If coefficient of performance of a refrigarator is $\beta $ and heat absorbed from refrigarated space is $Q$, then work done on the system 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 $(7/3)\, T_0$ . 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

An ideal monoatomic gas is taken round the cycle $ABCDA$ as shown in following $P-V$ diagram. The work done during the cycle is

Three moles of an ideal monoatomic gas perform a cycle as shown in the figure. The gas temperature in different states are: $T_1 = 400\, K,\, T_2 = 800\, K,\, T_3 = 2400\, K$ and $T_4 = 1200\,K$ . The work done by the gas during the cycle is  .... $kJ$

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

An ideal gas expands isothermally from a volume $V_1$ to $V_2$ and then compressed to original volume $V_1$ adiabatically. Initial pressure is $P_1$ and final pressure is $P_3$ . The total work done is $W$ . Then