light kerosene overlaps.345–470°C and 470–550°C represent heavy gas oils and atmospheric residue ranges, not kerosene.20–80°C is too light (light ends) and not a kerosene cut. Common Pitfalls: Assuming fixed boundaries; in practice, refineries adjust cut points based on product slate and quality, but educational ranges remain useful approximations. Final Answer: 220° to 345°C

Question 5

Gas turbines – effects of a high air–fuel ratio on performance and hardware In a gas-turbine combustor, if the overall air–fuel ratio is made high (i.e., the mixture is lean with much more air than stoichiometric), which outcome is most characterist…

Accepted Answer

Introduction / Context: A key knob in gas-turbine operation is the overall air–fuel ratio. Most practical engines run very lean (large air–fuel ratio) to control turbine inlet temperature, meet emissions, and protect turbine blades. Understanding how this ratio influences temperatures, power, and efficiency is essential for gas-turbine performance analysis. Given Data / Assumptions: Simple Brayton cycle viewpoint with combustion at (approximately) constant pressure. High air–fuel ratio means excess air relative to stoichiometric requirements. Comparisons are qualitative for a fixed fuel flow unless noted. Concept / Approach: At constant fuel flow, adding more air dilutes the combustion products, lowering flame temperature and consequently reducing turbine inlet and exhaust temperatures. Lower gas temperatures at turbine exit also reduce available exhaust enthalpy. While component maps and control schedules complicate details, the first-order effect of going leaner is cooler gas at the turbine and in the exhaust. Step-by-Step Solution: Model combustion as a mixing/heat-release process at nearly constant pressure.Increase total mass flow of air for the same fuel → mixture temperature drops because the released chemical energy is shared by more mass.Lower turbine inlet temperature leads to lower exhaust temperature after expansion.Therefore, the outcome most consistently associated with a high air–fuel ratio is reduced exhaust temperature. Verification / Alternative check: Engine test data commonly show exhaust gas temperature (EGT) decreasing as mixture is leaned (within stable-combustion limits). Control systems often schedule extra air for blade life and emissions, aware of the EGT impact. Why Other Options Are Wrong: Improves thermal efficiency: not necessarily; efficiency depends on pressure ratio, component efficiencies, and firing temperature. Leaner mixtures alone do not guarantee higher cycle efficiency. Do not damage turbine blades: the intent is blade protection, but the statement is not a guaranteed outcome; damage depends on temperature, cooling, and materials. Increases power output / raises turbine inlet temperature: the opposite is typical when only air is increased for the same fuel flow. Common Pitfalls: Assuming any change in air always improves efficiency; in reality, cycle design and permissible firing temperature dominate efficiency trends. Final Answer: reduces exhaust temperature

Question 6

Process identification from p * v^n = C If a compressible system follows the law p * v^n = constant and the polytropic index n tends to infinity (n → ∞), then the process is effectively which type?

Accepted Answer

Introduction / Context: The generalized polytropic law p * v^n = constant unifies several familiar processes. Recognizing special values and limits of n helps identify the corresponding physical process (isothermal, adiabatic, isobaric, or isochoric). Given Data / Assumptions: Quasi-equilibrium compression/expansion so that state variables are well defined. Polytropic index n is constant during the process. Ideal-gas intuition may be used for interpretation, though the identification via limits is general. Concept / Approach: Important polytropic special cases: n = 1 → isothermal (for ideal gases), n = γ → reversible adiabatic, n = 0 → isobaric. The limit n → ∞ forces the volume to remain constant to keep p * v^n finite, representing an isochoric (constant volume) process. Step-by-Step Solution: Start with p * v^n = C.Let n grow very large. Any small change in v would make v^n blow up or vanish unless v is fixed.Thus, to satisfy the relation with finite C, v must remain constant, i.e., an isochoric process.Therefore, the correct identification is constant volume process. Verification / Alternative check: Graphically on a p–v diagram, as n increases, polytropes get steeper, approaching a vertical line (v = constant) in the limit n → ∞. Why Other Options Are Wrong: Adiabatic corresponds to n = γ, not n → ∞. Isothermal corresponds to n = 1 (ideal gas). Isobaric corresponds to n = 0. Free expansion has no defined p–v path satisfying a polytropic law. Common Pitfalls: Confusing the adiabatic value γ (about 1.3–1.67) with very large n; they have very different geometric interpretations. Final Answer: constant volume process

