Question

Thermal coefficient of volume expansion at constant pressure for an ideal gas sample of $n$ moles having pressure $P_o$, volume $V_o$ and temperature $T_o$ is:

• A. $\frac{R}{P_o{V}_o}$
• B. $\frac{P_o{V}_o}{R}$
• C. $\frac{1}{T_o}$
• D. $\frac{1}{n{T}_o}$

Answer 1

The correct option is C $\frac{1}{T_o}$

From ideal gas equation,
$PV=nRT$........(1)
differentiating both sides
$PdV=nRdT$ [since $P$ is constant]
$\Rightarrow \frac{dV}{dT}=\frac{nR}{P}$........(2)
Now coefficient of volume expansion,
$dV=\gamma VdT$
$\Rightarrow \frac{dV}{dT}=V\gamma$...........(3)
From Eq. (2) and (3),
$\gamma =\frac{nR}{PV}$
$\Rightarrow \gamma =\frac{1}{T}$ [ from Eq. (1) ]
For the given condition $(P_o,V_o,T_o)$,
$\Rightarrow \gamma =\frac{1}{T_o}$
Hence, option $\left(c\right)$ is the correct answer.