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 gases $T_f$ , in terms of $T_0$ is

$P-V$ diagram of $2\,g$ of $He$ gas for $A \to B$ process is shown. What is the heat given to the gas ?

A carnot engine, having an efficiency of $\eta  = 1/10$ as heat engine, is used as a refrigetator. If the work done on the system is $10\,J$ , the amount of energy absorbed from the reservoir at lower temperature is ………. $\mathrm{J}$

An ideal heat engine operates on Carnot cycle between $227\,^oC$ and $127\,^oC$. It absorbs $6 \times 10^4\, cal$ at the higher temperature. The amount of heat converted into work equals to

The average degree of freedom per molecule of a gas is $6$ . The gas performs $25\ J$ work, while expanding at constant pressure. The heat absorbed by the gas is   …. $J$