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GATE thermodynamics (ME): 5 practice questions with answers

By the PrepMatic team · Updated 9 Oct 2026 · 4 min read

Thermodynamics is the biggest part of the "Fluid Mechanics and Thermal Sciences" section of the GATE ME paper, which also covers heat transfer, power cycles, IC engines, refrigeration and air conditioning, and turbomachinery. Most thermodynamics questions are numerical and use only a few relations, so accuracy depends on applying the right law and keeping units straight. The five original questions below cover the first law, the second law, a power cycle, refrigeration and entropy.

What GATE tests in thermodynamics

The GATE 2027 ME paper lists Fluid Mechanics and Thermal Sciences as one section, and the syllabus was revised, so confirm your list on the official syllabus page. Thermodynamics is also a section in Engineering Sciences (XE). The standard content is properties of pure substances and ideal gases, the first and second laws for closed and open systems, entropy and availability, gas and vapour power cycles (Otto, Diesel, Brayton, Rankine), refrigeration cycles, and psychrometry.

Typical questions give a process or a cycle and ask for work, heat, entropy change, efficiency or COP, often with tabulated property data supplied. The real paper has MCQ, MSQ and NAT questions. All five below are MCQ.

Practice questions

Question 1

One kilogram of air (R = 0.287 kJ/kg K) expands isothermally and reversibly at 300 K from 1 MPa to 0.5 MPa. The work done by the air, in kJ, is:

• A. 25.9
• B. 43.0
• C. 59.7
• D. 86.1

Question 2

A heat engine receives 1000 kJ from a source at 800 K, rejects 600 kJ to a sink at 300 K and produces 400 kJ of work. The entropy generated in the process (source, engine and sink together), in kJ/K, is:

• A. 0.75
• B. 1.25
• C. 2.00
• D. 0

Question 3

An ideal air-standard Otto cycle has a compression ratio of 8 and γ = 1.4. Given that 8^0.4 = 2.297, the thermal efficiency is closest to:

• A. 43.5%
• B. 47.0%
• C. 52.0%
• D. 56.5%

Question 4

A Carnot refrigerator extracts 20 kW of heat from a cold space at 270 K and rejects heat to surroundings at 300 K. The power input required, in kW, is:

• A. 1.80
• B. 2.22
• C. 2.50
• D. 9.00

Question 5

One kilogram of air (cp = 1.005 kJ/kg K) is heated at constant pressure from 300 K to 600 K. Taking ln 2 = 0.693, the increase in specific entropy, in kJ/kg K, is closest to:

• A. 0.70
• B. 0.35
• C. 1.00
• D. 1.39

Answers and explanations

1. C. For a reversible isothermal process in an ideal gas, W = m R T ln(P1 / P2) = 1 × 0.287 × 300 × ln 2 = 86.1 × 0.693 = 59.7 kJ. Option D forgets the logarithm, option B halves it, and option A uses the base-10 logarithm.
2. A. The entropy lost by the source is 1000 / 800 = 1.25 kJ/K, and the sink gains 600 / 300 = 2.00 kJ/K. The net generation is 2.00 − 1.25 = 0.75 kJ/K, which is positive, so the engine is possible but irreversible. The Carnot limit for these temperatures would allow 62.5% efficiency, against the actual 40%.
3. D. The Otto efficiency is η = 1 − 1 / r^(γ−1) = 1 − 1 / 8^0.4 = 1 − 1 / 2.297 = 1 − 0.4353 = 0.5647, which is about 56.5%. Option A (43.5%) is the fraction of heat rejected, not the efficiency.
4. B. The Carnot COP of a refrigerator is Tc / (Th − Tc) = 270 / 30 = 9. The work input is the heat extracted divided by the COP: 20 / 9 = 2.22 kW. Option D is the COP itself. The heat rejected to the surroundings would be 20 + 2.22 = 22.22 kW.
5. A. For a constant-pressure process in an ideal gas with constant specific heat, Δs = cp ln(T2 / T1) = 1.005 × ln 2 = 1.005 × 0.693 = 0.697 kJ/kg K, which is about 0.70. Option D comes from using the temperature ratio of 4 by mistake.

How to prepare thermodynamics

• Write the first and second law for every problem before reading the numbers. Decide whether the system is closed or open, and whether the process is reversible, then pick the relation.
• Make an ideal-gas process table: isothermal, isobaric, isochoric, isentropic and polytropic, with work, heat and entropy change for each. Questions 1 and 5 above come straight from it.
• Practise reading steam tables quickly, including saturated and superheated regions, quality, and interpolation. Know how to find a state from two properties.
• Learn the cycle diagrams on T-s and P-v axes for Otto, Diesel, Brayton and Rankine, with efficiency formulas, and the effects of reheat, regeneration and intercooling.
• Know the second-law tests: Clausius inequality, entropy generation, Carnot limits, and the meaning of availability.
• Revise the psychrometric chart and refrigeration cycle COP calculations, including the vapour compression cycle on a P-h diagram.

Thermodynamics shares the thermal sciences section with fluid mechanics, and the same paper tests strength of materials in the applied mechanics section. The GATE mechanical preparation guide gives the subject order and book list, and the maths used here (logarithms and integration) is in the calculus practice page.

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