A room has a window fitted with a single 1.0m 2.0m glass of thick… - Vidyadip

Question

A room has a window fitted with a single $1.0m \times 2.0m$ glass of thickness $2mm$.

Calculate the rate of heat flow through the closed window when the temperature inside the room is $32^\circ C$ and that outside is $40^\circ C$.
The glass is now replaced by two glasspanes, each having a thickness of $1mm$ and separated by a distance of $1mm$. Calculate the rate of heat flow under the same conditions of temperature. Thermal conductivity of window glass = $1.0Js^{-1}m^{-1^\circ}C^{-1}$ and that of air = $0.025Js^{-1}m^{-1^\circ}C^{-1}$.

✓

Answer

$\frac{\text{Q}}{\text{t}}=\frac{\text{KA}(\theta_1-\theta_2)}{\ell}$

$=\frac{1\times2\times1(40-32)}{2\times10^{-3}}$
$=8000\text{J/sec}.$

Resistance of glass $=\frac{\ell}{\text{ak}_\text{g}}+\frac{\ell}{\text{ak}_\text{g}}$

Resistance of air $=\frac{\ell}{\text{ak}_\text{a}}$
Net resistance $=\frac{\ell}{\text{ak}_\text{g}}+\frac{\ell}{\text{ak}_\text{g}}+\frac{\ell}{\text{ak}_\text{a}}$
$=\frac{\ell}{\text{a}}\Big(\frac{2}{\text{k}_\text{g}}+\frac{1}{\text{k}_\text{a}}\Big)$
$=\frac{\ell}{\text{a}}\Big(\frac{2\text{k}_\text{a}+\text{k}_\text{g}}{\text{k}_\text{g}\text{k}_\text{a}}\Big)$
$=\frac{1\times10^{-3}}{2}\Big(\frac{2\times0.025+1}{0.025}\Big)$
$=\frac{1\times10^{-3}\times1.05}{0.05}$
$\frac{\text{Q}}{\text{t}}=\frac{\theta_1-\theta_2}{\text{R}}$
$=\frac{8\times0.05}{1\times10^{-3}\times1.05}$
$=380.9\approx381\text{W}$

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