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il63 [147K]
3 years ago
10

A wall in a house contains a single window. The window consists of a single pane of glass whose area is 0.15 m2 and whose thickn

ess is 5 mm. Treat the wall as a slab of the insulating material Styrofoam whose area and thickness are 10 m2 and 0.15 m, respectively. Heat is lost via conduction through the wall and the window. The temperature difference between the inside and outside is the same for the wall and the window. Of the total heat lost by the wall and the window, what is the percentage lost by the window
Engineering
1 answer:
Oxana [17]3 years ago
4 0

Answer:

The percentage loss of the window is  E  = 97.3%

Explanation:

From the question we are told that

      The area of pane of glass is  A = 0.15 m^2

      The thickness is d = 5mm = \frac{5}{1000} = 0.005m

       The thickness of the wall is  D = 0.15m

       The area of the wall is  a = 10m^2

Generally the heat lost as a result of conduction of the window is  

              Q_{window} = \frac{j_{glass} * A * (\Delta T) }{d}

Where j_{glass} is the thermal conductivity of glass which has a constant value of

          j_{glass} = 0.80 J/(s \cdot m \cdot  C^o)

 Substituting values

                 Q_{window} = \frac{ 0.80  * 0.15  * (\Delta T) }{0.005}

                 Q_{window} = 24 \Delta T

Generally the heat lost as a result of conduction of the wall is  

              Q_{wall} = \frac{j_{styrofoam} * A * (\Delta T) }{d}

j_{styrofoam} s the thermal conductivity of Styrofoam which has a constant value of  j_{styrofoam} = 0.010J / (s \cdot m \cdot C^o)

       Substituting values

                 Q_{wall} = \frac{ 0.010  * 10  * (\Delta T) }{0.15}

                 Q_{wall} = 0.667 \  \Delta T

Now the net loss of heat is

         Q_{net} = Q_{window} +  Q_{wall}

  Substituting values

         Q_{net} = 24 + 0.667

         Q_{net} =  24.667

Now the percentage loss by the window is  

            E  = \frac{Q_{window} }{Q_{net}}  * 100

  Substituting value  

           E  = \frac{24}{24 .667}  * 100

           E  = 97.3%

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