Question 7

Cycle comparison – dual (limited pressure) vs. Diesel cycle For the same compression ratio, the air-standard efficiency of the dual-combustion (limited-pressure) cycle is __________ that of the Diesel cycle.

Accepted Answer

Introduction / Context: The dual (limited-pressure) cycle splits heat addition between constant volume and constant pressure phases. Comparing it with the Diesel cycle (heat addition at constant pressure) for the same compression ratio reveals how the mode of heat addition affects air-standard efficiency. Given Data / Assumptions: Air-standard assumptions (ideal gas with constant specific heats, internally reversible compression/expansion). Same compression ratio for the cycles compared. Qualitative comparison over typical parameter ranges. Concept / Approach: For a given compression ratio, an Otto-like portion of constant-volume heat addition raises peak temperature more effectively per unit heat than constant-pressure addition. The dual cycle includes a constant-volume stage, so its efficiency lies between Otto (highest at given r) and Diesel (lower at given r). Thus, η_Otto > η_Dual > η_Diesel for the same compression ratio. Step-by-Step Solution: Recognize Diesel adds heat at constant pressure, resulting in more entropy generation for the same temperature rise.Dual cycle adds part of the heat at constant volume, improving thermal efficiency relative to Diesel.Therefore, at the same compression ratio, the dual cycle is more efficient than the Diesel cycle. Verification / Alternative check: Analytical expressions for η in terms of r, cutoff ratio, and pressure ratio confirm the ordering η_Otto > η_Dual > η_Diesel over practical parameter ranges. Why Other Options Are Wrong: Equal to / less than contradicts standard air-standard comparisons. “Indeterminate” ignores typical monotonic relations for standard parameter ranges. “Same as Otto” is false; Otto remains the upper bound at the same r. Common Pitfalls: Comparing at unequal parameters (e.g., same maximum pressure instead of same compression ratio) can change conclusions; always note the specified basis. Final Answer: greater than

Question 8

Flue-gas mass per kilogram of fuel – carbon balance method In ultimate analysis calculations, the mass of dry flue gas per kilogram of fuel can be expressed as the ratio of which two masses?

Accepted Answer

Introduction / Context: Determining the amount of flue gas generated per kilogram of fuel is a common step in combustion calculations. One reliable approach uses a carbon balance, because essentially all fuel carbon appears in the products as CO2 and CO (for complete combustion, almost all as CO2). Given Data / Assumptions: Dry flue gas basis (water vapour removed) is used. All carbon in the fuel exits in the dry flue gas as CO2 (and possibly CO if incomplete, but measured in analysis). Elemental conservation applies exactly: input carbon equals output carbon. Concept / Approach: If m_fg is the mass of dry flue gas per kg of fuel, and if (C_fuel) is the mass of carbon in 1 kg of fuel, while (C_per_kg_fg) is the mass of carbon present in 1 kg of dry flue gas (obtainable from gas analysis), then by carbon balance: C_fuel = m_fg * C_per_kg_fg, hence m_fg = C_fuel / C_per_kg_fg. Step-by-Step Solution: Define C_fuel = mass of C in 1 kg fuel (kg C/kg fuel).From gas analysis, find C_per_kg_fg (kg C/kg dry flue gas).Apply conservation: C_fuel = m_fg * C_per_kg_fg → m_fg = C_fuel / C_per_kg_fg.Recognize that this equals “mass of carbon in 1 kg of fuel” divided by “mass of carbon in 1 kg of flue gas.” Verification / Alternative check: An equivalent oxygen-balance approach is possible but is more sensitive to incomplete combustion and to moisture; the carbon balance on a dry basis is robust. Why Other Options Are Wrong: The oxygen-based ratios reverse numerator/denominator and are not generally used in this simple form. Using nitrogen from fuel is inappropriate because fuel-bound nitrogen is small and most nitrogen in products comes from air. Option (d) inverts the correct ratio, yielding m_fg inverse. Common Pitfalls: Mixing wet and dry gas bases or forgetting that nearly all nitrogen in flue gas originates from the oxidizer (air), not the fuel. Final Answer: mass of carbon in 1 kg of fuel to the mass of carbon in 1 kg of flue gas

