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. At the start of compression the air is at 300 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 = 9T1 = 300 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 10. 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 = 10k = 1.4
η = %
3.Medium
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An ideal Diesel cycle has a compression ratio r = 18 and a cutoff ratio rc = v₃/v₂ = 2.5. 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 temperature T3 at the end of heat addition, in K.

r = 18rc = 2.5T1 = 295 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 = 1.8. At the start of compression the air is at 320 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 = 18rc = 1.8T1 = 320 Kk = 1.4
T3 = K
5.Hard
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A gas-turbine plant runs on a Brayton cycle with a compressor pressure ratio of 6. Air enters the compressor at 300 K and the turbine at 1400 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 = 6T1 = 300 KT3 = 1400 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 6. Air enters the compressor at 290 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 = 6T1 = 290 KT3 = 1100 Kk = 1.4cp = 1.005 kJ/(kg·K)
wnet = kJ/kg

Answer key

  1. 1. w = 326.5 kJ/kg
  2. 2. η = 60.19 %
  3. 3. T3 = 2344 K
  4. 4. T3 = 1830 K
  5. 5. wnet = 281.5 kJ/kg
  6. 6. wnet = 248.1 kJ/kg

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