In the following p-V diagram, the equation of state along the curved path is given by ${(V - 2)}^{2} = 4 a p,$ where $a$ is a constant. The total work done in the closed path is [2026]

Question

Smart Achievers · Accepted Answer

(4)

$w = Area of parabola$

$= \frac{2}{3} (Area of rectangle A C 31 A)$

$= \frac{2}{3} P_{0} (3 - 1) = \frac{4 P_{0}}{3}$

$When V = 1$

${(1 - 2)}^{2} = 4 a P_{0}$

$P_{0} = \frac{1}{4 a}$

$w = \frac{4}{3} P_{0} = \frac{4}{3} \cdot \frac{1}{4 a} = \frac{1}{3 a}$

$w_{gas} = - \frac{1}{3 a}$

Solution

Q.
In the following p-V diagram, the equation of state along the curved path is given by ${(V - 2)}^{2} = 4 a p,$ where $a$ is a constant. The total work done in the closed path is [2026]

1 $- \frac{1}{a}$

2 $+ \frac{1}{3 a}$

3 $\frac{1}{2 a}$

4 $- \frac{1}{3 a}$

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Solution

Q. In the following p-V diagram, the equation of state along the curved path is given by (V-2)2=4ap, where a is a constant. The total work done in the closed path is [2026]

1 -1a

2 +13a

3 12a

4 -13a