Question 9

Closed vs. open Brayton cycles – efficiency trend Compared with an open-cycle gas turbine, a closed-cycle gas turbine generally delivers __________ thermal efficiency (for similar component efficiencies and pressure ratios).

Accepted Answer

Introduction / Context: Gas turbines can operate in open cycles (air in, exhaust out) or closed cycles (working fluid recirculates through external heat exchangers). The architecture affects recuperation potential, pressure losses, and temperature control, influencing overall efficiency. Given Data / Assumptions: Comparable pressure ratio and component efficiencies are assumed. Closed cycle allows effective heat recovery via recuperators and has controlled working-fluid properties (e.g., helium, air, CO2). Pressure losses on the intake/exhaust (open cycle) are not present in the same way for a closed loop. Concept / Approach: Closed cycles commonly incorporate high-effectiveness recuperation using stable mass flow and controlled temperatures, raising the average temperature of heat addition and lowering that of heat rejection relative to the open cycle. Thus, the thermal efficiency tends to be higher for similar hardware efficiencies. Step-by-Step Solution: Compare heat-addition profiles: closed cycle uses external heaters and recuperators to preheat the working fluid before main heating.Recognize reduced stack/exhaust losses in closed loops.Conclude higher efficiency for closed Brayton configurations under similar design constraints. Verification / Alternative check: Textbook Brayton-with-recuperation analyses show that recuperation increases thermal efficiency, and closed cycles facilitate high recuperator effectiveness due to consistent, clean working fluids. Why Other Options Are Wrong: “Lower” and “same” contradict well-known recuperated closed-cycle results. “Depends only on fuel” is false—cycle efficiency is primarily thermodynamic, not fuel dependent. “Zero” is nonsensical. Common Pitfalls: Confusing closed-cycle recuperation advantages with combined-cycle improvements; they are different concepts. Final Answer: higher

Question 10

Kinetic theory – ratio of rms speed to mean speed For an ideal gas at a given temperature, what is the ratio of root-mean-square molecular speed to average (mean) molecular speed?

Accepted Answer

Introduction / Context: Kinetic theory provides several characteristic molecular speeds for gases: most probable speed, mean (average) speed, and root-mean-square (rms) speed. Their ratios are constants independent of gas species at a fixed temperature. Given Data / Assumptions: Maxwell–Boltzmann speed distribution applies. Definitions: v_mp = most probable, v_avg = average, v_rms = root-mean-square. Ideal-gas behavior and continuum of speeds. Concept / Approach: The standard formulas are v_mp = sqrt(2RT/M), v_avg = sqrt(8RT/(pi M)), and v_rms = sqrt(3RT/M), where R is the universal gas constant and M is molar mass. The ratio v_rms/v_avg = sqrt(3RT/M) / sqrt(8RT/(pi M)) = sqrt(3*pi/8) ≈ 1.086. Step-by-Step Solution: Write v_avg = sqrt(8RT/(pi M)).Write v_rms = sqrt(3RT/M).Form the ratio: v_rms / v_avg = sqrt(3RT/M) / sqrt(8RT/(pi M)).Simplify: v_rms / v_avg = sqrt(3 * pi / 8) ≈ sqrt(1.1781) ≈ 1.086. Verification / Alternative check: Other useful ratios: v_avg/v_mp = sqrt(pi/2) ≈ 1.253 and v_rms/v_mp = sqrt(3/2) ≈ 1.225; these constants corroborate the internal consistency of Maxwellian statistics. Why Other Options Are Wrong: 0.086, 3.086, 4.086 are numerically inconsistent and dimensionless outliers. 0.913 would be the inverse of 1.095-ish, not the correct ratio here. Common Pitfalls: Confusing “most probable” with “average” or mixing unit systems; these ratios are dimensionless constants for the Maxwell distribution. Final Answer: 1.086

