A nuclear reactor uses a steam Carnot engine which operates by exhaustingheat 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?b $()$ During the summer, the temperature increases to an average of $29\mathrm{.}5$C$,$ what is theefficiency during this time if the temperature of the hot reservoir is unchanged?c $()$ If $200$ m$3/$hr of steam water $($Assume $=1\mathrm{.}36\backslash$times $103$ g$/$ml$,$ c $=2\mathrm{.}00$ kJkg$$K $)$circulates in the nuclear reactor, how much extra energy must be produced by thenuclear reactor heating the steam in a day to increase the efficiency during the sameso that it is the same during the winter?