Consider 3 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 woodd 3.0 cm thick(0.33). What is the heat loss through one square meter of wall if the inside temperature is 20 degress celcius and the outside is -10 degrees celcius
Thermal resistance is series can be added. The SI units are, presumably,
Watts/*m^2^*degC)
Total thermal resistance = 0.033 + 2.97 + 0.33 = 3.33 W/m^2*C
Multiply that by tha area (1 m^2) and 30 C for the heat loss rate in Watts.
It looks like 100 Watts.
For a large house, that will lead to a big heating bill in winter.
To calculate the heat loss through a wall, we need to take into account the thermal resistance of each layer and the temperature difference between the inside and outside of the wall.
The total thermal resistance of the wall can be calculated as the sum of the thermal resistances of each layer. The thermal resistance (R) is inversely proportional to the thermal conductivity (k) of the material and the thickness (d) of the layer. Mathematically, it can be expressed as:
R = d / k
For the first layer (plaster), the thermal resistance (R1) can be calculated as:
R1 = 0.01 m / 0.033 SI units = 0.303 SI units
For the second layer (fiberglass insulation), the thermal resistance (R2) can be calculated as:
R2 = 0.089 m / 2.97 SI units = 0.03 SI units
For the third layer (wood), the thermal resistance (R3) can be calculated as:
R3 = 0.03 m / 0.33 SI units = 0.091 SI units
The total thermal resistance of the wall (R_tot) is the sum of R1, R2, and R3:
R_tot = R1 + R2 + R3 = 0.303 + 0.03 + 0.091 = 0.424 SI units
Now, we can calculate the heat loss (Q) through one square meter of the wall using the formula:
Q = (Ti - To) / R_tot
Where:
- Q is the heat loss through the wall in watts (W),
- Ti is the inside temperature in degrees Celsius,
- To is the outside temperature in degrees Celsius, and
- R_tot is the total thermal resistance of the wall in SI units.
Given that Ti = 20 degrees Celsius and To = -10 degrees Celsius, we can substitute these values into the formula:
Q = (20 - (-10)) / 0.424 = 30 / 0.424 ≈ 70.75 W
Therefore, the heat loss through one square meter of the wall is approximately 70.75 watts.