The following figure shows a Carnot engine that works between temperatures $T_1=400 \mathrm{K}$ and $T_2=200 \mathrm{K}$ and drives a Carnot refrigeration that works between temperatures $T_3=350 \mathrm{K}$ and $T_4=250 \mathrm{K}.$ The quantity $\frac{Q_3}{Q_1}$ will be

The $P-V$ diagram shown below indicates two paths along which a sample of gas can be taken from state $A$ to state $B$. The energy equal to $5 PV$ in the form of heat is required to be transferred if the Path-$1$ is chosen. How much energy in the form of heat should be transferred if Path-$2$ is chosen?

An air bubble rises from the bottom of a water tank of height $5 \mathrm{m}$. If the initial volume of the bubble is $3 {\mathrm{mm}}^3$. What will be its volume as it reaches the surface. Assume that its temperature does not change.

[$g=9.8 \mathrm{m} {\mathrm{s}}^{-2},1 \mathrm{atm}={10}^5 \mathrm{Pa}$, density of water $=1 \mathrm{gm} {\mathrm{cc}}^{-1}$]