Gas power cycles worksheet with answers

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, c_p = 1.005 kJ/(kg·K) and c_v = 0.718 kJ/(kg·K). Find the net work output w per kilogram of air, in kJ/kg.

In an ideal Otto cycle with a compression ratio of 6.5, air enters the compression stroke at 30 °C. Use the cold-air-standard assumptions: air is an ideal gas with constant specific heats, k = 1.4, c_p = 1.005 kJ/(kg·K) and c_v = 0.718 kJ/(kg·K). Find the temperature T₂ at the end of compression, in K.

An ideal Diesel cycle has a compression ratio r = 16 and a cutoff ratio r_c = v₃/v₂ = 2.5. 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, c_p = 1.005 kJ/(kg·K) and c_v = 0.718 kJ/(kg·K). Find the temperature T₃ at the end of heat addition, in K.

An ideal Diesel cycle has a compression ratio r = 20 and a cutoff ratio r_c = 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, c_p = 1.005 kJ/(kg·K) and c_v = 0.718 kJ/(kg·K). Find the temperature T₃ at the end of heat addition, in K.

An ideal Brayton cycle operates with a compressor pressure ratio of 15. Use the cold-air-standard assumptions: air is an ideal gas with constant specific heats, k = 1.4, c_p = 1.005 kJ/(kg·K) and c_v = 0.718 kJ/(kg·K). Find its thermal efficiency η in percent.

A gas-turbine plant runs on a Brayton cycle with a compressor pressure ratio of 12. Air enters the compressor at 295 K and the turbine at 1500 K. Both machines are isentropic. Use the cold-air-standard assumptions: air is an ideal gas with constant specific heats, k = 1.4, c_p = 1.005 kJ/(kg·K) and c_v = 0.718 kJ/(kg·K). Find the net work output w_net per kilogram of air, in kJ/kg.