Question

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

The given question is incomplete. The complete question is as follows.

A picture window has dimensions of 1.40 m, 2.50 m and is made of glass 6.00 mm thick. On a winter day, the outside temperature is $-15^{o}C$, while the inside temperature is a comfortable $21.0^{o}C$.

Part A

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

Express your answer using three significant figures.

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)?

Express your answer using three significant figures.

Explanation:

Formula for rate of heat transferred through single thick plane of glass is as follows.

       $(\frac{Q}{\Delta t)}_{single} = \frac{A(T_{h} - T_{c})}{\frac{L_{ghss}}{K_{ghss}}}$

                               = $\frac{1.4 \times 2.5 m^{2} \times 36^{o}C}{\frac{6.0 mm}{0.8 W/m K}}$

                           = $16.8 \times 10^{3} W$

When window is covered by paper then the rate of heat transfer is as follows.

$(\frac{Q}{\Delta t)}_{single} = \frac{A(T_{h} - T_{c})}{\frac{L_{ghss}}{K_{ghss}} + \frac{L_{paper}}{K_{paper}}}$

                 = $\frac{(1.4 \times 2.5 m^{2} \times 36^{o}C}{\frac{6.0 mm}{0.8 W/m K} + \frac{0.75 mm}{0.05 W/m K}}$

                 = $5.6 \times 10^{3} W$

Thus, we can conclude that heat lost is $5.6 \times 10^{3} W$.