
$\Delta U=0$
$\therefore \text { from } \Delta Q=\Delta U+W$
$=0+W$
$\Delta Q=W$
$=\text { Area }$
$=\pi r_{1} \cdot r_{2}$
$=\pi \times\left(10 \times 10^{3}\right)\left(10 \times 10^{-3}\right)$
$\Delta Q=100 \pi$
$\therefore \text { Ans. }=100$
The change in internal energy of the gas during the transition is ............$\;kJ$
(Graphs are schematic and are not to scale)
| $List-I$ | $List-II$ |
| ($I$) $10^{-3} kg$ of water at $100^{\circ} C$ is converted to steam at the same temperature, at a pressure of $10^5 Pa$. The volume of the system changes from $10^{-6} m ^3$ to $10^{-3} m ^3$ in the process. Latent heat of water $=2250 kJ / kg$. | ($P$) $2 kJ$ |
| ($II$) $0.2$ moles of a rigid diatomic ideal gas with volume $V$ at temperature $500 K$ undergoes an isobaric expansion to volume $3 V$. Assume $R=8.0 Jmol ^1 K^{-1}$. | ($Q$) $7 kJ$ |
| ($III$) On mole of a monatomic ideal gas is compressed adiabatically from volume $V=\frac{1}{3} m^3$ and pressure $2 kPa$ to volume $\frac{v}{8}$ | ($R$) $4 kJ$ |
| ($IV$) Three moles of a diatomic ideal gas whose molecules can vibrate, is given $9 kJ$ of heat and undergoes isobaric expansion. | ($S$) $5 kJ$ |
| ($T$) $3 kJ$ |
Which one of the following options is correct?