Question

The inner and outer surfaces of a 0.5 cm thick 2m x 2m window glass are 10°C and 3°C, respectively. If the thermal conductivity of the glass is 0.78 W/m*K, determine the amount of heat loss through the glass over a period of 5 hours.
1. What would be the answer if the glass were 1 cm thick?

Answer 1

Answer:

a) 78.6 MJ  b) 39.3 MJ

Explanation:

Assuming that the temperatures remain constant during the 5 hours, we can calculate the amount of the heat loss through the glass over this period, as follows:

ΔQ = $\frac{k*A*(Ti-To)*t}{d}$

where k = thermal conductivity of glass = 0.78 W/m*K

          A =  area of the window = 2m * 2 m = 4 m²

          Ti = temperature on the inner surface = 10ºC

          Ti = temperature on the outer surface = 3ºC

           d = glass layer thick = 0.5 cm = 0.005 m

            t = time over which the heat is lost = 5 hs = 18,000 sec

Replacing these values in the equation above:

ΔQ =$\frac{0.78 W/m*K*4 m2*7K*1.8e4s}{5e-3m} = 78.6 MJ$

If the glass layer were 1 cm thick, the above expression would become as follows:

ΔQ = $\frac{0.78 W/m*K*4 m2*7K*1.8e4s}{1e-2m} = 39.3 MJ$