Answer
(a) $382K$
(b) decreasd
(c) $327K$
Work Step by Step
(a) The temperature of the low temperature reservoir can be calculated as
$e=1-\frac{T_c}{T_h}$
This can be rearranged as:
$T_c=(1-e)T_h$
We plug in the known values to obtain:
$T_c=(1-0.3)(545K)$
$T_c=382K$
(b) We know that the efficiency is directly proportional to the temperature difference of both reservoirs, that is $T_h-T_c$. Hence, the low temperature reservoir temperature must be decreased to increase the efficiency of the engine $40\%$.
(c) We can find the required temperature as follows:
$T_c=(1-e)T_k$
We plug in the known values to obtain:
$T_c=(1-0.40)545K$
$T_c=327K$
