• Jun 13th 2006, 12:26 PM
mayster17
Could somebody Please work this problem out for me ?

The thermal efficiency,e, of a heat engine is
defined by e = (Qh-Qc)/Qh, where Qh is the heat absorbed in one cycle and Qc is the heat released into a reservoir in one cycle. Find (d^2e)/(dQh^2).
• Jun 13th 2006, 12:53 PM
CaptainBlack
Quote:

Originally Posted by mayster17
Could somebody Please work this problem out for me ?

The thermal efficiency,e, of a heat engine is
defined by e = (Qh-Qc)/Qh, where Qh is the heat absorbed in one cycle and Qc is the heat released into a reservoir in one cycle. Find (d^2e)/(dQh^2).

$e=\frac{Q_h-Q_c}{Q_h}=1-\frac{Q_c}{Q_h}$

Assuming that $Q_c$ is not a function of $Q_h$:

$\frac{de}{dQ_h}=\frac{Q_c}{Q_h^2}$

so:

$\frac{d^2e}{dQ_h^2}=-2\frac{Q_c}{Q_h^3}$

RonL