Question

A thermally insulated rigid container of $1 L$ 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)
$\Delta p=10^{5}Pa, V=1\,L=10^{-3}m^{3}$
so, $\Delta p=\frac{5}{2}\times10^{5}\times10^{-3}=250\,J$