How much heat is lost in an hour through a glass window measuring 2.0 m by 2.5 m when the inside temperature is 25°C and that of the outside is 5°C, the thickness of the glass is 0.8 cm and the value of k for glass is 0.8Wm⁻¹K⁻¹? Ans. (3.6x10⁷J)


Given:

Time = t = 1 hour = 3600 seconds
Area of the Glass Window = A = 2.0 m ｘ 2.5 m = 5 m² 
Mass of ice  = m = 100 g = 0.1 kg
Temperature inside of window = T₁ = 25°C = (25 + 273) K = 298 K
Temperature inside of home  = T₂ = 5°C = (5 + 273) K = 278 K
Thickness of the Glass= L = 0.8 cm = 0.008 m
Coefficient of Thermal Conductivity of Glass  = k = 0.8 Wm⁻¹K⁻¹

To Find:

Heat Loss through the Glass Window  = Q  = ?

Solution: 


We know that 

Rate of flow of heat = `\frac {Q}{t}` = `\frac {kA (T₁-T₂)}{L}`

0r

Q = `\frac {kA (T₁-T₂)t}{L}`

by putting values

Q = `\frac {0.8 Wm⁻¹K⁻¹ ｘ 5 m² (298 K-278 K)ｘ3600s}{ 0.008 m}`

Q = `\frac {4 WmK⁻¹ ｘ 20K ｘ3600s}{ 0.008 m}`

Q = `\frac {288,000 Wms}{ 0.008 m}`

Q = 36,000,000 Ws

Q = 3.6 ｘ10⁷  Ws

As (1 Watt sec = 1 J ) so,

Q = 3.6 ｘ10⁷  J

Thus Heat Loss through the Glass Window in one hour according the given condition is 3.6 ｘ10⁷  J.  

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