Question

Calculate the energy required to raise the temperature of the water in a 40. gallon home water heater from 18 ºC to 60. ºC (assume the density of water is 1.00 g/ml).

Answer 1

The important factor about this problem is that a ONLY temperature change is involved. Therefore, the equation to use is:

q = (mass) (Δt) (C_p)

This summarizes the information needed:

Δt = (60- 18) °C = 42 °C

volume 40 gallons = 151.416 liters
The mass = Density X volume

                 =1000kg/m3X 151.416 = 151.416kg
C_p = 4.184 J g¯¹ °C¯¹

Only one calculation is needed and it is:

q = (151.416 kg) (42 °C) (4.184 J g¯¹ °C¯¹) = 26608.030848 kjoules