One mole of an ideal gas is contained with in a cylinder by a frictionless piston and is initially at temperature $T$. The pressure of the gas is kept constant while it is heated and its volume doubles. If $R$ is molar gas constant, the work done by the gas in increasing its volume is

$N$ moles of an ideal diatomic gas are in a cylinder at temperature $T$. suppose on supplying heat to the gas, its temperature remain constant but $n$ moles get dissociated into atoms. Heat supplied to the gas is

One mole of an ideal gas in initial state $\mathrm{A}$ undergoes a cyclic process $A B C A$, as shown in the figure. Its pressure at $A$ is $\mathrm{P}_0$. Choose the correct option$(s)$ from the following

$(A)$ Internal energies at $\mathrm{A}$ and $\mathrm{B}$ are the same

$(B)$ Work done by the gas in process $\mathrm{AB}$ is $\mathrm{P}_0 \mathrm{~V}_0 \ln 4$

$(C)$ Pressure at $C$ is $\frac{P_0}{4}$

$(D)$ Temperature at $\mathrm{C}$ is $\frac{\mathrm{T}_0}{4}$

When a system is taken from state $i$ to state $f$ along the path $iaf$, it is found that $Q=50$ $cal$ and $W=20$ $cal$ Along the path $ibf\ Q = 36\ cal. \ W$ along the path $ibf$ is …….  $ cal$

In the $p-V$ diagram below, the dashed curved line is an adiabat.For a process that is described by a straight line joining two points $X$ and $Y$ on the adiabat (solid line in the diagram) heat is (Hint consider the variation in temperature from $X$ to $Y$ along the straight line)