$1.(0\mathrm{.}5)$ During an experiment conducted in a room at $\backslash (25^\{\backslash$circ$\}\backslash$mathrm$\{$C$\}\backslash ),$ a laboratory assistant measures that a refrigerator that draws $2$ kW of power has removed $\backslash (30,000\backslash$mathrm$\{$~kJ$\}\backslash )$ of heat from the refrigerated space, which is maintained at $\backslash (-30^\{\backslash$circ$\}\backslash$mathrm$\{$C$\}\backslash ).$ The running time of the refrigerator during the experiment was $20$ minutes. Determine if these measurements are reasonable by providing calculations.

$2.$ A heat engine receives heat from a source at $\backslash (2190^\{\backslash$circ$\}\backslash$mathrm$\{$F$\}\backslash )$ and has a Carnot thermal efficiency of $\backslash (40\backslash \%\backslash ).$ The heat engine does maximum work equal to $475$ Btu $.$ Determine:

a$.(0\mathrm{.}15)$ The heat supplied to the heat engine by the heat source, in Btu

b$.(0\mathrm{.}15)$ The heat rejected to the heat sink, in Btu

c$.(0\mathrm{.}2)$ The temperature of the heat sink, in $\backslash (\{\}^\{\backslash$circ$\}\backslash$mathrm$\{$F$\}\backslash )$