Black sphere of radius R radiates power P at certain temperature $T$. If the temperature is doubled, the radius gets doubled. Now the power radiated would be

Three samples $X, Y$, and $Z$ of same gas have equal volumes and temperatures. The volume of each sample is doubled, the process being isothermal for X , adiabatic for Y and isobaric for Z . If the final pressures are equal for the three samples, the ratio of the initial pressures is ( $\gamma=3$ / 2)

Two rods of different materials have lengths ' $l$ ' and ' $l_2$ ' whose coefficient of linear expansions are ' $\alpha_1$ ' and ' $\alpha_2$ ' respectively. If the difference between the two lengths is independent of temperature then

The molar specific heat of an ideal gas at constant pressure and constant volume is ' $\mathrm{C}_{\mathrm{p}}$ ' and ' $\mathrm{C}_{\mathrm{v}}$ ' respectively. If ' R ' is a universal gas constant and the ratio of ' $\mathrm{C}_{\mathrm{p}}$ ' to ' $\mathrm{C}_{\mathrm{v}}$ ' is $\gamma$, then ' $\mathrm{C}_{\mathrm{p}}$ ' is equal to