Question

Three different processes that can occur in an ideal monoatomic gas are shown in the $P$ vs $V$ diagram. The paths are labelled as $A\to B$, $A\to C$ and $A\to D$. The change in internal energies during these process are taken as $E_{AB},E_{AC}$ and $E_{AD}$ and the workdone as $W_{AB},W_{AC}$ and $W_{AD}$. The correct relation between these parameters are

• A. $E_{AB}=E_{AC}<E_{AD},W_{AB}>0,W_{AC}=0,W_{AD}<0$
• B. $E_{AB}=E_{AC}=E_{AD},W_{AB}>0,W_{AC}=0,W_{AD}<0$
• C. $E_{AB}<E_{AC}<E_{AD},W_{AB}>0,W_{AC}>W_{AD}$
• D. $E_{AB}>E_{AC}>E_{AD},W_{AB}<W_{AC}<W_{AD}$

Answer 1

The correct option is B $E_{AB}=E_{AC}=E_{AD},W_{AB}>0,W_{AC}=0,W_{AD}<0$

Temperature change $\Delta T$ is same for all three processes $A\to B,A\to C$ and $A\to D$
$\Delta U=n{C}_v\Delta T=$ same
$E_{AB}=E_{AC}=E_{AD}$
Work done, $W=P\times \Delta V$
For process $AB\to$ volume is increasing $\Rightarrow W_{AB}>0$
For process $AD\to$ volume is decreasing $\Rightarrow W_{AD}<0$
For process $AC\to$ volume is constant $\Rightarrow W_{AC}=0$