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 6. At the start of compression the air is at 295 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 = 6T1 = 295 KT3 = 2400 Kk = 1.4cv = 0.718 kJ/(kg·K)
w = kJ/kg
2.Easy
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In an ideal Otto cycle with a compression ratio of 10, 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 = 10T1 = 15 °Ck = 1.4
T2 = K
3.Medium
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An ideal Diesel cycle has a compression ratio r = 19 and a cutoff ratio rc = v₃/v₂ = 3. 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 = 19rc = 3T1 = 320 Kk = 1.4
T3 = K
4.Medium
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An ideal Diesel cycle has a compression ratio r = 20 and a cutoff ratio rc = v₃/v₂ = 2. 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 = 20rc = 2T1 = 300 Kk = 1.4cp = 1.005 kJ/(kg·K)
qin = kJ/kg
5.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 = %
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 295 K and the turbine at 1400 K. The compressor has an isentropic efficiency of 82% 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 = 6T1 = 295 KT3 = 1400 Kηc = 82%ηt = 90%k = 1.4cp = 1.005 kJ/(kg·K)
wnet = kJ/kg

Answer key

  1. 1. w = 659.8 kJ/kg
  2. 2. T2 = 723.8 K
  3. 3. T3 = 3117 K
  4. 4. qin = 999.3 kJ/kg
  5. 5. η = 50.83 %
  6. 6. wnet = 265.7 kJ/kg

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