You're having your home's heating system replaced, and the...

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?

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Key Concepts

Heating System Capacity

This concept refers to the maximum power output that a heating system can deliver, typically measured in kilowatts (kW). It is crucial to ensure that the system's capacity is sufficient to counteract the heat losses in a building in extreme weather conditions.

Heat Loss Rate

Heat loss rate quantifies how much energy is lost from a building per unit of time for each degree of temperature difference between the inside and outside. Understanding this helps in calculating the total energy needed to maintain a desired indoor temperature during the coldest weather.

Temperature Differential

The temperature differential is the difference between the desired indoor temperature and the outdoor temperature. This concept directly influences the total heat energy requirement, as a larger differential leads to increased energy loss and higher heating demands.

Comparison of Energy Requirements and System Output

This involves computing the total heat loss by multiplying the heat loss rate by the temperature differential, then comparing this requirement with the heating system's maximum capacity. This assessment determines whether the system can effectively maintain the target indoor temperature under worst-case conditions.

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