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 $=831$ $\mathrm{J} \mathrm{mol}^{-1} \mathrm{~K}^{-1}$ )

Two objects made of the same material have masses $m$ and $2 m$ and are at temperatures $2 T$ and $T$ respectively. When heat $Q$ is supplied to the object of mass $2 m$, its temperature raises to $2 T$. If the same heat is supplied to the object of mass $m$, its temperature raises to

On a new temperature scale, the melting point of ice is $20^{\circ} \mathrm{X}$ and the boiling point of water is $110^{\circ} \mathrm{X}$. A temperature of $40^{\circ} \mathrm{C}$ would be indicated on this new temperature scale as