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## Homework Statement

Air at pressure 20[atm] enters an air machine and leaves at 1[atm]. what must be the temperature of the air at the entrance so that when it leaves it is 0

^{0}C.

Assume adiabatic process.

## Homework Equations

PV=nRT

Adiabatic: ##P_1V_1^\gamma=P_2V_2^\gamma##

## The Attempt at a Solution

The air expands and only the mass per second is unchanged. i take 1[mol] at the exit:

$$PV=nRT\rightarrow 1[atm]\cdot V_2=1\cdot 0.08208\cdot 273\rightarrow V_2=22.4[liter]$$

$$P_1V_1^\gamma=P_2V_2^\gamma \rightarrow 20\cdot V_1^{1.4}=22.4^{1.4}\rightarrow V_1=2.63[liter]$$

$$P_1V_1=nRT_1\rightarrow 20\cdot 2.63=1\cdot 0.08208\cdot T_1\rightarrow T_1=642^0K=369^0C$$

Is it correct?

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