A picture window has dimensions of 1.40 m×2.50 m and is made of glass 5.50 mm th

Question

A picture window has dimensions of 1.40 m×2.50 m and is made of glass 5.50 mm thick. On a winter day, the outside temperature is -17.0 C , while the inside temperature is a comfortable 20.5 C .

A. At what rate is heat being lost through the window by conduction? Express your answer using three significant figures.

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/mK)? Express your answer using three significant figures.

Explanation / Answer

area A = 1.40*2.50 = 3.5 m^2

glass thickness L = 5.50 mm = 0.0055 m

T2 = -17 C = -17+273 = 256 K

T1 = 20.5 C = 293.5 K

we know that

rate of heat loss dH/dt = -k*A*(T2-T1) / L

kglass = 0.8 W/mK

dH/dt = -0.8*3.5*(-293.5+256) / 0.0055

dH/dt = 19090.90 J/s

(b)

using fourier's law

heat flux q = -k*dT/L

k is the thermal conductivity.

the heat flux b/w two reservoirs remains constant

let temperature at the glass-paper interface = T

q1 = q2

-kglass*(T1 - T) / 0.0055 = -kpaper*(T - T2) / 0.0075

put alll the values

0.8*(20.5 - T) / 0.0055 = 0.05*(T + 17.5) / 0.0075

0.1181 = 0.00875*T

T = 13.49 C

heat flux q = -0.8*(20.5 - 13.49 ) / 0.0055

q = -1018.59 W/m^2

heat loss = q*A = -1018.59* 3.5

heat loss = -3565.09 W

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