Three different processes that can occur in an ideal monoatomic gas are shown in the $P$ vs $V$ diagram. The paths are labelled as $A \rightarrow B, A \rightarrow C$ and $A \rightarrow D .$ The change in internal energies during these process are taken as $E _{ AB }, E _{ AC }$ and $E _{ AD }$ and the work done as $W _{ AB }$ $W _{ AC }$ and $W _{ AD }$

The correct relation between these parameters are

If one mole of an ideal gas at $\left( P _{1}, V _{1}\right)$ is allowed to expand reversibly and isothermally ($A$ to $B$ ) its pressure is reduced to one-half of the original pressure (see $figure$). This is followed by a constant volume cooling till its pressure is reduced to one-fourth of the initial value $( B \rightarrow C ) .$ Then it is restored to its initial state by a reversible adiabatic compression ($C$ to $A$). The net workdone by the gas is equal to  …… .

A diatomic ideal gas undergoes a thermodynamic change according to the $P-V$ diagram shown in the figure. The heat given the gas in $AB$

$n$ mole a perfect gas undergoes a cyclic process $ABCA$ (see figure) consisting of the following processes.

$A \rightarrow B :$ Isothermal expansion at temperature $T$ so that the volume is doubled from $V _{1}$ to $V _{2}=2 V _{1}$ and pressure changes from $P _{1}$ to $P _{2}$

$B \rightarrow C :$ Isobaric compression at pressure $P _{2}$ to initial volume $V _{1}$

$C \rightarrow A$ : Isochoric change leading to change of pressure from $P _{2}$ to $P _{1}$

Total workdone in the complete cycle $ABCA$ is

Thermodynamic processes are indicated in the following diagram. 

Match the following

 $\begin{array}{|l|l|} \hline Column\,\,-\,\,1 & Column\,\,-\,\,2 \\ \hline P\,:\,Process\,\,-\,\,I & \,\,A\,\,:\,\,Adiabatic \\ \hline Q\,:\,Process\,\,-\,\,II & \,\,B\,\,:\,\,Isobaric \\ \hline R\,:\,Process\,\,-\,\,III & \,\,C\,\,:\,\,Isochoric \\ \hline S\,:\,Process\,\,-\,\,IV & \,\,D\,\,:\,\,Isothermal \\ \hline \end{array}$