An idealized representation of the air temperature as a function of distance from a single-pane window on a calm, winter day is shown in figure. The window dimensions are 60 cm × 60 cm × 0.50 cm. k ai

Question

An idealized representation of the air temperature as a function of distance from a single-pane window on a calm, winter day is shown in figure. The window dimensions are 60 cm × 60 cm × 0.50 cm. $k_{air} =$ $0.026 W / m - K, k_{glass} = 1.0 W / m - K$ . If rate of heat flow out through the window is 0.6 x then find the value of x.

TestHub · Accepted Answer

From the graph, the air temperature changes by 15 K across 8 cm.
$\frac{Δ T}{Δ x} = \frac{15}{0.08} = 187.5 K/m$
$A = 0.60 \times 0.60 = 0.36 m^{2}$
$\dot{Q} = k A \frac{Δ T}{Δ x}$
$\dot{Q} = 0.026 \times 0.36 \times 187.5 = 1.755 W \approx 1.8 W$
$0.6 x = 1.8 \Rightarrow x = 3$

Physics - Heat & Thermo Question with Solution | TestHub

Doubts & Discussion