The heat loss h (in watts) through a single-pane glass window varies jointly with the window's area A (in square meters) and the difference between the inside and outside temperatures d (in kelvins). Write an equation relating h, A, d, and a constant k. If a single-pane of glass with an area of 1.00 square meter and a temperature difference of 1.00 kelvin has a heat loss of 5.70 watts, then what is the heat loss through a single-pane window with an area of 2.50 square meters and a temperature difference of 20 kelvins?

Question

Phillip Conner

Mathematics

27 March, 22:43

The heat loss h (in watts) through a single-pane glass window varies jointly with the window's area A (in square meters) and the difference between the inside and outside temperatures d (in kelvins). Write an equation relating h, A, d, and a constant k. If a single-pane of glass with an area of 1.00 square meter and a temperature difference of 1.00 kelvin has a heat loss of 5.70 watts, then what is the heat loss through a single-pane window with an area of 2.50 square meters and a temperature difference of 20 kelvins?

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Alexander Garcia · Answer 1

Answer: 285 watts

Step-by-step explanation:

The heat loss h (in watts) through a single-pane glass window varies jointly with the window's area A (in square meters) and the difference between the inside and outside temperatures d (in kelvins). The equation relating h, A, d, and a constant k would be

h = kAd

If a single-pane of glass with an area of 1.00 square meter and a temperature difference of 1.00 kelvin has a heat loss of 5.70 watts, it means that

5.7 = k * 1 * 1

k = 5.7/1 = 5.7

The equation becomes

h = 5.7Ad

Therefore, the heat loss through a single-pane window with an area of 2.50 square meters and a temperature difference of 20 kelvins would be

h = 5.7 * 2.5 * 20

h = 285 watts