The efficiency of a reversible heat engine working between two temperatures is $50 \%$. The coefficient of performance of a refrigerator working between the same two temperatures but in reverse direction is

The total internal energy of 4 moles of a diatomic gas at a temperature of $27^{\circ} \mathrm{C}$ is (gas constant $=831$ $\mathrm{J} \mathrm{mol}^{-1} \mathrm{~K}^{-1}$ )

Steam at $100^{\circ} \mathrm{C}$ is added to 150 g water to increase its temperature from $20^{\circ} \mathrm{C}$ to $40^{\circ} \mathrm{C}$. The total mass of the water at $40^{\circ} \mathrm{C}$ is (specific heat capacity of water $=1 \mathrm{cal} \mathrm{g}^{-1}{ }^{\circ} \mathrm{C}^{-1}$ and latent heat of steam $\left.=540 \mathrm{cal} \mathrm{g}^{-1}\right)$

A blacksmith fixes circular iron frame on the wooden wheel of a bullock cart. The diameter of wooden wheel and circular iron frame are 5.012 m and 5 m respectively at $27^{\circ} \mathrm{C}$. The temperature (in ${ }^{\circ} \mathrm{C}$ ) to which iron ring must be heated so as to fit the wooden wheel is

(Coefficient of linear expansion of iron $\left.=1.2 \times 10^{-5}{ }^{\circ} \mathrm{C}^{-1}\right)$