Q. An ideal gas is taken from point A to the point B, as shown in the p-V diagram, keeping the temperature constant. The work done in the process is
A) $\left( p_{A} - p_{B} \right)(V_{B} - V_{A})$
B) $\frac{1}{2}\ (p_{B} - p_{A})(V_{B} + V_{A})$
C) $\frac{1}{2}\left( p_{B} - p_{A} \right)(V_{B} - V_{A})$
D) $\frac{1}{2}\left( p_{A} + p_{B} \right)(V_{B} - V_{A})$
Explanation
(d) The p-V diagram is shown below
Work done =area of ABCDEA
$= area\ of\ \mathrm{\Delta}ABE + area\ of\ rectangle\ BCDE$
$= \frac{1}{2}\left( p_{A} - p_{B} \right)\left( V_{B} - V_{A} \right) + p_{B}(V_{B} - V_{A})$
$= \left\lbrack \frac{1}{2}\left( p_{A} - p_{B} \right) + p_{B} \right\rbrack(V_{B} - V_{A})$
$= \frac{1}{2}\left( p_{A} + p_{B} \right)(V_{B} - V_{A})$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.