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A spherical black body with a …

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A spherical black body with a radius of 12cm radiates 440w power at 500K.If the radius were halved and the temperature doubled, the power radiated in watt would be

    • Posted by Ashok Kumar S 6 years, 9 months ago

    Entrance Exam > JEE main > Physics
    • 1 answers

    Sahdev Sharma 6 years, 9 months ago

    Let original radius = r

    Original temperature = T

    Original power radiated = P

    According to Stefan-Boltzmann Law, Power radiated by black body = {tex}P = σAT^4=\sigma 4\pi r^2T^4{/tex}

    {tex}=> 500 = 4\sigma \pi r^2T^4{/tex}

    New radius = {tex}r\over 2{/tex}

    New temperature = 2T

    New power P` = {tex}4\sigma \pi \times {r^2\over 4}\times 16T^4{/tex}

    {tex}4\times (4\sigma \pi r^2T^4)= 4\times P{/tex}{tex}= 4\times 450= 1800{/tex}

    Power becomes 1800 W

    1Thank You

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