A closed hollow insulated cylinder is filled with gas at $0 °\mathrm{C}$ and also contains an insulated piston of negligible weight and negligible thickness at the middle point. The gas on one side of the piston is heated to $100 °\mathrm{C}$. If the piston moves $5 \mathrm{cm}$, the length of the hollow cylinder is

The airtight and smooth pistons of a cylindrical vessel are connected with a string, as shown, initially, pressure and temperature of the gas are $P_0$ and $T_0$. The atmospheric pressure is also $P_0$. At a later time, the tension in the string is $\frac{3}{8}{P}_{0}A$ where $A$ is the cross-sectional area of the cylinder. At this time, the temperature of the gas has become

$P‐T$ graph for the same number of moles of two ideal gases is shown in the figure. Find the path along which volume decreases.