Q. The equation of state of a gas is given by $\left( P + \frac{aT^{2}}{V} \right)V^{c} = (RT + b),$ where $a,b,c$ and $R$ are constants. The isotherms can be represented by $P = AV^{m} - BV^{n},$ where $A$ and $B$ depend only on temperature and
A) $m = - c$ and $n = - 1$
B) $m = c$ and $n = 1$
C) $m = - c$ and $n = 1$
D) $m = c$ and $n = - 1$
Explanation
(a) $\left( P + \frac{aT^{2}}{V} \right)V^{c} = (RT + b) \Rightarrow P = (RT + b)V^{- c} - \left( aT^{2} \right)V^{- 1}$
Comparing this equation with $P = AV^{m} - BV^{n}$
We get $m = - c$ and $n = - 1$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.