For a diatomic gas undergoing a reversible process with its pressure inversely proportional to absolute temperature, its molar heat capacity is $\frac{xR}{2}$. The value of $x$ is:

Q. An ideal monoatomic gas undergoes a process where its pressure is inversely proportional to its temperature. The molar specific heat for the process is given by $\frac{xR}{2}$,then find $x$.

Q. The pressure $P$ of an ideal diatomic gas varies with its absolute temperature $T$ as shown in figure. The molar heat capacity of gas during this process is [$R$ is gas constant]

Q. An ideal monoatomic gas undergoes a process where its pressure is inversely proportional to its temperature. If the work done by two moles of gas if the temperature changes from $T_{1}to{T}_2$ is $xR(T_2-T_1)$. Find $x$

Q. The pressure $P$ of an ideal diatomic gas varies with its absolute temperature $T$ as shown in the figure. The molar heat capacity of the gas during this process is:
[$R$ is the gas constant]

Q. Molar heat capacity of an ideal gas in the process $P{V}^x$= constant, is given by:$C=\frac{R}{\gamma -1}+\frac{R}{1-x}.$ An ideal diatomic gas with $C_v=\frac{5R}{2}$ occupies a volume $V_1$ at pressure $P_1$. If this gas undergoes a process in which the pressure is proportional to the volume and it is found that the rms speed of the gas molecules has doubled from its initial value at the end of the process. Then