A room is maintained at ${20^o}C$ 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 $1{m^2}$ and thickness $0.2$ cm. What will be the temperature outside ....... $^oC$ ? Given that thermal conductivity $K=0.2$ for glass is and $J = 4.2 J/cal$
IIT 1978, Medium
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(a) 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^o}C$
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