Two spherical black bodies have radii ' $R_1$ ' and ' $\mathrm{R}_2$ '. Their surface temperatures are ' $\mathrm{T}_1$ ' and ' $T_2$ '. If they radiate same power, then $\frac{R_2}{R_1}$ is

An ideal gas taken through a process ABCA as shown in figure. If the net heat supplied to gas in the cycle is 5 J , then the work done by the gas in process from C to A is

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

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 $\left(\gamma=\frac{C_p}{C_v}\right)$