In cold climates, including the northern United States, a house can be built wit

Question

In cold climates, including the northern United States, a house can be built with very large windows facing south to take advantage of solar heating. Sunlight shining in during the daytime is absorbed by the floor, interior walls, and objects in the room, raising their temperature to 40.5°C. If the house is well insulated, you may model it as losing energy by heat steadily at the rate 5 825 W on a day in April when the average exterior temperature is 4°C and when the conventional heating system is not used at all. During the period between 5:00 p.m. and 7:00 a.m., the temperature of the house drops and a sufficiently large "thermal mass" is required to keep it from dropping too far. The thermal mass can be a large quantity of stone (with specific heat 850 J/kg · °C) in the floor and the interior walls exposed to sunlight. What mass of stone is required if the temperature is not to drop below 20.0°C overnight?

Answer in kg

Explanation / Answer

The amount of heat that leaves the house over that period is,

Qloss = Ploss * time = 5825 J/s * (14 h * 3600 s/h) = 293580000 J

This has to come from the stone cooling from 40.50C to 200C:

293580000 J = m * 850J/(kg0C) * (40.5-20)0C

=> m = 293580000 J / ( 850J/(kg0C) * (40.5-20)0C)

=> m = 1.68*104 kg

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