The equation of state of a gas is (P+aT2V)×Vc1=(RT+b) where a, b, c and R are constants. The isotherms can be represented by P=AVm−BVn where A and B depend only on temperature. Then,
m = - c, n = -1
Expanding the equation of state we have
PVc+aT2 Vc−1=RT+bor P=−aT2 V−1+RT V−c+bV−cor P=AV−c−BV−1 .....(i)where A=RT+b and B=aT2. We are given that P=A Vm−BVn .......(ii)
Comparing the power of V in (i) and (ii) we get m = -c and n = -1.