The state of an ideal gas is changed through an isothermal process at the temperature $T_0$ as shown in the figure. The work done by the gas in going from state $B$ to $C$ is double the work done by the gas in going from state $A$ to $B$. If the pressure in the state $B$ is $\frac{p_0}{2}$, then the pressure of the gas in the state $C$ is

$T‐V$ diagram of two moles of a mono-atomic gas is as shown in the figure. For the process, $abcda$ choose the correct options given below

The density $\left(\rho \right)$ versus internal energy $\left(U\right)$ Graph of gas is as shown in the figure. Choose the correct options.

Here, $W$ is work done by the gas and $Q$ is the heat given to the gas.

A cyclic process $1-2-3-4-1$ is depicted on $V-T$ diagram. The $p-T$ and $p-V$ diagrams for this cyclic process are given below. Select the correct choices (more than one options is/are correct)

One mole of a monatomic ideal gas is taken along the cycle $\mathrm{ABCA}$ as shown in the diagram.

The ratio of specific heat in the process $CA$ to the specific heat in the process $BC$ is

One mole of a monoatomic ideal gas is taken through the cycle $ABCDA$ as shown in the figure.

$T_A=1000 \mathrm{K} \text{and} \mathit{2}{p}_A\mathit{=}\mathit{3}{p}_B\mathit{=}\mathit{6}{p}_C$

The temperature at $B$ is

$\left[\text{Assume }{\left(\frac{2}{3}\right)}^{0.4}=0.85 \text{and }R=\frac{25}{3}\mathrm{J} {\mathrm{K}}^{-1} {\mathrm{mol}}^{-1}\right]$