Question 11

First law of thermodynamics – what principle does it embody? Which conservation principle is expressed by the first law of thermodynamics for closed and open systems?

Accepted Answer

Introduction / Context: The first law of thermodynamics is the formal energy accounting rule for systems undergoing work and heat interactions. It generalizes the concept that energy can change form but the total amount is conserved. Given Data / Assumptions: Closed systems: ΔU = Q − W (sign convention: heat into the system positive, work by the system positive). Open systems (control volumes): steady-flow energy equation includes enthalpy, kinetic, and potential terms. No creation or destruction of energy occurs. Concept / Approach: The first law is a statement of conservation of energy. For closed systems it relates heat and work to changes in internal energy. For flowing systems it tracks energy transport with mass and across the boundary as shaft work and heat. Step-by-Step Solution: Identify energy forms: internal, kinetic, potential, flow work, and shaft work.Apply the first law: total energy entering − leaving equals the change in stored energy.Conclude that energy is conserved though converted among forms; it is never created or destroyed. Verification / Alternative check: Engineering energy balances (e.g., turbines, compressors, heat exchangers) directly implement the first law and predict performance consistent with energy conservation. Why Other Options Are Wrong: Conservation of mass and momentum are separate laws (continuity; Newton’s 2nd law control-volume form). “Conservation of heat” is incorrect; heat is energy in transit, not a conserved property. Entropy is not conserved; it is generated in irreversible processes (second law). Common Pitfalls: Confusing heat with internal energy; heat is a mode of transfer, while internal energy is a state property. Final Answer: conservation of energy

Question 12

Air-standard Otto cycle – efficiency formula in terms of compression ratio For an air-standard Otto cycle, the thermal efficiency is given by which of the following expressions (r = compression ratio, γ = cp/cv)?

Accepted Answer

Introduction / Context: The Otto cycle models spark-ignition engines with heat addition at constant volume. Its air-standard efficiency depends only on compression ratio and the specific-heat ratio under ideal assumptions. Given Data / Assumptions: Air-standard assumptions: ideal gas with constant specific heats, internally reversible compression/expansion. Compression ratio r = V1/V2. γ = cp/cv. Concept / Approach: The well-known result for the Otto cycle is η_Otto = 1 − 1 / r^(γ − 1). It shows that increasing compression ratio raises theoretical efficiency, with diminishing returns governed by γ. Step-by-Step Solution: Relate temperatures across isentropic compression: T2/T1 = r^(γ − 1).Relate temperatures across isentropic expansion similarly.Use η = 1 − (Q_out/Q_in) with constant-volume heat addition/removal proportional to temperature differences.Algebraic elimination yields η = 1 − 1 / r^(γ − 1). Verification / Alternative check: Limits: as r → 1, efficiency → 0; as r increases, η approaches 1. Real engines deviate due to dissociation, heat losses, and incomplete combustion. Why Other Options Are Wrong: “1 + r^(γ − 1)” and “r^(γ − 1) − 1” are dimensionless but not efficiency forms (and can exceed 1). “1 − r^(γ − 1)” becomes negative at typical r > 1. “1 − 1 / r^γ” uses the wrong exponent; the correct exponent is γ − 1. Common Pitfalls: Mistyping the exponent or forgetting that efficiency must lie between 0 and 1. Final Answer: 1 − 1 / r^(γ − 1)

Question 13

Second law (Clausius statement) – feasibility of heat transfer from cold to hot Evaluate the statement: “It is impossible to transfer heat from a body at a lower temperature to a body at a higher temperature without the aid of an external source.”

