Two cylinders $A$ and $B$ fitted with pistons contain equal number of moles of an ideal monoatomic gas at $400 \,K$. The piston of $A$ is free to move while that of $B$ is held fixed. The same amount of heat energy is given to the gas in each cylinder. If the rise in temperature of the gas in $A$ is $42 \,K$, what is the rise in temperature of the gas in $B$ (in $\,K$)? (Given $\gamma = 5/3$)

The specific heat at constant pressure of a real gas obeying $PV^2=RT$ equation is:

$A$ container is filled with $20$ moles of an ideal diatomic gas at absolute temperature $T$. When heat is supplied to the gas,the temperature remains constant,but $8$ moles dissociate into atoms. The heat energy given to the gas is ......... (in $R T$)

In a certain thermodynamical process,the pressure of a gas depends on its volume as $P = kV^{3}$. The work done when the temperature changes from $100^{\circ}C$ to $300^{\circ}C$ will be .......... $nR$,where $n$ denotes the number of moles of a gas.

$A$ student records $\Delta Q, \Delta U,$ and $\Delta W$ for a thermodynamic cycle $A \rightarrow B \rightarrow C \rightarrow A$. Certain entries are missing in the table below. Find the correct entry from the following options.

	$AB$	$BC$	$CA$
$\Delta W$	$40 \, J$		$30 \, J$
$\Delta U$		$50 \, J$
$\Delta Q$	$150 \, J$	$10 \, J$

One mole of an ideal gas undergoes two different cyclic processes $I$ and $II$,as shown in the $P-V$ diagrams below. In cycle $I$,processes $a, b, c$ and $d$ are isobaric,isothermal,isobaric and isochoric,respectively. In cycle $II$,processes $a^{\prime}, b^{\prime}, c^{\prime}$ and $d^{\prime}$ are isothermal,isochoric,isobaric and isochoric,respectively. The total work done during cycle $I$ is $W_I$ and that during cycle $II$ is $W_{II}$. The ratio $W_I / W_{II}$ is . . . .