Question

On a cool night, a passive solar house is losing 20,000 kJ/hr to the outside surroundings. The house contains 75 kg air and a water tank which when exposed to sunlight during the day heats up to 80 oC. What is the mass of water in the tank required to maintain the house air temperature at 22 oC for 10 hours overnight? The Cp for water is 4.184 kJ/kg/K and Cv for air = 0.718 kJ/kg/K.

Answer 1

`m = 824.157\,kg`

Step-by-step explanation:

The total amount of heat released from the passive solar house is:

`Q = \left(20000\,(kJ)/(h) \right)\cdot (10\,h)`

`Q = 200000\,kJ`

The mass of water required to maintain indoor air temperature is:

`m = (200000\,kJ)/(\left(4.184\,(kJ)/(kg\cdot K) \right)\cdot (80\,^(\circ)C - 22\,^(\circ)C))`

`m = 824.157\,kg`