A gas is made to undergo a change of state from an initial state to a final state along different paths by adiabatic process only. Therefore.

In the given figure, an ideal gas is trapped between a mercury column and the closed end of a uniform vertical tube. The upper end of the tube is open to the atmosphere. Initially, the lengths of the mercury column and the trapped air column are $12 \mathrm{cm}$ and $50 \mathrm{cm}$, respectively. When the tube is tilted slowly in a vertical plane through an angle of $30°$ with horizontal, then the new length of air column is $\frac{x }{41} \mathrm{m}$. Find $x$ (assume the temperature to remain constant $(P_{\mathrm{atm}}=76 \mathrm{cm} \text{of} \mathrm{Hg})$).

Two moles of an ideal monoatomic gas undergo a cyclic process which is indicated on a $P-U$ diagram where $U$ is the internal energy of the gas. The work done by the gas in the cycle is $k\times {10}^2\ln 2$. Find $k$.

A cyclic process $\mathrm{ABCD}$ is shown in the P–V diagram. ($\mathrm{BC}$ and $\mathrm{DA}$ are isothermal)

Which of the following curves represent the same process?