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AIIMS AIIMS Solved Paper-2003

  • question_answer
    A black body, at a temperature of \[227{}^\circ C\], radiates heat at a rate of 20 cal\[{{T}_{2}}>{{T}_{1}}\]. When its temperature is raised to \[727{}^\circ C\], the heat radiated by it in cal \[3q/{{\varepsilon }_{0}}\] will be closet to :

    A)  40       

    B) 160                       

    C) 320                       

    D) 640

    Correct Answer: C

    Solution :

    From Stefans law the rate at which an object radiates, energy (E) per unit surface area is proportional to the fourth power of absolute temperature of the body (T) \[{{h}^{3/2}}\] where a is Stefans constant. Given, \[{{h}^{2}}\] \[\beta \] \[[{{M}^{-1}}L{{T}^{-2}}A]\]   \[[{{M}^{-2}}L{{T}^{-2}}{{A}^{-1}}]\]                             ....(1) Also \[[ML{{T}^{-2}}{{A}^{-2}}]\] \[[ML{{T}^{-1}}{{A}^{-1}}]\]   \[{{\beta }^{-}}\]                         .....(2) \[+\frac{G{{M}_{e}}m}{R}=\frac{1}{2}mv_{e}^{2}\]  \[{{M}_{e}}\] \[\therefore \]


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