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 305 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 = 7.5T1 = 305 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 11. 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 = 11T1 = 305 KT3 = 1800 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 = 17 and a cutoff ratio rc = v₃/v₂ = 2.2. At the start of compression the air is at 305 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 temperature T3 at the end of heat addition, in K.

r = 17rc = 2.2T1 = 305 Kk = 1.4
T3 = K
4.Medium
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An ideal Diesel cycle has a compression ratio r = 18 and a cutoff ratio rc = v₃/v₂ = 2.5. 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 = 18rc = 2.5k = 1.4
η = %
5.Hard
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A gas-turbine plant runs on a Brayton cycle with a compressor pressure ratio of 10. Air enters the compressor at 295 K and the turbine at 1500 K. The compressor has an isentropic efficiency of 80% 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 = 10T1 = 295 KT3 = 1500 Kηc = 80%ηt = 88%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 12. Air enters the compressor at 288 K and the turbine at 1100 K. Both machines are isentropic. 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 = 1100 Kk = 1.4cp = 1.005 kJ/(kg·K)
wnet = kJ/kg

Answer key

  1. 1. w = 523.3 kJ/kg
  2. 2. w = 444.7 kJ/kg
  3. 3. T3 = 2084 K
  4. 4. η = 60.94 %
  5. 5. wnet = 294.6 kJ/kg
  6. 6. wnet = 262.7 kJ/kg

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