JEE Main & Advanced Physics Transmission of Heat Question Bank Critical Thinking

  • question_answer
    A room is maintained at \[{{20}^{o}}C\] 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 is \[320\ kcal/{{m}^{2}}\ min\] and J = 4.2 J/cal [IIT 1978]

    A)            \[{{15.24}^{o}}C\]              

    B)            15.00°C

    C)            \[{{24.15}^{o}}C\]              

    D)            None of the above

    Correct Answer: A

    Solution :

                       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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