$1\,g$ of a liquid is converted to vapour at $3 \times 10^5\,Pa$ pressure. If $10\%$ of the heat supplied is used for increasing the volume by $1600\,cm^3$ during this phase change,then the increase in internal energy in the process will be $............\,J$.

Two cylinders $A$ and $B$ fitted with pistons contain equal amounts of an ideal diatomic gas at $300 \ K$. The piston of $A$ is free to move,while that of $B$ is held fixed. The same amount of heat is given to the gas in each cylinder. If the rise in temperature of the gas in $A$ is $30 \ K$,then the rise in temperature of the gas in $B$ is ..... $K$.

Column-$I$ shows graphs of thermodynamic processes, and column-$II$ contains information about various thermodynamic variables. Match column-$I$ with the information in column-$II$.

Column-$I$	Column-$II$
$(A)$ $PV$ vs $V$ (Isothermal expansion)	$(P)$ $W$ > 0
$(B)$ $P$ vs $T$ (Isochoric heating)	$(Q)$ $W$ < 0
$(C)$ $P$ vs $V$ (Isobaric expansion)	$(R)$ $\Delta Q$ > 0
$(D)$ $V$ vs $T$ (Isobaric compression)	$(S)$ $\Delta U$ > 0
	$(T)$ $\Delta U$ < 0

An engineer claims to have made an engine delivering $10 \ kW$ of power with a fuel consumption of $1 \ g/s$. The calorific value of the fuel is $2 \ kcal/g$. Is the claim of the engineer valid?

Initial pressure and volume of a gas are $P$ and $V$ respectively. First,it is expanded isothermally to volume $4V$ and then compressed adiabatically to volume $V$. The final pressure of the gas will be