Answer
The efficiency of the cell is 22.5%
Work Step by Step
We can find the rate at which the cell receives energy:
$P_0 = (2.0~mW/cm^2)(5.0~cm^2) = 1.0\times 10^{-4}~W$
We can find the current $i$:
$V = \mathscr{E}-ir$
$i = \frac{\mathscr{E}-V}{r}$
$i = \frac{0.30~V-0.15~V}{1000~\Omega}$
$i = 1.5\times 10^{-4}~A$
We can find the rate at which the cell generates thermal energy:
$P_r = i^2~r$
$P_r = (1.5\times 10^{-4}~A)^2(1000~\Omega)$
$P_r = 2.25\times 10^{-5}~W$
We can find the efficiency of the cell:
$\frac{2.25\times 10^{-5}~W}{1.0\times 10^{-4}~W}\times 100\% = 22.5\%$
The efficiency of the cell is 22.5%
