$A$ gas undergoes a change of state during which $100 \ J$ of heat is supplied to it and it does $20 \ J$ of work. The system is brought back to its original state through a process during which $20 \ J$ of heat is released by the gas. The work done by the gas in the second process is ....... $J$

Two cylinders $A$ and $B$ fitted with pistons contain equal amounts of an ideal diatomic gas at $300 \ K$. The piston of $A$ is free to move,while that of $B$ is held fixed. The same amount of heat is given to the gas in each cylinder. If the rise in temperature of the gas in $A$ is $30 \ K$,then the rise in temperature of the gas in $B$ is ..... $K$.

For the $P-V$ diagram of a thermodynamic cycle as shown in the figure,processes $BC$ and $DA$ are isothermal. Which of the corresponding graphs is correct?

Heat energy of $735\,J$ is given to a diatomic gas allowing the gas to expand at constant pressure. Each gas molecule rotates around an internal axis but does not oscillate. The increase in the internal energy of the gas will be $..........\,J$

$A$ monoatomic gas at pressure $P$ having volume $V$ expands isothermally to a volume $3V$ and then adiabatically to a volume $81V$. The final pressure of the gas is $(\gamma = 5/3)$.

What are the limitations of the first law of thermodynamics?