Question

A window has a glass surface of 2314 cm2 and a thickness of 3.5 mm.

A) Find the rate of energy transfer by conduc- tion through this pane when the temperature of the inside surface of the glass is 71◦F and the outside temperature is 81 ◦F. Assume the thermal conductivity of window glass is 0.8 J/s · m · ◦ C. Answer in units of kW.

B) Find the rate of energy transfer for the same inside temperature and an outside tempera- ture of 0◦F. Answer in units of kW.

Answer 1

Area A = 2314 cm ²

= 0.2314 m ²

Thickness L = 3.5 x10 ^-3 m

the thermal conductivity of window glass K = 0.8 J/s · m · ◦ C

Temperature difference dF = 81 ^o F - 71 ^o F = 10 ^o F

We know dC / 100 = dF / 180

dC = (100/180) (10 )

= 5.555 ^o C

the rate of energy transfer by conduc- tion through this pane when the temperature of the inside surface of the glass is 71◦F and the outside temperature is 81 ◦F is

Q = KAdC / L

= (0.8)(0.2314)(5.5555) /(3.5 x10 ^-3 )

= 293.84 W

= 0.29384 kW

(B).

Temperature difference dF = 71 ^o F - 0 ^o F = 70 ^o F

We know dC / 100 = dF / 180

dC = (100/180) (70 )

= 38.888 ^o C

the rate of energy transfer for the same inside temperature and an outside tempera- ture of 0◦F is

Q ' = KAdC / L

= (0.8)(0.2314)(38.8888) /(3.5 x10 ^-3 )

= 2056.88 W

= 2.05688 kW