Question

A picture window has dimensions of 1.40 m×2.50 m and is made of glass 5.30 mm thick. On a winter day, the outside temperature is -15.0 ∘C , while the inside temperature is a comfortable 21.0 ∘C . Part A At what rate is heat being lost through the window by conduction? Part B At what rate would heat be lost through the window if you covered it with a 0.750 mm-thick layer of paper (thermal conductivity 0.0500 W/m⋅K)?

Answer 1

A.

rate of heat loss is given by:

Q/t = k*A*dT/x

x = thickness of glass = 5.3*10^-3

A = area of window = 1.4*2.5

k = thermal conductivity of window = 0.8W/m-K

dT = temp. difference = 21 - (-15) = 36 C

So using the given values:

Q/t = 0.8*1.4*2.5*36/(5.3*10^-3) = 19018.87 W

Q/t = 19.018 kW

B.

if window is covered with paper:

Q/t = A*dT/[Xg/kg + Xp/kp]

Xp = thichkness of paper = 0.750*10^-3

kp = thermal conductivity of paper = 0.05 W/m-K

So,

Q/t = 1.4*2.5*36/(5.3*10^-3/0.8 + 0.75*10^-3/0.05)

Q/t = 5826.59 W

Q/t = 5.826 kW