On an isothermal process, there are two POINTs `A` and `B` at which pressures and volumes are `(2P_(0), V_(0))` and `(P_(0), 2V_(0))` respectively. If `A` and `B` are connected by a straight line, find the pressure at a POINT on this straight line at which temperature is maximum

Options

A. `(4 P_(0))/(3)`
B. `(5)/(4) P_(0)`
C. `(3)/(2) P_(0)`
D. `(7)/(5) P_(0)`

Answer

C

Explanation

c. `P = - ((P_(0))/(V_(0))) V + 3P_(0)`
`PV = - (P_(0))/(V_(0)) V^(2) + 3 P_(0)V`
or `T = (1)/(nR) [- (P_(0))/(V_(0)) V^(2) + 3 P_(0) V]`
For `T_(max), (dT)/(dV) = 0`
or `+ 3 P_(0) - (2 P_(0) V)/(V_(0)) = 0` or `V = (3)/(2) V_(0)`
From Eq. (i), `P = + (3)/(2) P_(0)`