A sample of gas at temperature $T$ is adiabatically expanded to double its volume. Adiabatic constant for the gas is $\gamma=3 / 2$. The work done by the gas in the process is:
$(\mu=1 \text { mole })$
Solution
<p>$$\begin{aligned}
& w=\frac{-n R}{\gamma-1}(\Delta T) \\
&=\frac{-R}{1 / 2}\left(\frac{T}{\sqrt{2}}-T\right) \\
&=2 R\left(\frac{\sqrt{2} T-T}{\sqrt{2}}\right) \\
&=R T(2-\sqrt{2}) \\
& \therefore \quad T V_\gamma^{-1}=\text { cons. } \\
& T V_\gamma^{-1}=T_f(2 V)^{\gamma-1} \\
& T_f=\frac{T}{\sqrt{2}}
\end{aligned}$$</p>
About this question
Subject: Physics · Chapter: Thermodynamics · Topic: Thermodynamic Processes
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