Two moles of a gas are expanded to double their volume by two different processes. One is isobaric and the other is isothermal. If $W_1$ and $W_2$ are the works done, respectively, then:

The $P-V$ diagram shown represents the thermodynamic cycle of an engine operating with an ideal monatomic gas. The amount of heat extracted from the source in a single cycle is:

The efficiency of a thermodynamic cycle $1-2-3-1$ (see picture) is $20\%$ and for another thermodynamic cycle $1-3-4-1$ efficiency is equal to $10\%$. Determine the efficiency $\eta$ (in $\%$) of the thermodynamic cycle $1-2-3-4-1$. The gas is assumed to be ideal.

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.

$A$ cyclic process $ABCD$ is shown in the $P-V$ diagram. Which of the following curves represent the same process?

The figure shows a cylindrical adiabatic container of total volume $2V_0$ divided into two equal parts by a conducting piston (which is free to move). Each part contains an identical gas at pressure $P_0$. Initially,the temperature of the left and right parts is $4T_0$ and $T_0$ respectively. An external force is applied on the piston to keep it at rest. Find the value of the external force required when thermal equilibrium is reached. ($A =$ Area of the piston)