Gas power cycles worksheet with answers

Free printable Gas power cycles worksheet: 6 problems from easy to exam level, with an answer key. Print it or save it as a PDF.

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1.Easy
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An ideal Otto cycle has a compression ratio of 7.5. At the start of compression the air is at 295 K, and the highest temperature in the cycle is 1500 K. Use the cold-air-standard assumptions: air is an ideal gas with constant specific heats, k = 1.4, cp = 1.005 kJ/(kg·K) and cv = 0.718 kJ/(kg·K). Find the net work output w per kilogram of air, in kJ/kg.

r = 7.5T1 = 295 KT3 = 1500 Kk = 1.4cv = 0.718 kJ/(kg·K)
w = kJ/kg
2.Easy
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An ideal Otto cycle has a compression ratio of 9. At the start of compression the air is at 310 K, and the highest temperature in the cycle is 2400 K. Use the cold-air-standard assumptions: air is an ideal gas with constant specific heats, k = 1.4, cp = 1.005 kJ/(kg·K) and cv = 0.718 kJ/(kg·K). Find the net work output w per kilogram of air, in kJ/kg.

r = 9T1 = 310 KT3 = 2400 Kk = 1.4cv = 0.718 kJ/(kg·K)
w = kJ/kg
3.Medium
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An ideal Diesel cycle has a compression ratio r = 19 and a cutoff ratio rc = v₃/v₂ = 3. Use the cold-air-standard assumptions: air is an ideal gas with constant specific heats, k = 1.4, cp = 1.005 kJ/(kg·K) and cv = 0.718 kJ/(kg·K). Find its thermal efficiency η in percent.

r = 19rc = 3k = 1.4
η = %
4.Medium
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An ideal Diesel cycle has a compression ratio r = 16 and a cutoff ratio rc = v₃/v₂ = 2. At the start of compression the air is at 310 K. Use the cold-air-standard assumptions: air is an ideal gas with constant specific heats, k = 1.4, cp = 1.005 kJ/(kg·K) and cv = 0.718 kJ/(kg·K). Find the heat added qin per kilogram of air, in kJ/kg.

r = 16rc = 2T1 = 310 Kk = 1.4cp = 1.005 kJ/(kg·K)
qin = kJ/kg
5.Hard
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A gas-turbine plant runs on a Brayton cycle with a compressor pressure ratio of 12. Air enters the compressor at 288 K and the turbine at 1400 K. The compressor has an isentropic efficiency of 85% and the turbine 90%. Use the cold-air-standard assumptions: air is an ideal gas with constant specific heats, k = 1.4, cp = 1.005 kJ/(kg·K) and cv = 0.718 kJ/(kg·K). Find the net work output wnet per kilogram of air, in kJ/kg.

rp = 12T1 = 288 KT3 = 1400 Kηc = 85%ηt = 90%k = 1.4cp = 1.005 kJ/(kg·K)
wnet = kJ/kg
6.Hard
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An ideal Brayton cycle operates with a compressor pressure ratio of 14. Use the cold-air-standard assumptions: air is an ideal gas with constant specific heats, k = 1.4, cp = 1.005 kJ/(kg·K) and cv = 0.718 kJ/(kg·K). Find its thermal efficiency η in percent.

rp = 14k = 1.4
η = %

Answer key

  1. 1. w = 333.5 kJ/kg
  2. 2. w = 694.2 kJ/kg
  3. 3. η = 59.79 %
  4. 4. qin = 944.4 kJ/kg
  5. 5. wnet = 291.6 kJ/kg
  6. 6. η = 52.95 %

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