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

  • question_answer
    Two spheres of same material have radius 1m and 4 m and temperature 4000K and 2000K respectively. The energy radiated per second by the first sphere is

    A) Greater than that by the second

    B) Less than that by the second

    C) Equal in both cases

    D) The information is incomplete

    Correct Answer: C

    Solution :

    Energy radiated per sec \[\frac{Q}{t}=P=A\varepsilon \sigma {{T}^{4}}\] \[P\propto {{r}^{2}}{{T}^{4}}\Rightarrow \frac{{{P}_{2}}}{{{P}_{1}}}=\frac{r_{2}^{2}}{r_{1}^{2}}.\frac{T_{2}^{4}}{T_{1}^{4}}=\frac{{{4}^{2}}}{{{1}^{2}}}\times {{\left( \frac{2000}{4000} \right)}^{4}}=1\]

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