A nuclear reactor uses a steam Carnot engine which operates by exhausting

heat to the environment. During the winter, the ambient temperature in this region averages

$6\mathrm{.}5$C and the engine has a maximum theoretical efficiency of $57\mathrm{.}5\%.$

a $()$ What is the temperature of the heat reservoir for this engine?

$[$A: Th $=658$ K$]$

b $()$ During the summer, the temperature increases to an average of $29\mathrm{.}5$C$,$ what is the

efficiency during this time if the temperature of the hot reservoir is unchanged?

$[$A: $54\mathrm{.}0\%]$

c $()$ If $200$ m$3/$hr of steam water $($Assume $\backslash$rho $=1\mathrm{.}36\backslash$times $103$ g$/$ml$,$ c $=2\mathrm{.}00$ kJ

kg$$K $)$

circulates in the nuclear reactor, how much extra energy must be produced by the

nuclear reactor heating the steam in a day to increase the efficiency during the same

so that it is the same during the winter?