JEE PYQ: Thermodynamics Question 22
Question 22 - 2020 (05 Sep Shift 1)
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 processes 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 :
(1) $E_{AB} = E_{AC} < E_{AD}$, $W_{AB} > 0$, $W_{AC} = 0$, $W_{AD} < 0$
(2) $E_{AB} = E_{AC} = E_{AD}$, $W_{AB} > 0$, $W_{AC} = 0$, $W_{AD} > 0$
(3) $E_{AB} < E_{AC} < E_{AD}$, $W_{AB} > 0$, $W_{AC} > W_{AD}$
(4) $E_{AB} > E_{AC} > E_{AD}$, $W_{AB} < W_{AC} < W_{AD}$
Show Answer
Answer: (2)
Solution
Temperature change $\Delta T$ is same for all three processes $A \to B$; $A \to C$ and $A \to D$.
$\Delta U = nC_v\Delta T =$ same
$E_{AB} = E_{AC} = E_{AD}$
Work done, $W = P \times \Delta V$
$AB \to$ volume is increasing $\Rightarrow W_{AB} > 0$
$AD \to$ volume is decreasing $\Rightarrow W_{AD} < 0$
$AC \to$ volume is constant $\Rightarrow W_{AC} = 0$
BETA
