The graph of pressure $(P)$ and volume $(V)$ according to $PV^n = C$,where $n = 1.4$. Identify the correct graph.

$A$ thermodynamic process for one mole of an ideal gas is shown below on a $P-V$ diagram. If $V_{2} = 2V_{1}$, then the ratio of temperature $T_{2} / T_{1}$ is ...... .

In a thermodynamic process, $2 \, \text{moles}$ of a monatomic ideal gas obey $P \propto V^{-2}$. If the temperature of the gas increases from $300 \, K$ to $400 \, K$, find the work done by the gas in terms of $R$ (where $R$ is the universal gas constant).

$0.02 \, mol$ of an ideal diatomic gas with initial temperature $20^{\circ} C$ is compressed from $1500 \, cm^3$ to $500 \, cm^3$. The thermodynamic process is such that $p V^2 = \beta$,where $\beta$ is a constant. Then,the value of $\beta$ is close to (the gas constant,$R = 8.31 \, J / K / mol$).

An ideal gas expands in such a way that $PV^2 = \text{constant}$ throughout the process.

The specific heat of a gas in a polytropic process is given by