A passive solar house is losing heat to the outside at a rat

A passive solar house is losing heat to the outside at a rate of 55,000 kj/hour. The house is maintained at 22C during a winter night that lasts 10 hours. The owners asks you how many 50 liter water containers are needed so that he will not have to use an electric heater. Each water containers starts the evening at a temp of 70C. Assume the specific heat of the containers is 4.18 kj/kgC and the mass density of water is one kilogram per liter.

Solution

Given: Q = 55000 kJ/hr, t =10hrs = 36000s, c_p = 4.18 kJ/kg^oC, T_w = 70^oC, T_h = 22^oC, m=50 L = 0.05m³

Let n be number of water containers,

Q = 1000*n*m*c_p*(T_w - T_h) /t

Substituting and solving, we get

n = 55