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 7.5. At the start of compression the air is at 300 K, and the highest temperature in the cycle is 1600 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 = 300 KT3 = 1600 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 7.5. 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 = 7.5T1 = 305 KT3 = 2200 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 = 2.2. At the start of compression the air is at 310 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 = 2.2T1 = 310 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 = 18 and a cutoff ratio rc = v₃/v₂ = 1.8. At the start of compression the air is at 310 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 = 310 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 8. Air enters the compressor at 290 K and the turbine at 1100 K. The compressor has an isentropic efficiency of 80% and the turbine 88%. 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 = 8T1 = 290 KT3 = 1100 Kηc = 80%ηt = 88%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. w = 368.8 kJ/kg
  2. 2. w = 602.8 kJ/kg
  3. 3. qin = 1287 kJ/kg
  4. 4. T3 = 1773 K
  5. 5. wnet = 140.2 kJ/kg
  6. 6. η = 52.95 %

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