If one mole of an ideal gas goes through the process $A \rightarrow B$ and $B \rightarrow C$ as shown in the $P-V$ diagram. Given that $T_A = 400 \, K$ and $T_C = 400 \, K$. If $\frac{P_B}{P_A} = \frac{1}{5}$,then find the total heat supplied to the gas (in $J$). (in $.2$)

$A$ quantity of heat $Q$ is supplied to a monoatomic ideal gas which expands at constant pressure. What is the fraction of heat converted into work? Given $\gamma = \frac{C_p}{C_v} = \frac{5}{3}$.

$A$ monoatomic gas performs a work of $\frac{Q}{4}$,where $Q$ is the heat supplied to it. The molar heat capacity of the gas during this transformation will be $xR$,where $R$ is the gas constant. Find the value of $x$.

Carbon monoxide is carried around a closed cycle $abc$ in which $bc$ is an isothermal process as shown in the figure. The gas absorbs $7000 \; J$ of heat as its temperature increases from $300 \; K$ to $1000 \; K$ in going from $a$ to $b$. The quantity of heat rejected by the gas during the process $ca$ is ..... $J$. (in $; J$)

An office room contains about $2000$ moles of air. The change in the internal energy of this much air when it is cooled from $34^{\circ} C$ to $24^{\circ} C$ at a constant pressure of $1.0 \text{ atm}$ is (Use $\gamma_{\text{air}} = 1.4$ and universal gas constant $R = 8.314 \text{ J/mol-K}$)

An ideal gas at pressure $P_0$ undergoes an isothermal expansion until its volume is $8.0$ times its initial volume. The gas is slowly and adiabatically compressed back to its original volume. If the adiabatic constant of the gas is $\gamma = 4/3$, then the ratio of the average kinetic energy per molecule in this final state to that in the initial state is