In the following $p - V$ diagram the equation of state along the curved path is given by $(V - 2)^{2

Question

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

Accepted Answer

$W =$ Area of parabola$$\begin{matrix} & \ = \frac{2}{3}(	ext{~}	ext{Area of rectangle}	ext{~}AC31	ext{ }A) \ & \ = \frac{2}{3}P_{0}(3 - 1) = \frac{4P_{0}}{3} \end{matrix}$$When $V = 1$$$\begin{matrix} & \ (1 - 2)^{2} = 4{aP}_{0} \ & P_{0} = \frac{1}{4a} \ & 	ext{ }W = \frac{4}{3}P_{0} = \frac{4}{3}\frac{1}{4a} = \frac{1}{3a} \ & {	ext{ }W}_{	ext{gas~}} = \frac{- 1}{3a} \end{matrix}$$

Question

Options

Solution

More Thermodynamics Questions