Accepted Answer

Introduction / Context: This is the Clausius statement of the second law of thermodynamics. It expresses the directionality of spontaneous heat flow and the necessity of external work (or equivalent agency) to move heat from cold to hot. Given Data / Assumptions: Thermal reservoirs at different temperatures. No external work or effect unless stated. Macroscopic, classical thermodynamic setting. Concept / Approach: Clausius statement: No process is possible whose sole result is the transfer of heat from a cooler to a hotter body. Refrigerators and heat pumps perform cold-to-hot transfer only by consuming external work, fully consistent with the statement. Step-by-Step Solution: Identify spontaneous direction: hot → cold.Recognize that reversing this direction requires an external agency doing work.Therefore the statement as written is correct. Verification / Alternative check: Coefficient-of-performance formulas for refrigerators explicitly include input work to move heat against the natural gradient, demonstrating compliance with the second law. Why Other Options Are Wrong: “Incorrect” and conditional variants contradict the second-law principle. “Happens spontaneously” is false; spontaneous heat flow is from hot to cold. Common Pitfalls: Confusing the descriptive possibility (refrigeration exists) with the prohibition (not without external aid). Final Answer: Correct

Question 14

Heating a gas at constant pressure – distribution of the supplied heat When a gas is heated at constant pressure (isobaric process), the supplied heat is used to accomplish which of the following?

Accepted Answer

Introduction / Context: Specific heats at constant pressure (cp) and constant volume (cv) differ because, at constant pressure, a portion of the heat input must push back the surroundings as the gas expands. This explains why cp > cv for ideal gases. Given Data / Assumptions: Ideal-gas model for clarity. Isobaric (constant-pressure) heating with a movable boundary (e.g., piston). No phase change occurs. Concept / Approach: First law for a quasi-static process: δQ = dU + δW. At constant pressure, δW = p dV. For an ideal gas, dU = m * cv * dT, and δQ = m * cp * dT, with cp = cv + R (per unit mass basis), showing that part of the heat goes into internal energy rise and part into boundary work. Step-by-Step Solution: Write δQ = dU + p dV.Use ideal-gas relation at constant p: p dV = m R dT.Relate internal energy change: dU = m cv dT.Thus δQ = m (cv dT + R dT) = m cp dT, where cp = cv + R.Interpretation: heat input raises internal energy and performs external work simultaneously. Verification / Alternative check: Calorimetry experiments consistently measure cp > cv, directly confirming that additional heat beyond dU is required to provide boundary work at constant pressure. Why Other Options Are Wrong: “Internal energy only” corresponds to constant-volume heating. “External work only” would imply dU = 0, which is false for temperature rise in a gas. “None” and “condensing” do not describe an isobaric heating of a gas. Common Pitfalls: Confusing heat (a path function) with internal energy (a state property). The split cp = cv + R captures the dual role of the heat input at constant pressure. Final Answer: increasing the internal energy of gas and also for doing some external work

Question 15

Thermodynamic Cycles – Check the Process Types Both the Ericsson cycle and the Joule (Brayton) cycle each contain two constant-pressure (isobaric) heat-transfer processes, used respectively for heat addition and heat rejection in their ideal represe…

