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 kW. You know that your house loses energy at the rate of 1.3 kW per temperature difference between interior and exterior, and the minimum winter temperature in your area is You’d like to maintain indoors. Should you go with the system your contractor recommends?

Question

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 kW. You know that your house loses energy at the rate of 1.3 kW per temperature difference between interior and exterior, and the minimum winter temperature in your area is You’d like to maintain indoors. Should you go with the system your contractor recommends?

Answer 1

what temp outside?

what temp inside?

kw needed = 1.3(temp difference)

Answer 2

To determine whether you should go with the heating system recommended by your contractor, we need to calculate the heating requirements for your house.

The formula to calculate the heating requirements is:

Heat loss (kW) = U-value (W/m²K) x Area (m²) x Temperature difference (K)

However, in this case, we are given the heat loss rate per temperature difference, so we'll rearrange the formula:

Temperature difference (K) = Heat loss (kW) / Heat loss rate (kW/K)

Let's calculate the temperature difference using the given heat loss rate of 1.3 kW per temperature difference:

Temperature difference = 40 kW / 1.3 kW/K
Temperature difference ≈ 30.77 K

Now, subtract the minimum winter temperature in your area from the desired indoor temperature:

Temperature difference = Desired indoor temperature - Minimum winter temperature

Let's assume the desired indoor temperature is 20°C (293.15 K):

Temperature difference = 293.15 K - Minimum winter temperature

Now, we can compare the two temperature differences to see if they are within a reasonable range.

If the temperature difference calculated using the heat loss rate by the contractor is smaller than the temperature difference calculated using the desired indoor temperature and the minimum winter temperature, then the recommended heating system should be sufficient.

If the temperature difference calculated using the heat loss rate is larger, it means that the recommended system may not be able to provide enough heating capacity to maintain the desired indoor temperature.

Therefore, compare the two temperature differences and make a decision based on which one is larger.