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 ratio of the work done, change in internal energy, and heat absorbed when a diatomic gas expands at constant pressure is

The internal energy of an ideal diatomic gas corresponding to volume $V$ and pressure $P$ is $2.5 PV$. The gas expands from $1 \text{ litre}$ to $2 \text{ litre}$ at a constant pressure of $10^5 \text{ N/m}^2$. The heat supplied to the gas is: (in $\text{ J}$)

Three samples $X, Y$,and $Z$ of the same gas have equal volumes and temperatures. The volume of each sample is doubled. The process is isothermal for $X$,adiabatic for $Y$,and isobaric for $Z$. If the final pressures are equal for the three samples,find the ratio of the initial pressures. (Take adiabatic exponent $\gamma = 3/2$)

An engine operates by taking $n$ moles of an ideal gas through the cycle $ABCDA$ shown in the figure. The thermal efficiency of the engine is: (Take $C_v = 1.5 R$,where $R$ is the gas constant)

An ideal gas,initially in state $(P_{12}, V_1, T_1)$ is expanded isobarically to $(P_{12}, V_2, T_2)$,then adiabatically to $(P_{34}, V_3, T_3)$. It is then contracted isobarically to $(P_{34}, V_4, T_4)$ and finally adiabatically back to the initial state. The efficiency of this cycle is