A room is maintained at $20^{\circ} C$ by a heater of resistance $20$ ohm connected to $200$ volt mains. The temperature is uniform throughout the room and heat is transmitted through a glass window of area $1 m^{2}$ and thickness $0.2$ cm. What will be the temperature outside? Given that thermal conductivity K for glass $0.2 c a l / m \times \circ_{C} \times s e c$ and $J = 4.2 J / c a l :$

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$15 . 00^{\circ} C$

$24 . 15^{\circ} C$

None of the above

$15 . 24^{\circ} C$

answer is A.

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Detailed Solution

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

$\begin{array}{l} \frac{1}{J} (\frac{V^{2}}{R} t) = K A \frac{Δ θ}{l} . t \\ \frac{1}{4.2} \times \frac{(200)^{2}}{20} = \frac{0.2 \times 1 \times (20 - θ)}{0.2 \times 10^{- 2}} \\ θ = 15.24 ° C [where θ = temperature of outside] \end{array}$