The ratio $C_P/C_V=1.5$ for a certain ideal gas. The gas is taken at an initial pressure of $2$ kPa and compressed suddenly to $\dfrac14$ of its initial volume. The final pressure is:
1. $\dfrac12$ kPa
2. $4$ kPa
3. $8$ kPa
4. $16$ kPa

An ideal gas is enclosed in a volume by means of a piston-cylinder arrangement as shown in the adjacent diagram. The piston as well as the walls of the cylinder are non-conducting. The cross-sectional area of the piston is $A.$ Gravity $g$ is acting downward. A small block of mass $m$ is placed on top of the piston. There is no atmospheric pressure outside. An amount of thermal energy $\Delta Q$ is slowly supplied to the gas, and its temperature rises. Then, the gas:

In a reversible process, the change in internal energy $U$ of an ideal gas $(C_P/C_V=\gamma)$ is zero, while the volume increases from $V$ to $2V$. If the initial pressure is $P$, the final pressure will be:

The quantity of heat required to take a system from $\mathrm{A}$ to $\mathrm{C}$ through the process $\mathrm{ABC}$ is $20$ cal. The quantity of heat required to go from $\mathrm{A}$ to $\mathrm{C}$ directly is: