Question

A room is maintained at 20^0C by a heater of resistance 20 ohm connected to 200 volt mains. The temperature is uniform through out the room and heat is transmitted through a glass window of area 1 m² and thickness 0.2 cm. What will be the temperature outside? Given that thermal conductivity K for glass is 0.2 cal/m ×^0C× sec and J = 4.2 J/cal

• A. 15.24 ^0C
• B. 15.00 ^0C
• C. 24.15 ^0C
• D. None of the above

Answer 1

Answer: (A)

15.24 ^0C

Answer 2

As the temperature of room remain constant therefore the rate of heat generation from the heater should be equal to the rate of flow of heat through a glass window

$\frac{1}{J}\left( \frac{V^{2}}{R}t \right) = KA\frac{\Delta\theta}{l}.t$

⇒ $\frac{1}{4.2} \times \frac{(200)^{2}}{20} = \frac{0.2 \times 1 \times (20 - \theta)}{0.2 \times 10^{- 2}}$ ⇒ θ = 15.24^oC

[where θ = temperature of outside]