The given question is incomplete. The complete question is as follows.
If gas in a cylinder is maintained at a constant temperature T, the pressure P is related to the volume V by a formula of the form
P = [tex]\frac{nRT}{(V - nb)} - \frac{an^2}{V^2}[/tex], in which a, b, n, and R are constants. Find [tex]\frac{dP}{dV}[/tex].
Explanation:
We will use the quotient rule for each of the two terms on the right side as follows.
P = [tex]\frac{nRT}{V - nb} - \frac{an^{2}}{V^{2}}[/tex]
[tex]\frac{dP}{dV} = \frac{0(V - nb) - nRT(1)}{(V - nb)^{2}} - \frac{0(V)^{2} - an^{2}(2V)}{V^{4}}[/tex]
= [tex]\frac{-nRT}{(V - nb)^{2}} - \frac{-2an^{2}V}{V^{4}}[/tex]
= [tex]\frac{-nRT}{(V - nb)^{2}} + \frac{2an^{2}}{V^{3}}[/tex]
= [tex]\frac{2an^{2}}{V^{3}} - \frac{nRT}{(V - nb)^{2}}[/tex]
[tex]\frac{dP}{dV} = \frac{2an^{2}}{V^{3}} - \frac{nRT}{(V - nb)^{2}}[/tex]
Thus, we can conclude that the value of [tex]\frac{dP}{dV} = \frac{2an^{2}}{V^{3}} - \frac{nRT}{(V - nb)^{2}}[/tex].
