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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In an ideal Otto cycle with a compression ratio of 8.5, air enters the compression stroke at 27 °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 = 8.5T1 = 27 °Ck = 1.4
T2 = K
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 310 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 = 11T1 = 310 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 = 18 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 temperature T3 at the end of heat addition, in K.

r = 18rc = 1.5T1 = 295 Kk = 1.4
T3 = K
4.Medium
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An ideal Diesel cycle has a compression ratio r = 17 and a cutoff ratio rc = v₃/v₂ = 2. 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 = 17rc = 2T1 = 295 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 18. Air enters the compressor at 288 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 = 18T1 = 288 KT3 = 1300 Kηc = 88%ηt = 85%k = 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 12. 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 = 12k = 1.4
η = %

Answer key

  1. 1. T2 = 706.5 K
  2. 2. w = 704.6 kJ/kg
  3. 3. T3 = 1406 K
  4. 4. T3 = 1832 K
  5. 5. wnet = 202 kJ/kg
  6. 6. η = 50.83 %

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