Question

A room is maintained at ${20}^{\circ }C$ by a heater of resistance 20ohmconnected to 200voltmains. The temperature is uniform through out the room and heat is transmitted through a glass window of area 1 $m^2$ and thickness 0.2cm. What will be the temperature outside? Given that thermal conductivityKfor glass is 0.2 cal/m/°C andJ= 4.2J/cal

• A. 15.24°C
• B. 15.00°C
• C. 24.15°C
• D. None of the above

Answer 1

The correct option is A

15.24°C

Heat developed by the heater

H = $\frac{V^2}{R}.\frac{t}{J}=\frac{(200{)}^2\times t}{20\times 4.2}$

Heat conducted by the glass H = $\frac{0.2\times 1\times (20-\theta )t}{0.002}$

Hence $\frac{(200{)}^2\times t}{20\times 4.2}=\frac{0.2\times (20-\theta )t}{0.002}\Rightarrow \theta ={15.24}^{\circ }C$