One mole of a gas expands such that its volume $V$ changes with absolute temperature $T$ in accordance with the relation $V = K T^2$,where $K$ is a constant. If the temperature of the gas changes by $60 \text{ K}$,then the work done by the gas is ($R$ is the universal gas constant).

The $P-V$ diagram of a certain process (Carnot cycle) is as shown. The process is also represented as:

$A$ quantity of heat $Q$ is supplied to a monoatomic ideal gas which expands at constant pressure. What is the fraction of heat converted into work? Given $\gamma = \frac{C_p}{C_v} = \frac{5}{3}$.

One mole of a monoatomic gas and one mole of a diatomic gas are initially in the same state. Both gases are expanded isothermally and then adiabatically,such that they acquire the same final state. Choose the correct statement.

Given $P_A = 3 \times 10^4 \, Pa$,$P_B = 8 \times 10^4 \, Pa$,$V_A = 2 \times 10^{-3} \, m^3$,and $V_D = 5 \times 10^{-3} \, m^3$. An ideal gas absorbs $600 \, J$ of heat in the process $AB$ and $200 \, J$ of heat in the process $BC$. Find the change in internal energy between $A$ and $C$ in $J$.

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 ..... $K$.