91Ó°ÊÓ

1. Thickness of the glass,$L=3.0\text{mmor}0.003\text{″¾}$
2. Thermal conductivity of the glass,$k_{glass}=1\text{ W/³¾°­}$
3. Thermal conductivity of air,$k_{air}=0.026\text{ W/³¾°­}$
4. The surroundings temperature,$T_{out}=−20\text{ °¹óor}244.26\text{‿é}$
5. The internal temperature,$T_{in}=+72\text{ °¹óor}295.37\text{‿é}$
6. Air gap between the two windows,$L_{air}=7.5\text{cmor}0.075\text{″¾}$

Thermal radiation is the process of transferring heat through electromagnetic radiation that is produced by the thermal motion of matter particles. The rate at which the energy is lost per the given area can be given using the given formula and further solving for the case of multiple layers connection of a body having energy loss is given by simply considering the respective thermal conductivities and their respective thickness through which the transfer is being held.

Formula:

The rate of energy transfer via emits thermal radiation, $\frac{P_{cond}}{A}=\frac{k\left(\mathrm{Δ}T\right)}{L}$ …(¾±)

The rate of energy transfer via radiation through multiple layers,

$\frac{P_{cond}}{A}=\frac{\left(\mathrm{Δ}T\right)}{{\displaystyle ∑\frac{L}{k}}}$ …(¾±¾±)

The temperature difference of the system is given as:

$\begin{array}{c}\mathrm{Δ}T=295.37\text{‿é}−244.26\text{‿é}\\ =51.11\text{‿é}\end{array}$

Using equation (i) and the respective given values, the rate of energy loss by the glass plate can be given as:

$\begin{array}{c}\frac{P_{cond}}{A}=\frac{1\text{ W/³¾°­}\left(51.11\text{‿é}\right)}{0.003\text{m}}\\ =1.7×{10}^4{\text{W/m}}^{\text{2}}\end{array}$

Hence, the rate of energy loss per square meter through the glass is$1.7×{10}^4{\text{W/m}}^{\text{2}}$

Similarly, the rate of energy loss through the window having two glasses with an air gap is given using the formula of equation (ii), which can be calculated as follows:

$\begin{array}{c}\frac{P_{cond}}{A}=\frac{\left(51.11\text{‿é}\right)}{\frac{2×0.003\text{″¾}}{1\text{ W/³¾°­}}+\frac{0.075\text{″¾}}{0.026\text{ W/³¾°­}}}\\ =17.681{\text{W/m}}^{\text{2}}\\ ≈18{\text{W/m}}^{\text{2}}\end{array}$

Hence, the rate of energy loss is$18{\text{W/m}}^{\text{2}}$