One mole of a diatomic gas does a work $\frac{Q}{3}$,when the amount of heat supplied is $Q$. In this process,the molar heat capacity of the gas is:

One mole of an ideal gas undergoes a cyclic process,consisting of two isochores and two isobars. Temperatures at points $1$ and $3$ are $T_1$ and $T_3$ respectively. Find the work done by the gas over the cycle,if points $2$ and $4$ lie on the same isotherm.

The relation between efficiency $(\eta)$ of a Carnot engine and the coefficient of performance $(\beta)$ of a refrigerator working between the same temperatures is:

Match the "Technology" given in List-$1$ with the "Principle of Physics" given in List-$2$.

$A$. Steam engine	$I$. Magnetic confinement of plasma
$B$. Electron microscope	$II$. Laws of thermodynamics
$C$. Non-reflecting coatings	$III$. Wave nature of electrons
$D$. Tokamak	$IV$. Interference of light

One mole of an ideal gas at initial temperature $T$ undergoes a quasi-static process during which the volume $V$ is doubled. During the process,the internal energy $U$ obeys the equation $U = a V^3$,where $a$ is a constant. The work done during this process is

An ideal gas is subjected to a cyclic process $A B C D$ as depicted in the $p-V$ diagram given below. Which of the following curves represents the equivalent cyclic process?