JEE Main & Advanced Physics Transmission of Heat Question Bank Topic Test - Transmission of Heat (3-5-21)

  • question_answer
    A black body radiates energy at the rate of \[1\times {{10}^{5}}J/s\times {{m}^{2}}\] at temperature of \[227{}^\circ C\]. The temperature to which it must be heated so that it radiates energy at rate of \[1\times {{10}^{9}}J\text{/}s{{m}^{2}}\], is         

    A) 5000 K

    B) 5000\[{}^\circ C\]

    C) 500 K

    D) 500\[{}^\circ C\]

    Correct Answer: A

    Solution :

    \[\frac{{{E}_{2}}}{{{E}_{1}}}={{\left( \frac{{{T}_{2}}}{{{T}_{1}}} \right)}^{4}}\] \[\Rightarrow \] \[\frac{{{T}_{2}}}{{{T}_{1}}}={{\left( \frac{{{E}_{2}}}{{{E}_{1}}} \right)}^{1/4}}={{\left( \frac{{{10}^{9}}}{{{10}^{5}}} \right)}^{1/4}}=10\]             \[\Rightarrow \] \[{{T}_{2}}=10{{T}_{1}}=10\times (273+227)=5000\,K\]

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