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Answer :
The family room can be up to 125 square feet without exceeding the capacity of the air conditioner.
Describe Heat Capacity?
Heat capacity is a physical property of a substance that describes the amount of heat energy required to raise the temperature of a given mass of the substance by one degree Celsius (or one Kelvin). It is a measure of the substance's ability to absorb heat energy without undergoing a change in temperature.
To determine how many square feet the family room can be without exceeding the capacity of the air conditioner, we need to use the heat capacity formula, which is:
Q = BTU = (Area) × (Temperature Difference) × (Heat Transfer Coefficient)
where:
Q is the heat load in BTU
Area is the area of the room in square feet
Temperature Difference is the difference between the indoor and outdoor temperatures in °F
Heat Transfer Coefficient is a constant that depends on the insulating properties of the materials used in the walls, windows, and roof.
Assuming that the temperature difference is 20°F (a typical value for air conditioning), and using a heat transfer coefficient of 0.2 (a typical value for well-insulated walls), we can rearrange the formula to solve for the maximum area:
Area = Q / (Temperature Difference × Heat Transfer Coefficient)
The capacity of Matt's air conditioner is 5,000 BTU, so:
Area = 5,000 / (20 × 0.2) = 125
Therefore, the family room can be up to 125 square feet without exceeding the capacity of the air conditioner.
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