How much thermal mass is needed to absorb solar gains in the

How much thermal mass is needed to absorb solar gains in the proposed building?

What is the minimum amount of thermal mass needed (in Btu/hr) to absorb the daytime solar heat gain through the windows, without rising above 78ºF? (Round the final result to the nearest integer.)

You\'ve been asked to help design a modular computer lab for a school in Sacramento, where average high temperatures are 92°F during the day in July and August. Electricity prices are going up, so you\'d like to avoid having to turn on the air conditioner all summer long. Your plan is to use a building material with good thermal mass, blow outside air over it at night to cool it down, and then let it absorb solar gains during the day. You propose a modular building similar to the one shown. The structure has four 10\'x8\' south-facing windows. Each window receives an average solar radiation intensity of 275 Btu/fta over the course of the day. As the structure has been sited on the school\'s property, there are large shrubs shading the west- facing windows, making the solar gain on that side of the building negligible. You assume that nighttime ventilation will be sufficient to cool the mass to the average daily low temperature of 54°F. To maintain comfortable conditions, your goal is to provide enough mass so that the indoor temperature does not rise above 78°F during the day

Solution

Area of each window

A=10*8 =80 ft²

Total area of 4 windows

A_total=4*80=320 ft²

Amount of solar heat gain in the lab ,if it receives a fullday of sunlight is

Q=275*320

Q=88,000 btu/day

Thermal mass needed is

TM =Q/(T₂-T₁) =88000/(78-54)

TM=3667 BTU/^oF