The efficiency of a carnot engine is $0.6$.It rejects total $20 \ J$ of heat. The work done by the engine is   …. $J$

In thermodynamic process pressure of a fixed mass of gas is changed in such a manner that the gas releases $30$ joule of heat and $18$ joule of work was done on the gas. If the initial internal energy of the gas was $60$ joule, then, the final internal energy will be  ….. $J$

In a Carnot engine, the temperature of reservoir is $927\ ^oC$ and that of sink is $27\ ^oC.$ If the work done by the engine is $12.6 \times 10^6 J,$ the quantitiy of heat absorbed by the engine from the reservoir is

If $R =$ universal gas constant, the amount of heat needed to raise the temperature of $2\, mol$ of an ideal monoatomic gas from $273\, K$ to $373\, K$ when no work is done is

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 $\left( {\frac{7}{3}} \right){T_0}$. 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