what compression ration (V max /V min ) will raise the temperature of the air fr

Question

what compression ration (Vmax/Vmin) will raise the temperature of the air from 20 degrees celcius to 1100 degrees celcius in an adiabatic process, and what pressure ratio does this process have (Pmax/Pmin)?

Explanation / Answer

For an adiabatic process, with Q = 0, the first law of thermodynamics is: Change in thermal energy = Work. Compressing a gas adiabatically (W > 0) increases the thermal energy. So an adiabatic compression raises the temperature of a gas. Pf = Pi(Vi/Vf)^gamma gamma = 1.40 for a diatomic gas (like air) Pf = Pi(Vmax/Vmin)^1.40 Wait a minute: (Tf) Vf^(gamma - 1) = (Ti) Vi^(gamma - 1) (1,373K)Vf^(gamma-1) = (293K)Vi^(gamma -1) (1,373K) Vf^0.4 = (293K) Vi^0.4 1,373K / 293K = Vmax^0.4/Vmin^0.4 4.686 = (Vmax^0.4 / Vmin^0.4) (4.686)^2.5 = (Vmin^0.4 / Vmax^0.4)^2.5 Vmax/Vmin = 47.534 So you would need to increase pressure to 3035.9 psi if you started from atmospheric pressure.

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