A calorimeter contains 10 g of water at $20^{\circ} \mathrm{C}$. The temperature fall to $15^{\circ} \mathrm{C}$ in 10 min . When calorimeter contains 20 g of water at $20^{\circ} \mathrm{C}$, it takes 15 min . for the temperature to become $15^{\circ} \mathrm{C}$. The water equivalent at the calorimeter is

Under isothermal conditions, two soap bubbles of radii $r_1$ and $r_2$ coalesce to form a big drop. The radius of the big drop is

The frequencies for series limit of Balmer and Paschen series are ' $\mathrm{V}_1$ ' and ' $\mathrm{V}_3$ ' respectively. If frequency of first line of Balmer series ' $\mathrm{V}_2$ ' then the relation between $V_1, V_2$ and $V_3$ is

Two cylinders A and B fitted with piston contain equal amount of an ideal diatomic gas at temperature T K. The piston of cylinder A is free to move while that of cylinder $B$ is held fixed. The same amount of heat is given to the gas in each cylinder. If the rise of temperature of the gas in A is $\mathrm{dT}_{\mathrm{A}}$, then the rise in temperature of the gas in B is $\left(\gamma=\frac{C_p}{C_v}\right)$