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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
$E _{ AB }= E _{ AC }= E _{ AD }, W _{ AB }>0, W _{ AC }=0,$ $W _{ AD }>0$
$E _{ AB }< E _{ AC }< E _{ AD }, W _{ AB }>0, W _{ AC }> W _{ AD }$
$E _{ AB }= E _{ AC }< E _{ AD }, W _{ AB }>0, W _{ AC }=0$ $W _{ AD }<0$
$E _{ AB }> E _{ AC }> E _{ AD }, W _{ AB }< W _{ AC }< W _{ AD }$
Solution
$\Delta U = nC _{ v } \Delta T =$ same
$AB \rightarrow$ volume is increasing $\Rightarrow W >0$
$AD \rightarrow$ volume is decreasing $\Rightarrow W <0$
$AC \rightarrow$ volume is constant $\Rightarrow W =0$
