Question

A wall of dimensions $2.00m$ by $3.50m$ has a single-pane window of dimensions $0.75$m by $1.20m$ If the inside temperature is $20$ and the outside temperature is $-10$, effective thermal resistance of the opaque wall and window are $2.10K{W}^{-1}$ and $0.21K{W}^{-1}$ respectively. The heat flow through the entire wall will be.

• A. $215W$
• B. $205W$
• C. $175W$
• D. $110W$

Answer 1

The correct option is A $215W$

The wall and the window are in a parallel arrangement, so net heat flow is the sum of the heat flow through the wall and the window.
The temperature difference,
$T_H-T_C=30K$
Area of window,
$A_1=\left(0.75\right)\left(1.20\right)=0.90$
Heat flow through window pane,
${\left(\frac{dQ}{dt}\right)}_1=\frac{T_H-T_C}{R_1}$

$=\left(0.90\right)\frac{30}{0.21}$

$=128.6W$
The area of the wall,
Heat flow through the wall,
${\left(\frac{dQ}{dt}\right)}_2=\frac{T_H-T_C}{R_2}$

$=\frac{\left(6.10\right)\left(30\right)}{\left(2.10\right)}$

$=87W$
Net heat flow, $\frac{dQ}{dt}=128.6+87$

$=215.6W$