Consider three layers of a wall. The first layer is plaster 1.0 cm thick (R = 0.033 SI units), the second layer is fiberglass insulation 8.9 cm thick (R = 2.97), and the outside layer is wood 3.0 cm thick (R = 0.33). What is the heat loss through one square meter of wall if the inside temperature is 20 °C and the outside is −10°C?
To calculate the heat loss through the wall, we need to find the total thermal resistance (R) of each layer, and then use the formula:
Heat loss = (Temperature difference) / (Total thermal resistance)
First, let's calculate the total thermal resistance of each layer:
1. Plaster layer:
R1 = 0.033 SI units
Thickness (d1) = 1.0 cm
2. Fiberglass insulation layer:
R2 = 2.97
Thickness (d2) = 8.9 cm
3. Wood layer:
R3 = 0.33
Thickness (d3) = 3.0 cm
Now, let's calculate the total thermal resistance of each layer:
Total thermal resistance of plaster layer:
R_total1 = R1 / (d1 / 100) (convert thickness from cm to m)
R_total1 = 0.033 / (1.0 / 100)
R_total1 = 3.3 SI units
Total thermal resistance of fiberglass insulation layer:
R_total2 = R2 / (d2 / 100) (convert thickness from cm to m)
R_total2 = 2.97 / (8.9 / 100)
R_total2 = 33.37 SI units
Total thermal resistance of wood layer:
R_total3 = R3 / (d3 / 100) (convert thickness from cm to m)
R_total3 = 0.33 / (3.0 / 100)
R_total3 = 11 SI units
Next, let's find the total thermal resistance of the entire wall:
Total thermal resistance of the wall:
R_total = R_total1 + R_total2 + R_total3
R_total = 3.3 + 33.37 + 11
R_total = 47.67 SI units
Now, we can calculate the heat loss through the wall:
Temperature difference = (20 °C) - (-10 °C) = 30 °C
Heat loss = Temperature difference / R_total
Heat loss = 30 / 47.67
Heat loss ≈ 0.629 W/m^2
Therefore, the heat loss through one square meter of wall is approximately 0.629 W/m^2.
To calculate the heat loss through the wall, we need to first find the overall thermal resistance (R-value) of the wall. The overall R-value is the sum of R-values of each layer in the wall. Let's calculate it step by step.
R-value of the first layer (plaster):
R1 = 0.033 m²·K/W
R-value of the second layer (fiberglass insulation):
R2 = 2.97 m²·K/W
R-value of the third layer (wood):
R3 = 0.33 m²·K/W
Now, we can find the overall R-value of the wall:
R_total = R1 + R2 + R3
Next, we can calculate the temperature difference across the wall:
ΔT = T_inside - T_outside
= 20°C - (-10°C)
= 30°C
The heat loss (q) through the wall can be calculated using the formula:
q = ΔT / R_total
Now, let's substitute the values and calculate the heat loss:
q = 30°C / (R1 + R2 + R3)
= 30°C / (0.033 + 2.97 + 0.33) m²·K/W
= 30°C / 3.333 m²·K/W
≈ 9.003 W
Therefore, the heat loss through one square meter of wall is approximately 9.003 Watts.