Question

A house has a ktot of 200 w/k (total heat loss coefficient). (a) Calculate the total amount of heat gain in the house if there are: ��� 4 people that generate 65 w of heat per person ��� 600 w of lighting and equipment gains ��� 25 w/m2 of solar flux through windows of 10 m2 area. After finding the total amount of heat gain, (b) find the balance point temperature if ti = 21 ��c.

Answer 1

The total heat gain in the house is 1110 W, contributed by people, lighting, equipment, and solar flux. The balance point temperature, where the internal and external temperatures equalize without additional heating, is 15.45 °C, assuming an inside temperature of 21 °C.

Step-by-step explanation:

To calculate the total amount of heat gain in the house, we add up all the internal heat sources:

• Heat from people: 4 people × 65 W/person = 260 W
• Heat from lighting and equipment: 600 W
• Heat from solar flux: 25 W/m² × 10 m² = 250 W

Total heat gain = 260 W + 600 W + 250 W = 1110 W

To find the balance point temperature (Tbp), we use the heat loss rate (ktot) and the total heat gain as follows:

Heat loss = ktot × (Ti - Tbp)

Since the heat loss equals the heat gain at the balance point, we can set them equal and solve for Tbp:

1110 W = 200 W/°C × (21 °C - Tbp)

Tbp = 21 °C - (1110 W / 200 W/°C)

Tbp = 21 °C - 5.55 °C

Tbp = 15.45 °C

Therefore, if the house generates a total of 1110 W of internal heat, the balance point temperature outside would be 15.45 °C for the inside temperature to remain at 21 °C without any additional heating.