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

Consider two containers $A$ and $B$ containing monoatomic gases at the same Pressure $(P)$,Volume $(V)$ and Temperature $(T)$. The gas in $A$ is compressed isothermally to $\frac{1}{8}$ of its original volume while the gas $B$ is compressed adiabatically to $\frac{1}{8}$ of its original volume. The ratio of final pressure of gas in $B$ to that of gas in $A$ is ...........

One mole of a monoatomic ideal gas $\left(c_{V} = \frac{3}{2} R\right)$ undergoes a cycle where it first goes isochorically from the state $\left(\frac{3}{2} P_{0}, V_{0}\right)$ to $\left(P_{0}, V_{0}\right)$,and then is isobarically contracted to the volume $\frac{1}{2} V_{0}$. It is then taken back to the initial state by a path which is a quarter ellipse on the $P-V$ diagram. The efficiency of this cycle is

There are two samples $A$ and $B$ of a certain gas,which are initially at the same temperature and pressure. Both are compressed from volume $V$ to $\frac{V}{2}$. Sample $A$ is compressed isothermally while sample $B$ is compressed adiabatically. The final pressure of $A$ is

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 $\gamma = 5/3$)

$A$ certain amount of gas of volume $V$ at $27^{\circ}C$ temperature and pressure $2 \times 10^{7} \; N m^{-2}$ expands isothermally until its volume gets doubled. Later it expands adiabatically until its volume gets redoubled. The final pressure of the gas will be (Use $\gamma = 1.5$)