Question

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:

• A. $T_{2}=T_{1}\times \left(\right.0.5\left(\left.\right)^{2 / 3}$
• B. $T_{2}=T_{1}$
• C. $T_{2}=T_{1}\left(\right.2\left(\left.\right)^{- 1 / 3}$
• D. $T_{2}=\frac{T_{1}}{2}$

Answer 1

Answer: (B)

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