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 9.5. At the start of compression the air is at 295 K, and the highest temperature in the cycle is 2000 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 = 9.5T1 = 295 KT3 = 2000 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 7. At the start of compression the air is at 295 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 = 7T1 = 295 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 = 20 and a cutoff ratio rc = v₃/v₂ = 1.5. At the start of compression the air is at 295 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 = 20rc = 1.5T1 = 295 Kk = 1.4cp = 1.005 kJ/(kg·K)
qin = kJ/kg
4.Medium
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An ideal Diesel cycle has a compression ratio r = 15 and a cutoff ratio rc = v₃/v₂ = 1.8. 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 = 15rc = 1.8k = 1.4
η = %
5.Hard
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A gas-turbine plant runs on a Brayton cycle with a compressor pressure ratio of 8. Air enters the compressor at 300 K and the turbine at 1300 K. The compressor has an isentropic efficiency of 85% and the turbine 92%. 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 = 8T1 = 300 KT3 = 1300 Kηc = 85%ηt = 92%k = 1.4cp = 1.005 kJ/(kg·K)
wnet = kJ/kg
6.Hard
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A gas-turbine plant runs on a Brayton cycle with a compressor pressure ratio of 15. Air enters the compressor at 290 K and the turbine at 1300 K. The compressor has an isentropic efficiency of 82% and the turbine 88%. 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 = 15T1 = 290 KT3 = 1300 Kηc = 82%ηt = 88%k = 1.4cp = 1.005 kJ/(kg·K)
wnet = kJ/kg

Answer key

  1. 1. w = 543 kJ/kg
  2. 2. w = 682.5 kJ/kg
  3. 3. qin = 491.3 kJ/kg
  4. 4. η = 61.4 %
  5. 5. wnet = 250.6 kJ/kg
  6. 6. wnet = 204.3 kJ/kg

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