An ideal monoatomic gas is taken through a process $dQ = 2dU$. The molar heat capacity for the process is:

The $P-V$ diagram shown represents the thermodynamic cycle of an engine operating with an ideal monatomic gas. The amount of heat extracted from the source in a single cycle is:

Two containers $A$ and $B$ contain equal volumes of an identical gas at the same pressure and temperature. The gas in container $A$ is compressed to half its original volume isothermally,while the gas in container $B$ is compressed to half its original volume adiabatically. The ratio of the final pressure of gas in container $B$ to that of gas in container $A$ is

An office room contains about $2000$ moles of air. The change in the internal energy of this much air when it is cooled from $34^{\circ} C$ to $24^{\circ} C$ at a constant pressure of $1.0 \text{ atm}$ is (Use $\gamma_{\text{air}} = 1.4$ and universal gas constant $R = 8.314 \text{ J/mol-K}$)

In thermodynamic processes, which of the following statements is not true?

$A$ monoatomic gas of $n$-moles is heated from temperature $T_1$ to $T_2$ under two different conditions: $(i)$ at constant volume and (ii) at constant pressure. The change in internal energy of the gas is