Question

In column-l, some situations are given, and in column-II, their results are given. Match the proper entries from column-II to column-I using the codes given below the columns.

Column-I	Column-II
(P) $0^{\circ }C$ ice kept at atmospheric pressure, melts and converts into $0^{\circ }C$ water $({\rho }_{ice}=0.9{\rho }_{water})$ For the ice-water system during this process,	(1)Net work is done by the system
(Q) A gas is undergoing a cyclic process. Density $\left(\rho \right)$ vs internal energy (U) graph is as shown. Here process $B-C$ is an adiabatic process. Consider the gas as the system. For the complete cyclic process,	(2 )Net work is done on the system
(R) In a closed, non-conducting room, a fan is turned on. Consider the air in the room as a system. During this process,	(3) Internal energy of the system increases

• A. p-1; q-2; r-3
• B. p-2; q-2; r-3
• C. p-1; q-1; r-3
• D. p-2; q-1; r-3

Answer 1

The correct option is D p-2; q-1; r-3

(p) When $0^{\circ }C$ ice converts into $0^{\circ }C$ water, volume decreases slightly, so $W_{system}$ is negative. To melt the ice, some heat has to be given $(Q=m{L}_f)$ which is almost equal to increase in internal energy.

(Q)

Since P-V cycle is clockwise, $W_{net}$ is positive and $(\Delta U{)}_{cycle}=0$

(R)
By the fan, some work is done on the room air. Due to this, temperature of the gas increases slightly, so internal energy will increase slightly. Mathematically,
$$\begin{array}{c}Q=W+\Delta U\\ Q=-ve+\Delta u\Rightarrow \Delta u=+ve\end{array}$$