Accepted Answer

Introduction / Context: Engineering thermodynamics uses ideal cycles to model real machines. The Ericsson and the Joule (Brayton) cycles are both gas-turbine–type cycles. A frequent point of confusion is which processes are isobaric, isentropic, or isothermal. This question asks whether both cycles include two constant-pressure processes. Understanding this helps with drawing correct p–v and T–s diagrams and applying the proper equations for work and heat. Given Data / Assumptions: Idealized cycles with negligible pressure losses in heat exchangers and ducts. Internally reversible compression and expansion unless otherwise noted. Perfect-gas behavior with nearly constant specific heats for introductory analysis. Concept / Approach: The ideal Joule (Brayton) cycle has two isentropic processes (compression in the compressor and expansion in the turbine) and two isobaric processes (heat addition in the combustor/heater and heat rejection in the cooler/exhaust). The ideal Ericsson cycle consists of two isothermal processes (compression at the low temperature and expansion at the high temperature) combined with two isobaric regenerative processes that transfer heat internally. Thus, in both cycles the heat-transfer segments occur at essentially constant pressure, justifying the statement. Step-by-Step Solution: Identify Joule (Brayton): compressor (isentropic), heater (isobaric), turbine (isentropic), cooler/exhaust (isobaric).Identify Ericsson: isothermal compression at T_L, isobaric regeneration heating, isothermal expansion at T_H, isobaric regeneration cooling.Count isobaric legs in each: two for Joule; two for Ericsson.Conclude the statement holds for both cycles under ideal assumptions. Verification / Alternative check: T–s diagrams show horizontal isobars for the heat-transfer portions in both cycles; the remaining legs are isentropic (Joule) or isothermal (Ericsson). Regeneration in Ericsson shifts heat between the two isobars and enables high efficiency when idealized. Why Other Options Are Wrong: “False because they are isothermal” confuses Ericsson’s isothermal legs with its additional isobaric legs; Joule is not isothermal. “True only for open cycles” is incorrect because closed versions also use isobaric heat exchangers. “True only if regeneration is used” is wrong since Joule does not require regeneration to have isobars. Common Pitfalls: Mixing up Ericsson with Stirling (which uses isochoric regeneration), or assuming all constant-pressure segments imply open-cycle combustion. Pressure losses in real heat exchangers modify but do not negate the ideal isobaric model. Final Answer: True

Question 16

Basic Chemistry – Select the Atomic (Relative Atomic) Mass of Sulphur Choose the standard atomic mass of sulphur used in stoichiometric calculations and periodic-table data.

Accepted Answer

Introduction / Context: Atomic (relative atomic) mass values are the foundation for stoichiometry, balancing chemical equations, and converting between moles and grams. The element sulphur, symbol S, commonly appears in combustion, environmental, and process-engineering problems. Knowing its standard atomic mass avoids calculation errors in mass and mole balances. Given Data / Assumptions: Atomic masses are expressed relative to carbon-12 = 12 exactly. Periodic-table values are averaged over natural isotopic abundances. Engineering calculations often round to convenient integers when suitable. Concept / Approach: The commonly used atomic mass for sulphur in introductory and engineering problems is approximately 32 (more precisely about 32.06). For stoichiometry involving compounds such as SO2, SO3, H2S, or sulphates, rounding to 32 is standard practice and provides sufficient accuracy for most educational exercises and preliminary design work. Step-by-Step Solution: Consult standard periodic-table data: sulphur’s atomic mass ≈ 32.06.Adopt the rounded value used in many textbooks: 32.Compare with the provided options; select 32.Use this value in molar-mass calculations (e.g., M_SO2 = 32 + 216 = 64). Verification / Alternative check: Look at common compounds: sulphuric acid H2SO4 has molar mass ≈ 21 + 32 + 4*16 = 98 g/mol, which aligns with the accepted atomic mass of sulphur near 32. Why Other Options Are Wrong: 12 is carbon, 14 is nitrogen, 16 is oxygen (atomic mass, not S), and 28 is silicon (approximate). Choosing any of these would cause large mole-balance errors. Common Pitfalls: Confusing atomic number (16 for S) with atomic mass (~32). Also, mixing isotope mass numbers (e.g., 32, 34) with the average atomic mass used for bulk natural sulphur. Final Answer: 32

Question 17

Heating a Gas at Constant Pressure – What Does the Supplied Heat Do? For a fixed mass of ideal gas heated at constant pressure (isobaric process), identify which effects always occur under the ideal-gas model.

