- #1

- 1,380

- 22

## Homework Statement

10 liters of air at atmospheric pressure and temperature 300

^{0}K were isothermally compressed to a volume of 2[liter] and then freely expanded adiabatically to their original volume. what's the final temperature.

## Homework Equations

Adiabatic process: ##T_1V_1^{\gamma-1}=T_2V_2^{\gamma-1}##

γ of air=1.4

## The Attempt at a Solution

I ignore the first isothermic stage and start from the end conditions of the first stage: $$V_1=2[liter], T_1=300^0K$$:

##T_1V_1^{\gamma-1}=T_2V_2^{\gamma-1}\rightarrow 300\cdot 2^{0.4}=T_2\cdot 10^{0.4}##

##\rightarrow T_2=158^0K=-115^0C##

It should be -102

^{0}C