The temperatures of equal masses of three different liquids $A, B$ and $C$ are $15^{\circ} \mathrm{C}, 24^{\circ} \mathrm{C}$ and $30^{\circ} \mathrm{C}$, respectively. The resultant temperature when liquids $A$ and $B$ are mixed is $20^{\circ} \mathrm{C}$ and when liquids $B$ and $C$ are mixed is $26^{\circ} \mathrm{C}$. Then, the ratio of specific heat capacities of the liquids $A, B$ and $C$ is

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 rod of same area of cross-section have lengths $L$ and $2 L$ and coefficients of linear expansions $2 \alpha$ and $a$ respectively. If they are welded to form a composite rod of length $3 L$ then the coefficient of linear expansion of the composite rod is