First slide

Thermodynamic processes

Question

On an isothermal process, there are two points A and B at which pressures and volumes are (2P₀, V₀) and (P₀, 2V₀) 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:

Moderate

A

$\frac{4 P_{0}}{3}$
B

$\frac{5}{4} P_{0}$
C

$\frac{3}{2} P_{0}$
D

$\frac{7}{5} P_{0}$

Solution

$P = - (\frac{P_{0}}{V_{0}}) V + 3 P_{0}$
$PV = - \frac{P_{0}}{V_{0}} V^{2} + 3 P_{0} V$ ………(i)
$T = \frac{1}{nR} [- \frac{P_{0}}{V_{0}} V^{2} + 3 P_{0} V]$ ………(ii)
For $T_{max}, \frac{dT}{dV} = 0$
$+ 3 P_{0} - \frac{2 P_{0} V}{V_{0}} = 0 or V = \frac{3}{2} V_{0}$ ………(iii)
From Eq. (i), $P = + \frac{3}{2} P_{0}$

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