$P_i, V_i$ and $P_f, V_f$ are initial and final pressures and volumes of a gas in a thermodynamic process respectively. If $PV^n = \text{constant}$, then the amount of work done is

$0.02 \, mol$ 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,$R = 8.31 \, J / K / mol$).

One mole of an ideal monoatomic gas at temperature $T_0$ expands slowly according to the law $P = kV$ ($k$ is a constant). If the final temperature is $2T_0$,the heat supplied to the gas is:

Two thermodynamic processes are shown in the figure. The molar heat capacities for processes $A$ and $B$ are $C_A$ and $C_B$. The molar heat capacities at constant pressure and constant volume are represented by $C_P$ and $C_V$,respectively. Choose the correct statement.

An ideal gas mixture filled inside a balloon expands according to the relation $PV^{2/3} = \text{constant}$. The temperature inside the balloon is

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