Accepted Answer

Introduction / Context: Processes at constant pressure are common in heating ducts, boilers, and combustors. Under the ideal-gas assumption, understanding how heat input splits between raising temperature and doing boundary work clarifies energy accounting and helps prevent misconceptions in first-law applications. Given Data / Assumptions: Fixed mass of an ideal gas. Isobaric heating (p = constant). Quasi-equilibrium path with negligible kinetic/potential energy changes. Concept / Approach: For an ideal gas, enthalpy h depends only on temperature, so dh = Cp * dT. During isobaric heating, the gas expands as temperature rises (since p is fixed), performing boundary work W = ∫ p dV. The first law for a closed system gives δQ = dU + δW. Because temperature increases, both internal energy U (via Cv * dT) and enthalpy h rise; simultaneously, boundary work is positive. Among the options provided, the correct guaranteed outcomes are the temperature rise and the performance of external work, collectively listed in option (D). Step-by-Step Solution: At constant p, ideal gas relation gives V ∝ T → volume increases with heating.Boundary work: δW = p dV > 0 during expansion.Energy split: δQ = dU + δW with dU = m * Cv * dT and δW = p dV.Therefore, T increases and external work is done; option (D) is correct. Verification / Alternative check: Using enthalpy: δQ = dH for isobaric processes in closed systems with only p–V work, and dH = m * Cp * dT, which is positive; the accompanying expansion implies positive work. Why Other Options Are Wrong: (A) alone is incomplete; although U increases, the option does not acknowledge the simultaneous work. (E) claims no work, contradicting expansion at constant pressure. (B) or (C) alone omit the other inevitable effect. Common Pitfalls: Assuming δQ equals only temperature rise (forgetting work), or using Cv instead of Cp when analyzing isobaric heating. Also, confusing constant-pressure (p constant) with constant-volume (V constant) heating. Final Answer: Both (B) and (C)

Question 18

Feasibility of a Practical Carnot Engine – Statement Check Is it possible to construct and operate a real, practical engine that exactly follows the ideal, perfectly reversible Carnot cycle between two reservoirs?

Accepted Answer

Introduction / Context: The Carnot cycle defines the theoretical upper bound on efficiency for any heat engine operating between two fixed temperatures. It comprises perfectly reversible isothermal and adiabatic steps. This question probes whether such a cycle can be realized exactly in a real engine, not merely approximated. Given Data / Assumptions: Carnot cycle requires zero entropy generation (fully reversible processes). Heat transfer must occur with infinitesimal temperature differences. No pressure drops, no friction, no leakage, and perfectly slow (quasi-static) operation. Concept / Approach: Real devices inevitably have irreversibilities: mechanical friction, finite temperature gradients for practical heat transfer, fluid flow losses, valve and seal leakage, and finite-rate processes. Eliminating these entirely is impossible. While some laboratory setups can approach reversible behavior at vanishing power, an engine that exactly executes a Carnot cycle in finite time with finite power cannot exist. Therefore, the statement about making an engine working exactly on the Carnot cycle is judged impossible in practice, though it remains a useful ideal for benchmarking. Step-by-Step Solution: Define reversibility: process and surroundings are restored without net change; entropy generation equals zero.Note real heat transfer needs finite ΔT, causing positive entropy generation.Account for friction and fluid losses, which also produce entropy.Conclude exact Carnot execution is impossible in practice. Verification / Alternative check: Exergy analyses of any functioning engine show nonzero exergy destruction T0 * S_gen > 0. Only in the limit of infinitely slow, zero-power operation can processes approach reversibility—still not an exact, usable engine. Why Other Options Are Wrong: Claims of possibility (with exotic media or huge heat exchangers) overlook the requirement of zero entropy generation. “Zero power output” or “infinite exchangers” still do not yield an exact Carnot engine; they only approach it in limiting cases. Common Pitfalls: Confusing “approach Carnot efficiency” with “achieve Carnot exactly”; ignoring the power-efficiency trade-off in near-reversible operation. Final Answer: impossible

Question 19

Coal Technology – Definition Check for Coking Bituminous Coal A bituminous coal with carbon content in the range of about 78% to 81% is generally classified as coking bituminous coal suitable for producing metallurgical coke. Evaluate the statement.

