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100 millicuries of radon which emits 5.5 MeV alpha- particles are contained in a glass capillary tube 5 cm long with internal and external diameters 2 and 6 m m respectively Neglecting and effects and assuming that the inside of the uniformly irrandicated by the particles which are stopped at the surface calculate the temperature difference between the walls of aa tube when steady thermalconditions have been reached. Thermal conductivity of glass = 0.025 Cal cm^(-2) s^(-1)C^(-1) Curie = 3.7 xx 10^(10) disintergration per second J = 4.18 joule Cal^(-1)s |
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Answer» Solution :The FLOW of heat in a material placed between the walls of a coaxial cyclinder is given by `(dQ)/(dt)=(2piKL(T_(1)-T_(2)))/(L n((r_(2))/(r_(1))))` Number of decays of radon atoms per SECOND `(dN)/(dt)=100xx10^(-3)xx3.7xx10^(10)=3.7xx10^(9)` disntegration/second Energy deposited by `alpha's=3.7xx10^(9)xx5.5 MeV//s` `=2.035xx10^(10)MeV//s=3.256xx10^(-7)J=0.779xx10^(-3)Cla//s` Using the values . `k=0.025 Cal cm^(-2)s^(-1)C^(-1), L=5 cm, r_(1)=2 MM` and `=r_(2)=6mm` in (1), and solving for `(T_(1)-T_(2))` we find `(T_(1)-T_(2))=1.09^(@)C` |
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