A picture window has dimensions of 1.40 m×2.50 m and is made of glass 5.30 mm th

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 20.0 C .

(PLEASE EXPLAIN ALL THE STEPS TO GET TO THE ANSWER, THANKS)

Part A

At what rate is heat being lost through the window by conduction?

Express your answer using three significant figures.

H = _____ W

Part B

At what rate would heat be lost through the window if you covered it with a 0.750mm-thick layer of paper (thermal conductivity 0.0500 W/mK)?

Express your answer using three significant figures.

Explanation / Answer

Rate of heat loss , dH/dt = kA*/L
= temp.difference, L = glass thickness

dH/dt = 0.80 * (1.40 * 2.50)m² * (15.0 + 20.0) / 0.0053 m
dH/dt = 18490.5 J/s
dH/dt = 18490.5 W

Rate is heat being lost through the window by conduction, dH/dt = 18490.5 W

(B)
Let T_interface be the temperature at the glass-paper interface. Then:

q = -k_glass*(T_interior - T_interface)/(5.30mm) = -k_paper*(T_interface - T_outside)/(0.750mm)
0.8 * (20 - Tin) / (5.30) = 0.05 * (Tin + 15) / 0.750
Tin = 9.3 o

Now,
q = k_glass*(T_interior - T_interface)/(5.30mm)
q = 0.8 * (20 - 9.3) / (5.30)
q =  1615

dh/dt = 1615 * (1.40 * 2.50) W
dh/dt = 5652.85 W

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