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 8. At the start of compression the air is at 305 K, and the highest temperature in the cycle is 2200 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 = 8T1 = 305 KT3 = 2200 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 12. At the start of compression the air is at 310 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 = 12T1 = 310 KT3 = 2000 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 = 1.8. At the start of compression the air is at 300 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 = 17rc = 1.8T1 = 300 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 = 17 and a cutoff ratio rc = v₃/v₂ = 2.5. At the start of compression the air is at 300 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 = 17rc = 2.5T1 = 300 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 18. Air enters the compressor at 288 K and the turbine at 1200 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 = 18T1 = 288 KT3 = 1200 Kk = 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 20. 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 = 20k = 1.4
η = %

Answer key

  1. 1. w = 607.9 kJ/kg
  2. 2. w = 525.7 kJ/kg
  3. 3. qin = 749.1 kJ/kg
  4. 4. qin = 1405 kJ/kg
  5. 5. wnet = 306.4 kJ/kg
  6. 6. η = 57.51 %

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