Question

A thermally insulated rigid container of $1L$ volume contains a diatomic ideal gas a t room temperature. A small paddle installed inside the container is rotated from the outside, such that the pressure rises by $10^{5}Pa$. The change in internal energy is close to

• A. zero
• B. 67 J
• C. 150 J
• D. 250 J

Answer 1

Answer: (D)

Change in internal energy of $n$ moles of an ideal gas, when temperature changes by $\Delta T$ is
$\Delta U=n\cdot \frac{f}{2}\cdot R\cdot \Delta T$
$=\frac{f}{2}\left(nR\Delta T\right)=\frac{f}{2}\left(\Delta p\cdot V\right)$
[$\therefore$ for ideal gas $pV=nRT$]
Here, $f=5$ (gas is diatomic)
$\Delta p=10^{5}Pa,V=1L=10^{-3}{m}^3$
so, $\Delta p=\frac{5}{2}\times 10^5\times 10^{-3}=250J$