Heat and Thermodynamics 3 Question 33

33. A solid copper sphere (density ρ and specific heat c ) of radius r at an initial temperature 200K is suspended inside a chamber whose walls are at almost 0K. The time required for the temperature of the sphere to drop to 100K is ……

(1991, 2M)

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Solution:

  1. Area of sphere, A=4πr2

Mass of sphere, m=(43πρr3)

Now, energy radiated per second =(σAT4)

mc(dTdt)=σAT4

or 0tdt=(mcσA)200100T4dT

or t=mc3σA[1(100)31(200)3]

=7mc3×8σA×106=7mc×10624σA

Substituting the values,

t=(7×43πρr3)(c)×1063×8×5.67×108×4πr2=1.71ρrc



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