Consider two processes on a system as shown in figure. The volume… - Vidyadip

Question

Consider two processes on a system as shown in figure.

The volumes in the initial states are the same in the two processes and the volumes in the final states are also the same. Let $\Delta\text{W}_1$ and $\Delta\text{W}_2$ be the work done by the system in the processes A and B respectively.

$\Delta\text{W}_1>\Delta\text{W}_2.$
$\Delta\text{W}_1=\Delta\text{W}_2.$
$\Delta\text{W}_1<\Delta\text{W}_2.$
Nothing can be said about the relation between $\Delta\text{W}_1$ and $\Delta\text{W}_2.$

✓

Answer

$\Delta\text{W}_1<\Delta\text{W}_2.$

Explanation:

Work done by the system, $\Delta\text{W}=\text{P}\Delta\text{V}$

Here,

P = Pressure in the process

$\Delta\text{V}$ = Change in volume during the process

Let V_i and V_f be the volumes in the initial states and final states for processes A and B, respectively. Then,

$\Delta\text{W}_1=\text{P}_1\Delta\text{V}_1$

$\Delta\text{W}_2=\text{P}_2\Delta\text{V}_2$

But $\Delta\text{V}_2=\Delta\text{V}_1,$ $\big[(\text{V}_{\text{f}_1}-\text{V}_{\text{i}_1})=(\text{V}_{\text{f}_2}-\text{V}_{\text{i}_2})\big]$

$\Rightarrow\frac{\Delta\text{W}_1}{\Delta\text{W}_2}=\frac{\text{P}_1}{\text{P}_2}$

$\Rightarrow\Delta\text{W}_1<\Delta\text{W}_2\ [\because\text{P}_2>\text{P}_1]$

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