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A solid copper sphere of dimater 10mm is...

A solid copper sphere of dimater `10mm` is cooled to temperature of `150K` and is then placed in an enclousure at `290K` Assuming that all interchange of heat is by radiation, calculate the initial rate of rise of temperature of the sphere The sphere may be treated as a black body `rho_(copper) =8.93xx 10^(3)kg//m^(3)`
`s = 3.7xx10^(2) Jkg^(-2) K^(-1) , sigma = 5.7 xx 10^(8) Wm^(-2) K^(-4)` .

Text Solution

Verified by Experts

Using Stefan's law, the rate of increase of temperature is
`(dT)/(dt)=(sigma)/(rho)(A)/(V)((T_(0)^(4)-T^(4)))/(s)`
where `rho=8.93xx10^(3)kg//m^(3)`, `s=3.7xx10^(2)J//kg//K`.
`A//V="area"//"volume ratio"`
`(A)/(V)=(6)/(d)`, `d=`diameter of the sphere.
`T_(0)=` temperature of the surrounding `=290K`
`T=` temperature of the body `=150K`
`:. (dT)/(dt)=(6sigma)/(rhosd)(T_(0)^(4)-T^(4))=0.068Ks^(-1)`
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