Accepted Answer

Introduction / Context: Coking bituminous coal is the primary feedstock for metallurgical coke used in blast furnaces. Its classification depends on several quality metrics, among which fixed carbon percentage is a key indicator. The statement claims that 78–81% carbon content corresponds to coking bituminous coal. We assess this within typical industrial ranges and definitions used in fuel technology. Given Data / Assumptions: Bituminous rank with volatile matter and plasticity adequate for caking behavior. Carbon content discussed on a typical as-received or dry basis near standard lab conditions. Other quality parameters (ash, sulphur, moisture) assumed within acceptable metallurgical limits. Concept / Approach: Coking coals generally exhibit fixed carbon roughly from the upper 70s into the 80s percent range, along with appropriate volatile matter to soften, swell, and resolidify in the oven. A carbon range of 78–81% falls squarely within customary coking grades for many sources, provided detrimental impurities (e.g., sulphur) are controlled. Thus, the classification indicated is reasonable and widely used in educational and preliminary industrial contexts. Step-by-Step Solution: Identify rank: bituminous with caking properties (G index/FSI not explicitly given but implied acceptable).Compare carbon content: 78–81% aligns with common metallurgical coking specifications.Acknowledge that coke quality also depends on ash, sulphur, and petrographic composition.Conclude that the statement is acceptable in the sense of typical classification. Verification / Alternative check: Standard fuel-technology texts list bituminous coking coals with fixed carbon near 80% and volatile matter in mid ranges; high-temperature carbonisation yields hard coke when other contaminants are within limits. Why Other Options Are Wrong: Rejecting the statement outright ignores accepted ranges. Tying coking strictly to zero sulphur or extremely low ash is unrealistic; although low impurities are desired, moderate levels do not negate coking properties if other parameters qualify. Common Pitfalls: Confusing “coking” (ability to form coherent coke) with rank alone; assuming carbon percentage alone guarantees metallurgical suitability without considering ash fusion and reactivity indices. Final Answer: Agree

Question 20

Identify the Ideal Reversible Cycle – Process Combination A thermodynamic cycle composed of two isothermal processes and two isentropic (adiabatic, reversible) processes is known as the Carnot cycle. Choose the correct name for this cycle.

Accepted Answer

Introduction / Context: Recognizing cycles from their process makeup is a core skill for thermodynamics and heat-engine analysis. The Carnot cycle is the gold standard for maximum possible efficiency between two fixed temperatures, consisting of perfectly reversible legs only. This question tests identification based on process types. Given Data / Assumptions: Two isothermal processes (heat addition at T_H and heat rejection at T_L). Two isentropic processes (reversible adiabatic compression and expansion). Ideal reversible behavior with no entropy generation. Concept / Approach: Among classical cycles, only the Carnot cycle pairs isothermal legs with isentropic legs. The Stirling cycle uses isothermal plus constant-volume regenerative legs. The Ericsson cycle uses isothermal plus constant-pressure regenerative legs. The Joule (Brayton) cycle has isentropic legs with constant-pressure heat addition/rejection. Therefore, “two isothermal + two isentropic” uniquely identifies Carnot. Step-by-Step Solution: List process sets for candidate cycles.Match the given set (2 isothermal + 2 isentropic) with Carnot.Exclude others: Stirling (isochoric regen), Ericsson (isobaric regen), Joule (isobaric heat transfer).Confirm: Carnot is the only correct match. Verification / Alternative check: On a T–s diagram, Carnot appears as two horizontal lines (isotherms) connected by two vertical lines (isentropes). This geometric signature is unique among the classical textbook cycles. Why Other Options Are Wrong: Each alternative contains different non-isothermal heat-transfer legs or lacks isothermal processes entirely, disqualifying them from the given description. Common Pitfalls: Confusing Stirling and Ericsson because both can, in principle, approach Carnot efficiency with perfect regeneration, yet their process types differ from Carnot’s definition. Final Answer: Carnot cycle

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