The relation between $U, P$ and $V$ for an ideal gas in an adiabatic process is given by relation $U=a+b P V .$ Find the value of adiabatic exponent $(\gamma)$ of this gas

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Aicharya · Accepted Answer

$U=a+b P V$
In adiabatic change,
$d U=-d W=\frac{n R}{\gamma-1}\left(T_{2}-T_{1}ight)=\frac{n R}{\gamma-1}(d T)$
$\Rightarrow U=\int d U=\frac{n R}{\gamma-1} \int d T$
or $\quad U=\left(\frac{n R}{\gamma-1}ight) T+a=\frac{P V}{\gamma-1}+a \ldots \ldots(2)$
where $a$ is the constant of integration.
Comparing (1) and (2), we get $b=\frac{1}{\gamma-1} \Rightarrow \gamma=\frac{b+1}{b} .$ ^

The relation between $U, P$ and $V$ for an ideal gas in an adiabatic process is given by relation $U=a+b P V…

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