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(B) The compression of air in a compressor is an adiabatic process.Using the adiabatic relation $P^{1-\gamma} T^{\gamma} = 	ext{constant}$, we have $

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an air-conditioner to cool the air injected into the cabin

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(B) The compression of air in a compressor is an adiabatic process.Using the adiabatic relation $P^{1-\gamma} T^{\gamma} = 	ext{constant}$, we have $P_{	ext{in}}^{1-\gamma} T_{	ext{in}}^{\gamma} = P_{	ext{out}}^{1-\gamma} T_{	ext{out}}^{\gamma}$.Given $P_{	ext{in}} = 0.28 \,atm$, $T_{	ext{in}} = -40^{\circ} C = 233 \,K$, $P_{	ext{out}} = 1 \,atm$, and $\gamma = 1.4 = 7/5$.Substituting the values: $(0.28)^{1-1.4} (233)^{1.4} = (1)^{1-1.4} (T_{	ext{out}})^{1.4}$.$(0.28)^{-0.4} (233)^{1.4} = (T_{	ext{out}})^{1.4}$.$T_{	ext{out}} = 233 	imes (0.28)^{-0.4/1.4} = 233 	imes (0.28)^{-2/7}$.Calculating this, $T_{	ext{out}} \approx 233 	imes 1.48 \approx 345 \,K$.Since $345 \,K$ is approximately $72^{\circ} C$, which is much higher than the required cabin temperature of $25^{\circ} C$, an air-conditioner is needed to cool the air.

Similar Questions

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