JEE Main 2006 — Thermodynamics

The work of $146 \mathrm{~kJ}$ is performed in order to compress one kilo mole of gas adiabatically and in this process the temperature of the gas increases by $7^{\circ} \mathrm{C}$. The gas is $\left(\mathrm{R}=8.3 \mathrm{~J} \mathrm{~mol}^{-1} \mathrm{~K}^{-1}\right)$

Assuming the sun to be a spherical body of radius $\mathrm{R}$ at a temperature of $\mathrm{T} \mathrm{K}$, evaluate the total radiant power, incident on Earth, at a distance $r$ from the Sun.

Two rigid boxes containing different ideal gases are placed on a table. Box A contains one mole of nitrogen at temperature $T_0$, while Box $B$ contains one mole of helium at temperature $(7 / 3) T_0$. The boxes are then put into thermal contact with each other and heat flows between them until the gases reach a common final temperature. (Ignore the heat capacity of boxes). Then, the final temperature of the gases, $T_f$, in terms of $T_0$ is