To determine the rate of heat flow through the window, we need to use the formula that relates the thermal conductivity, area of the window, thickness, and the temperature difference across the window.
The formula for heat flow rate [tex]\( Q \)[/tex] is:
[tex]\[ Q = \frac{k \cdot A \cdot \Delta T}{d} \][/tex]
where:
- [tex]\( k \)[/tex] is the thermal conductivity (in J/s·m·°C),
- [tex]\( A \)[/tex] is the area of the window (in square meters),
- [tex]\( \Delta T \)[/tex] is the temperature difference (in °C),
- [tex]\( d \)[/tex] is the thickness of the window (in meters).
Let's break this down into steps:
1. Calculate the area of the window:
[tex]\[
A = \text{width} \times \text{height} = 4 \, \text{m} \times 12 \, \text{m} = 48 \, \text{m}^2
\][/tex]
2. Determine the temperature difference:
[tex]\[
\Delta T = \text{temp}_{\text{inside}} - \text{temp}_{\text{outside}} = 20^\circ\text{C} - 13^\circ\text{C} = 7^\circ\text{C}
\][/tex]
3. Given values:
[tex]\[
k = 0.84 \, \text{J/s·m·°C}
\][/tex]
[tex]\[
d = 0.3 \, \text{m}
\][/tex]
4. Plug these values into the heat flow rate formula:
[tex]\[
Q = \frac{k \cdot A \cdot \Delta T}{d}
\][/tex]
[tex]\[
Q = \frac{0.84 \, \text{J/s·m·°C} \times 48 \, \text{m}^2 \times 7^\circ\text{C}}{0.3 \, \text{m}}
\][/tex]
5. Calculate the result step-by-step:
[tex]\[
Q = \frac{0.84 \times 48 \times 7}{0.3}
\][/tex]
[tex]\[
Q = \frac{282.24}{0.3}
\][/tex]
[tex]\[
Q = 940.8 \, \text{J/s}
\][/tex]
This indicates that the rate of heat flow through the window is [tex]\( 940.8 \, \text{J/s} \)[/tex].
Therefore, the correct answer is:
c. 940.8 J/s
