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Thermodynamics: board exam questions with solutions

On the ECE exam under General Engineering and Applied Sciences (GEAS) and the REE exam under Engineering Sciences and Allied Subjects (ESAS). Try each question before you open its solution, then practise with fresh numbers below: 2 computed question types on this topic.

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Questions

1. Express 25 °C in kelvin.

  1. 248.15 K
  2. 77 K
  3. 25 K
  4. 298.15 K
Show the answer and solution

Answer: D. 298.15 K

T(K) = T(°C) + 273.15 = 298.15 K.

2. What is the maximum (Carnot) efficiency of a heat engine operating between 527 °C and 27 °C?

  1. 62.5%
  2. 94.9%
  3. 37.5%
  4. 51.2%
Show the answer and solution

Answer: A. 62.5%

η = 1 − T_C/T_H = 1 − 300/800 = 0.625 = 62.5%. Using Celsius gives the wrong 94.9%.

3. How much heat raises 2 kg of water from 20 °C to 80 °C? (c = 4.186 kJ/kg·K)

  1. 251.2 kJ
  2. 502.3 kJ
  3. 669.8 kJ
  4. 837.2 kJ
Show the answer and solution

Answer: B. 502.3 kJ

Q = mcΔT = 2 × 4.186 × 60 = 502.3 kJ.

4. One mole of ideal gas expands isothermally and reversibly at 300 K to twice its volume. How much work does it do?

  1. 2.49 kJ
  2. 0.75 kJ
  3. 3.46 kJ
  4. 1.73 kJ
Show the answer and solution

Answer: D. 1.73 kJ

W = nRT ln(V₂/V₁) = 1 × 8.314 × 300 × ln 2 = 1729 J ≈ 1.73 kJ.

5. Which equation states the first law of thermodynamics for a closed system, with W as the work done BY the system?

  1. ΔU = Q + W
  2. ΔU = Q − W
  3. Q = W
  4. ΔS = Q/T
Show the answer and solution

Answer: B. ΔU = Q − W

Energy is conserved: the change in internal energy equals the heat added minus the work done by the system.

6. What is the Carnot coefficient of performance of a refrigerator working between −5 °C and 35 °C?

  1. 7.70
  2. 0.87
  3. 6.70
  4. 0.15
Show the answer and solution

Answer: C. 6.70

COP_R = T_L/(T_H − T_L) = 268.15/(308.15 − 268.15) = 268.15/40 = 6.70. 7.70 is the heat-pump COP.

7. Air (k = 1.4) at 300 K is compressed reversibly and adiabatically to one-eighth of its volume. Find the final temperature.

  1. 689 K
  2. 2400 K
  3. 300 K
  4. 522 K
Show the answer and solution

Answer: A. 689 K

T₂ = T₁(V₁/V₂)^(k − 1) = 300 × 8^0.4 = 300 × 2.297 = 689 K.

8. An ideal 1.5 kW water heater warms 10 kg of water from 25 °C to 55 °C with no losses. How long does this take? (c = 4186 J/kg·K)

  1. 8.37 min
  2. 27.91 min
  3. 13.95 min
  4. 4.65 min
Show the answer and solution

Answer: C. 13.95 min

Q = 10 × 4186 × 30 = 1 255 800 J. t = Q/P = 1 255 800/1500 = 837.2 s = 13.95 min.

Worked examples with computed numbers

These numbers are fixed on this page; in practice they change every time.

9. How long does a 3500 W heater take to raise 25 L of water by 44 °C, assuming no losses? (c = 4186 J/kg·K; 1 L of water = 1 kg)

  1. 0.0219 min
  2. 1320 min
  3. 21.9 min
  4. 0.365 min
Show the answer and solution

Answer: C. 21.9 min

Q = mcΔT = 25 × 4186 × 44 = 4.6 MJ; t = Q/P = 1316 s = 21.9 min (no losses).

10. What is the Carnot efficiency of an engine working between 291 °C and 27 °C?

  1. 90.7%
  2. 53.2%
  3. 46.8%
  4. 45.4%
Show the answer and solution

Answer: C. 46.8%

η = 1 − Tc/Th in kelvin = 1 − 300.15/564.15 = 46.8%.

Other topics in the same subjects

Physics: mechanics · Physics: waves, electricity and magnetism · General chemistry · Engineering materials · Engineering economics · Engineering management · Computer fundamentals and programming · RA 9292 and ethics (electronics) · Fluid mechanics · Strength of materials · RA 7920 and ethics (electrical) · PEC Part 1: general requirements

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