Q. An ideal gas initially at temperature $T_{1}$ with $\gamma =5/3$ expands adiabatically into vacuum to double its volume. The final temperature $T_{2}$ is given by:

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Solution:

For adiabatic expansion against vacuum.
$q=0w=0,\because P_{ext}=0$
$ΔU=q+w$
$ΔU=0$
$\Rightarrow nC_{vm}ΔT=0\Rightarrow ΔT=0$
$T_{1}=T_{2}$