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Chapter 16: Problem 36

You're having your home's heating system replaced, and the heating contractor has specified a new system that supplies energy at the maximum rate of \(40 \mathrm{kW}\). You know that your house loses energy at the rate of \(1.3 \mathrm{kW}\) per \(^{\circ} \mathrm{C}\) temperature difference between interior and exterior, and the minimum winter temperature in your area is \(-15^{\circ} \mathrm{C}\). You'd like to maintain \(20^{\circ} \mathrm{C}\left(68^{\circ} \mathrm{F}\right)\) indoors. Should you go with the system your contractor recommends?

Short Answer

Expert verified
No, you should not go with the system your contractor recommends because it is not capable of supplying enough energy to compensate for the energy loss during winter.

Step by step solution

01

Determine the temperature difference

First, we need to calculate the difference in temperature between the interior and exterior of the house during winter. Given that the minimum winter temperature outside is \(-15^{\circ} \mathrm{C}\) and the desired indoor temperature is \(20^{\circ} \mathrm{C}\), the difference is \(20^{\circ} \mathrm{C} - (-15^{\circ} \mathrm{C}) = 35^{\circ} \mathrm{C}\)
02

Calculate the energy loss

We also know that the house loses energy at the rate of \(1.3 \mathrm{kW}\) per \(^{\circ} \mathrm{C}\) temperature difference. So, the total energy loss in the house during peak winter temperature is \(35^{\circ} \mathrm{C} \times 1.3 \mathrm{kW}/^{\circ} \mathrm{C} = 45.5\mathrm{kW}\)
03

Compare with the proposed system

Now, compare this energy loss with the energy supplied by the new heating system, which is \(40 \mathrm{kW}\). If the energy loss is greater than the energy supplied, then the new heating system will not be sufficient. Since \(45.5 \mathrm{kW} > 40 \mathrm{kW}\), the heating system proposed by the contractor isn't enough to counter the energy loss during winter.

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Most popular questions from this chapter

Stainless-steel cookware often has a layer of aluminum or copper embedded in the bottom. Why?

A Canadian meteorologist predicts an overnight low of \(-15^{\circ} \mathrm{C}\) How would a U.S. meteorologist express that prediction?

After a calm, cold night, the temperature a few feet above ground often drops just as the Sun comes up. Explain in terms of convection.

You bring a \(350-\mathrm{g}\) wrench into the house from your car. The house is \(15^{\circ} \mathrm{C}\) warmer than the car, and it takes \(2.52 \mathrm{kJ}\) to warm the wrench by this amount. Find (a) the heat capacity of the wrench and (b) the specific heat of the metal it's made from.

Why does the temperature in a stone building usually vary less than in a wooden building?
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