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JEE Main & Advanced Physics Transmission of Heat Question Bank Radiation Stefan's law

  • question_answer
    Two spherical black bodies of radii \[{{r}_{1}}\] and \[{{r}_{2}}\] and with surface temperature \[{{T}_{1}}\]and \[{{T}_{2}}\] respectively radiate the same power. Then the ratio of \[{{r}_{1}}\] and \[{{r}_{2}}\] will be  [KCET 2001; UPSEAT 2001]

    A)            \[{{\left( \frac{{{T}_{2}}}{{{T}_{1}}} \right)}^{2}}\]   

    B)            \[{{\left( \frac{{{T}_{2}}}{{{T}_{1}}} \right)}^{4}}\]

    C)            \[{{\left( \frac{{{T}_{1}}}{{{T}_{2}}} \right)}^{2}}\]   

    D)            \[{{\left( \frac{{{T}_{1}}}{{{T}_{2}}} \right)}^{4}}\]

    Correct Answer: A

    Solution :

                       For black body, \[P=A\varepsilon \sigma {{T}^{4}}\]. For same power \[A\propto \frac{1}{{{T}^{4}}}\] Þ \[{{\left( \frac{{{r}_{1}}}{{{r}_{2}}} \right)}^{2}}={{\left( \frac{{{T}_{2}}}{{{T}_{1}}} \right)}^{4}}\]Þ \[\frac{{{r}_{1}}}{{{r}_{2}}}={{\left( \frac{{{T}_{2}}}{{{T}_{1}}} \right)}^{2}}\]


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