In the cyclic process shown in the P - V diagram calculate the work done.

Question

In the cyclic process shown in the P - V diagram calculate the work done. (A)  π((V2-V1/2))2  (B)  π((P2-P1/2))2  (C)  (π/4)(P2-p1)(V2-V1)  (D)  π(P2V2-p1V1)

Tardigrade Admin · Accepted Answer

Work done = area enclosed by the cycle consider cycle to be an ellipise ∴ Area =x[(P2-P1/2)] [(V2-V1/2)] =(π/4)(p2-P1)(V2-V1)

Q. In the cyclic process shown in the $P$ - $V$ diagram calculate the work done.

$π (\frac{V _{2} - V _{1}}{2})^{2}$

$π (\frac{P _{2} - P _{1}}{2})^{2}$

$\frac{π}{4} (P_{2} - p_{1}) (V_{2} - V_{1})$

$π (P_{2} V_{2} - p_{1} V_{1})$

Work done = area enclosed by the cycle consider cycle to be an ellipise
$∴$ Area $= x [\frac{P _{2} - P _{1}}{2}] [\frac{V _{2} - V _{1}}{2}]$
$= \frac{π}{4} (p_{2} - P_{1}) (V_{2} - V_{1})$

Q. In the cyclic process shown in the P - V diagram calculate the work done.

π(2V2​−V1​​)2

π(2P2​−P1​​)2

4π​(P2​−p1​)(V2​−V1​)

π(P2​V2​−p1​V1​)