ABE $3303$ Homework $1$

Problem $1$: A $1500W$ heater is frequently used to heat small rooms. During your morning shower $($on a cold day$)$ you decide to put the plug in the tub and capture the water $(50$ gallons$).$ The water is at $110$ degrees F$.$ You then let the water sit there until the water temperature stabilizes at the temperature of the house $(68F).$ Much of the heat that was contained in the shower water has now been transferred to the house. For how many minutes would you have to run a $1500W$ heater to get the same quantity of heat?

Hint:

The specific heat capacity of water $($Cp$)$ is $4,200$ Joules per kilogram per degree Celsius $(\frac{J}{k}gC).$

Water of density $()$ is $998\mathrm{.}2k\frac{g}{m^3}.$