The efficiency of a Carnot's heat engine is $\frac{1}{3}$. If the temperature of the source is decreased by $50^{\circ} \mathrm{C}$ and the temperature of the sink is increased by $25^{\circ} \mathrm{C}$, the efficiency of the engine becomes $\frac{3}{16}$. The initial temperature of the sink is

The change in internal energy of given mass of a gas, when its volume changes from $V$ to $3 V$ at constant pressure $p$ is

( $\gamma=$ Ratio of the specific heat capacities of the gas)

A monoatomic gas at a pressure of 100 kPa expands adiabatically such that its final volume becomes 8 times its initial volume. If the work done during the process is 180 J , then the initial volume of the gas is

If a gaseous mixture consists of 3 moles of oxygen and 4 moles of argon at an absolute temperature $T$, then the total internal energy of the mixture is (neglect vibrational modes and $R=$ Universal gas constant)