The given curve represents the variation of temperature as a function of volume for one mole of an ideal gas. Which of the following curves best represent the variation of pressure as a function of volume?

Find work done by the gas in the process shown in figure.

For two thermodynamic process temperature and volume diagram are given. In first process, it is a straight line having initial and final coordinates as $\left(V_0\text{,} T_0\right)$ and $\left(2V_0\text{,} 2T_0\right)$, where as in second process it is a rectangular hyperbola having initial and final coordinates $\left(V_0\text{,} T_0\right)$ and $\left(2V_0\text{,} \frac{T_0}{2}\right)$. Then, the ratio of work done $\left(W_1:W_2\right)$ in the two processes must be,

The curve in the figure shows the adiabatic compression of an ideal gas from $15 {\mathrm{m}}^3 \text{to} 12 {\mathrm{m}}^3$ followed by an isothermal compression to a final volume of $3.0 {\mathrm{m}}^3$. There are $2.0 \mathrm{moles}$ of the gas. The total heat supplied to the gas is equal to $(\ln 2=0.693)$,

The figure shows a conducting cylinder containing a gas and closed by a movable piston. The cylinder is submerged in an ice-water mixture. The piston is quickly pushed down from position $\left(1\right)$ to position $\left(2\right)$. The piston is held at position $\left(2\right)$ until the gas is again at $0°\mathrm{C}$ and then is slowly raised back to position $\left(1\right)$.

The $P-V$ diagram for the above process is,

If ideal diatomic gas follows the process as shown in graph where $T$ is temperature in $\mathrm{kelvin}$ and $V$ is volume $\left({\mathrm{m}}^3\right)$, then molar heat capacity for this process will be [in terms of gas constant $R$],