The equation of state of gas is given `(P + (aT^(2))/(V))V^( c) = (RT + b)` where `a, b, c` and `R` are constant. The isotherms can be represented by `P = AV^(m) - BV^(n)`, where `A` and `B` depend only on temperature and

Options

A. `m = -c` and `n = -1`
B. `m = c` and `n = 1`
C. `m = - c` and `n = 1`
D. `m = c` and `n = -1`

Answer

A

Explanation

`(P + (aT^(2))/(V)) V^(c ) = RT + b`
`P = (RT + b)/(V^(c )) - (aT^(2))/(V)` (i)
`P = AV^(m) - BV^(n)` (ii)
Comparing (i) and (ii)
`m = - c, n = -1`