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 305 K, and the highest temperature in the cycle is 1800 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 = 305 KT3 = 1800 Kk = 1.4cv = 0.718 kJ/(kg·K)
w = kJ/kg
2.Easy
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In an ideal Otto cycle with a compression ratio of 10, air enters the compression stroke at 35 °C. 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 temperature T2 at the end of compression, in K.

r = 10T1 = 35 °Ck = 1.4
T2 = K
3.Medium
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An ideal Diesel cycle has a compression ratio r = 16 and a cutoff ratio rc = v₃/v₂ = 2.5. At the start of compression the air is at 290 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 = 2.5T1 = 290 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 = 19 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 = 19rc = 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 18. Air enters the compressor at 295 K and the turbine at 1500 K. The compressor has an isentropic efficiency of 82% and the turbine 85%. 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 = 18T1 = 295 KT3 = 1500 Kηc = 82%ηt = 85%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 88% and the turbine 85%. 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 = 88%ηt = 85%k = 1.4cp = 1.005 kJ/(kg·K)
wnet = kJ/kg

Answer key

  1. 1. w = 447.3 kJ/kg
  2. 2. T2 = 774 K
  3. 3. qin = 1325 kJ/kg
  4. 4. η = 64.88 %
  5. 5. wnet = 256.1 kJ/kg
  6. 6. wnet = 211.5 kJ/kg

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