Question

Calculate approximately the heat passing per hour through the walls and windows of room 5 by 5 meters if the walls are of bricks of thickness 30 cms and have windows of glass 3mm thick and total area 5 square meters. The temperature of the room is ${30}^{\circ }$ below that of the outside and the thermal conductivity of bricks and of glass is \(12 \times 10^{-4}\) and \(25 \times 10^{-4}\) C.G.S. units respectively.

• A. calories
• B. calories
• C. calories
• D. calories

Answer 1

The correct option is A calories

Let $Q_1$ be the heat passing through the walls, then
$Q=\frac{KA(T_1-T_2)t}{x}$
Here area of four walls including windows
$=500\times 500\times 4=10,00,000$
area of all windows
$=5sq.meter-50,000sq.cm$
$\therefore$ net area of brick walls
$=10,00,000-50,000=9,50,000sqcm$
$Kforbricks=12\times {10}^{-4}C.G.S.units$
$x=40cm,(T_1-T_2)={30}^{\circ }C$ and
t = 1 hr = 3600 sec.
$\therefore Q_1=\frac{(12\times {10}^{-4})(9,50,000)\left(30\right)\left(3600\right)}{30}$
= 4104000 cal
Heat passing through glass windows
$Q_2=\frac{(25\times {10}^{-4})(50,000)\left(30\right)\left(3600\right)}{0.3}$
= 45000000 cal.
Total heat passing
$Q=Q_1+Q_2$
= 4104000 + 45000000
$=49104\times {10}^{3}calories$