Question

The rate of heat conduction out of a window on a winter day is rapid enough to chill the air next to it. To see just how rapidly windows conduct heat, calculate the rate of conduction in watts through a 2.82 m2 window that is 0.675 cm thick if the temperatures of the inner and outer surfaces are 5.00°C and −10.0°C, respectively. This rapid rate will not be maintained — the inner surface will cool, and frost may even form. The thermal conductivity of glass is 0.84 J/(s · m · °C).

Answer 1

Q = - 5264 W = - 5.26 KW

Here, negative sign indicates the outflow of heat

Step-by-step explanation:

Fourier's Law of heat conduction, gives the following formula:

Q = - KAΔT/t

where,

Q = Rate of Heat Conduction out of window = ?

K = Thermal Conductivity of Glass = 0.84 W/m.°C

A =Surface Area of window = 2.82 m²

ΔT = Difference in Temperature of both sides of surface

ΔT = Inner Surface Temperature - Outer Surface Temperature= 5°C - (- 10°C)

ΔT = 15°C

t = thickness of window = 0.675 cm = 0.00675 m

Therefore,

Q = - (0.84 W/m.°C)(2.82 m²)(15°C)/0.00675 m

Q = - 5264 W = - 5.26 KW

Here, negative sign indicates the outflow of heat.