Question

An exterior wall of a house is 3 m tall and 10 m wide. It consists of a layer of drywall with an R factor of 0.56, a layer 3.5 inches thick filled with fiberglass batts, and a layer of insulated siding with an R factor of 2.6. The wall is built so well that there are no leaks of air through it. When the inside of the wall is at 22°C and the outside is at −2°C, what is the rate of heat flow through the wall?

(b) More realistically, the 3.5-inch space also contains 2-by-4 studs—wooden boards 1.5 inches by 3.5 inches oriented so that 3.5-inch dimension extends from the drywall to the siding. They are "on 16-inch centers," that is, the centers of the studs are 16 inches apart. What is the heat current in this situation? Don’t worry about one stud more or less.

Answer 1

The rate of heat flow through the wall can be calculated using the formula: Rate of heat flow = (Temperature outside - Temperature inside) / (R factor). For a wall with no studs, the rate of heat flow is approximately -7.59°C. For a wall with 2-by-4 studs, the rate of heat flow is approximately -6.99°C.

Step-by-step explanation:

To calculate the rate of heat flow through the wall, we can use the formula:

Rate of heat flow = (Temperature outside - Temperature inside) / (R factor)

For part (a), where there are no studs:

Rate of heat flow = (-2°C - 22°C) / (0.56 + 2.6)

Rate of heat flow = -24°C / 3.16

Rate of heat flow ≈ -7.59°C

For part (b), where there are 2-by-4 studs:

We need to account for the thermal conductivity of the studs. Let's assume the thermal conductivity of wood is around 0.13 W/m·K. We can calculate the R factor for the studs:

R factor of studs = thickness of studs / (k of studs)

R factor of studs = 0.035 m / 0.13 W/m·K

R factor of studs ≈ 0.27 m²·K/W

Now we can calculate the rate of heat flow:

Rate of heat flow = (-2°C - 22°C) / (0.56 + 0.27 + 2.6)

Rate of heat flow = -24°C / 3.43

Rate of heat flow ≈ -6.99°C