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 8. 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 = 8k = 1.4
η = %
2.Easy
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In an ideal Otto cycle with a compression ratio of 6.5, 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 = 6.5T1 = 27 °Ck = 1.4
T2 = K
3.Medium
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An ideal Diesel cycle has a compression ratio r = 16 and a cutoff ratio rc = v₃/v₂ = 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 = 16rc = 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 = 17 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 heat added qin per kilogram of air, in kJ/kg.

r = 17rc = 3T1 = 305 Kk = 1.4cp = 1.005 kJ/(kg·K)
qin = kJ/kg
5.Hard
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A gas-turbine plant runs on a Brayton cycle with a compressor pressure ratio of 20. Air enters the compressor at 310 K and the turbine at 1500 K. The compressor has an isentropic efficiency of 82% 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 = 20T1 = 310 KT3 = 1500 Kηc = 82%ηt = 88%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 12. Air enters the compressor at 288 K and the turbine at 1500 K. The compressor has an isentropic efficiency of 85% 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 = 12T1 = 288 KT3 = 1500 Kηc = 85%ηt = 85%k = 1.4cp = 1.005 kJ/(kg·K)
wnet = kJ/kg

Answer key

  1. 1. η = 56.47 %
  2. 2. T2 = 634.6 K
  3. 3. qin = 944.4 kJ/kg
  4. 4. qin = 1904 kJ/kg
  5. 5. wnet = 248.7 kJ/kg
  6. 6. wnet = 299.3 kJ/kg

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