Question

Volume of one mole gas changes according to the $V=\frac{a}{T}$. If temperature change is $\Delta T$, then work done will be

• A. $R\Delta T$
• B. $-R\Delta T$
• C. $\frac{R}{\gamma -1}\Delta T$
• D. $R(\gamma -1)\Delta T$

Answer 1

The correct option is B $-R\Delta T$

$PV=RT$ ;
$P=\frac{RT}{V}=\frac{R{T}^2}{a}$
$V=\frac{a}{T}$

$\therefore$$dV=-\frac{a}{T^2}dT$
W = $\int PdV$
= $\int \frac{R{T}^2}{a}(-\frac{a}{T^2}dT)$
$W=-R\Delta T$