When $80 \ J$ of heat is supplied to a gas at constant pressure,if the work done by the gas is $20 \ J$,then the ratio of the specific heat capacities of the gas is

In Column-$I$ processes and in Column-$II$ the first law of thermodynamics are given. Match them appropriately:

Column-$I$	Column-$II$
$(a)$ Adiabatic	$(i)$ $\Delta Q = \Delta U$
$(b)$ Isothermal	$(ii)$ $\Delta Q = \Delta W$
	$(iii)$ $\Delta U = -\Delta W$

The ratio of the slopes of isothermal and adiabatic curves is

One mole of a gas expands such that its volume $V$ changes with absolute temperature $T$ in accordance with the relation $V = K T^2$,where $K$ is a constant. If the temperature of the gas changes by $60 \text{ K}$,then the work done by the gas is ($R$ is the universal gas constant).

Suppose an ideal gas ($n$ moles) undergoes an expansion process $P = f(V)$ which passes through the point $(V_0, P_0)$. If the slope of the curve $P = f(V)$ is greater than the slope of the adiabatic curve passing through $(V_0, P_0)$,show that the gas absorbs heat at $(V_0, P_0)$.

Five moles of an ideal gas has pressure $p_0$, volume $V_0$, and temperature $T_0$. The gas is expanded to volume $3V_0$ along a path such that the pressure $p$ changes as a function of volume $V$ as $p = p_0(V/V_0)$. The pressure is then reduced to $p_0$ while maintaining constant volume. Finally, the gas undergoes an isobaric compression until the volume and temperature return to $V_0$ and $T_0$, respectively. The total work done by the gas during the entire process is: