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 10.5, air enters the compression stroke at 15 °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 = 10.5T1 = 15 °Ck = 1.4
T2 = K
2.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 310 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 = 7.5T1 = 310 KT3 = 1500 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 = 22 and a cutoff ratio rc = v₃/v₂ = 3. 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 = 22rc = 3T1 = 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 = 20 and a cutoff ratio rc = v₃/v₂ = 3. 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 = 20rc = 3T1 = 305 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 10. Air enters the compressor at 295 K and the turbine at 1100 K. The compressor has an isentropic efficiency of 88% and the turbine 90%. 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 = 1100 Kηc = 88%ηt = 90%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 14. 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 = 14k = 1.4
η = %

Answer key

  1. 1. T2 = 738.1 K
  2. 2. w = 320.2 kJ/kg
  3. 3. qin = 2007 kJ/kg
  4. 4. T3 = 3033 K
  5. 5. wnet = 166.1 kJ/kg
  6. 6. η = 52.95 %

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