An ideal gas is taken reversibly around the cycle $a-b-c-d-a$ as shown on the temperature $T$ - entropy $S$ diagram. The most appropriate representation of the above cycle on an internal energy $U$ - volume $V$ diagram is

An ideal gas at pressure $P_0$ undergoes an isothermal expansion until its volume is $8.0$ times its initial volume. The gas is slowly and adiabatically compressed back to its original volume. If the adiabatic constant of the gas is $\gamma = 4/3$, then the ratio of the average kinetic energy per molecule in this final state to that in the initial state is

$10 \text{ mole}$ of oxygen is heated at constant volume from $30^{\circ} C$ to $40^{\circ} C$. The change in the internal energy of the gas is . . . . . . $\text{cal}$. (The molecular specific heat of oxygen at constant pressure, $C_p = 7 \text{ cal/mol}^{\circ} C$ and $R = 2 \text{ cal/mol}^{\circ} C$.)

$A$ process is shown in the diagram. Which of the following curves may represent the same process?

$A$ heat engine is involved with an exchange of heat of $1915\, J,$ $-40\, J,$ $+125\, J,$ and $-Q\, J$ during one cycle,achieving an efficiency of $50.0 \%$. The value of $Q$ is ....... $J$.

The specific heat of hydrogen gas at constant pressure is $C_P = 3.4 \times 10^3 \text{ cal/kg } ^oC$ and at constant volume is $C_V = 2.4 \times 10^3 \text{ cal/kg } ^oC$. If $1 \text{ kg}$ of hydrogen gas is heated from $10^oC$ to $20^oC$ at constant pressure,the external work done by the gas is: