Question

For an ideal gas the fractional change in its volume per degree rise in temperature at constant pressure is equal to
$[T$ is the absolute temperature of gas $]$

• A. $T^2$
• B. $T^1$
• C. $T^{-1}$
• D. $T^{-2}$

Answer 1

The correct option is C $T^{-1}$

From the ideal gas equation,
$PV=nRT$ .............$\left(1\right)$
Differentiating $w.r.t$ $T$ on both sides,
$\Rightarrow \frac{PdV}{dT}=nR$ .............$\left(2\right)$
$[P,n$ and $R$ are constant $]$
On dividing $\left(2\right)$ by $\left(1\right)$,
$\Rightarrow \frac{\frac{PdV}{dT}}{PV}=\frac{nR}{nRT}$
$\Rightarrow \frac{dV}{VdT}=\frac{1}{T}=T^{-1}$
Hence, fractional change in volume per unit rise in temperature is $T^{-1}$.