A small quantity of water of mass ' $m$ ' at temperature $\theta^{\circ} \mathrm{C}$ is mixed with a large mass ' $M$ ' of ice which is at its melting point. If ' $s$ ' is specific heat capacity of water and ' $L$ ' is the latent heat of fusion of ice, then the mass of ice melted is

In a Carnot engine, if the absolute temperature of the source is $25 \%$ more than the absolute temperature of the sink, then the efficiency of the engine is

The work done by 6 moles of helium gas when its temperature increases by $20^{\circ} \mathrm{C}$ at constant pressure is (Universal gas constant $=8.31 \mathrm{Jmol}^{-1} \mathrm{~K}^{-1}$ )

If a heat engine and a refrigerator are working between the same two temperatures $T_1$ and $T_2\left(T_1>T_2\right)$, then the ratio of efficiency of heat engine to coefficient of performance of refrigerator is