Problem $3(10$ points$)-$ Energy Performance of Electric Heaters versus Heat Pumps

Answer the following questions:

a$.$ Which water heater will use less electricity, a water heater that uses an electric heater, or a water heater that uses an electric heat pump that has a coefficient of performance $($COP$)$ of $4?$

b$.$ A typically sized water heater for a household of $4$ people is $\backslash (0\mathrm{.}25\backslash$mathrm$\{$~m$\}^\{3\}\backslash ).$ Assuming you use the water heater with the electric heater, how much work is required to heat up this volume of water from $\backslash (25^\{\backslash$circ$\}\backslash$mathrm$\{$C$\}\backslash )$ to $\backslash (60^\{\backslash$circ$\}\backslash$mathrm$\{$C$\}\backslash )?$ Assume that the electric heater has an efficiency of $\backslash (100\backslash \%\backslash ).$

c$.$ Repeat the calculation from part $($b$)$ above, except this time assume that you are using the water heater with the electric heat pump $($COP $=4).$

d$.$ You decide to purchase the water heater that uses a heat pump and place it inside one of the rooms in your home. Assuming that the water heater is insulated very well, what effect will the water heater have on the temperature of that room? Would this be a good thing or a bad thing during Arizona's hot summer?