Question Detail
Question
Calculate the rate of heat flowing through a glass window 2.25 m × 1.75 m in area and 3.5 mm in thickness, if the temperatures at the outer and inner surfaces are 29.0°C and 16.0°C, respectively. Take conductivity of glass to be 0.84 J/(m·s·°C).
Correct Answer
Option A is the correct answer.
Detailed Explanation
The rate of heat transfer through a material by conduction is given by:
Rate of heat flow = (k × A × ΔT) / L
Where:
k = thermal conductivity = 0.84 J/(m·s·°C)
A = area of the window
ΔT = temperature difference
L = thickness of the glass
Step 1: Calculate the area
A = 2.25 m × 1.75 m
A = 3.9375 m²
Step 2: Convert thickness to meters
L = 3.5 mm
L = 3.5 × 10⁻³ m
L = 0.0035 m
Step 3: Find the temperature difference
ΔT = 29.0 − 16.0
ΔT = 13 °C
Step 4: Substitute into the formula
Rate = (0.84 × 3.9375 × 13) / 0.0035
Step 5: Calculate
0.84 × 3.9375 = 3.3075
3.3075 × 13 = 42.9975
42.9975 / 0.0035 ≈ 12,285.7
Final Answer:
Rate of heat flow ≈ 1.23 × 10⁴ W (about 12.3 kW).
Hint
Use Fourier's law of heat conduction: Q/t = kAΔT/d.