Answer
$e_D \lt(e_B\approx e_C)\lt e_A$
Work Step by Step
We can rank the given reservoir temperatures in order of increasing efficiency as follows:
$e=1-\frac{T_c}{T_h}$
We plug in the known values to obtain:
$e=1-\frac{400K}{800K}$
$e=1-\frac{1}{2}$
$e=\frac{1}{2}=50\%$
(b) $e=1-\frac{T_c}{T_h}$
We plug in the known values to obtain:
$e=1-\frac{400K}{600K}$
$e=1-\frac{2}{3}$
$e=\frac{1}{3}=33.3\%$
(c) $e=1-\frac{T_c}{T_h}$
We plug in the known values to obtain:
$e=1-\frac{800K}{1200K}$
$e=1-\frac{2}{3}$
$e=\frac{1}{3}=33.3\%$
(d) $e=1-\frac{T_c}{T_h}$
We plug in the known values to obtain:
$e=1-\frac{800K}{1000K}$
$e=1-\frac{4}{5}$
$e=\frac{1}{5}=20\%$
Now the order of increasing efficiencies is given as
$e_D \lt(e_B\approx e_C)\lt e_A$
