Question

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 then

• 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 1

Answer: (A)

$m = - c$and$n = - 1$

Answer 2

$\left( P + \frac{aT^{2}}{V} \right)V^{c} = RT + b$

⇒ $P + aT^{2}V^{- 1} = RTV^{- c} + bV^{- c}$

⇒ $P = (RT + b)V^{- c} - (aT^{2})V^{- 1}$

By comparing this equation with given equation $P = AV^{m} - BV^{n}$ we get $m = - c$ and $n = - 1$.