A solid copper sphere (density rho 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 …….

Answer

`1.71`

Explanation

Area of sphere, `A=4pir^(2)`
Mass of sphere, `m= ((4)/(3)pirhor^(3))`, Now, energy radiated per second `=(sigmaAT^(4))`
`thereforemc(-(dT)/(dt))=sigmaAT^(4)orint_(0)^(t)dt=((-mc)/(sigmaA))int_(200)^(100)T^(-4)dT`
`ort=(mc)/(3sigmaA)[(1)/((100)^(3))-(1)/((200)^(3))]=(7mc)/(3xx8sigmaA)xx10^(-6)=(7mCxx10^(-6))/(24sigmaA)`
Substituting the values,
`t=((7xx(4)/(3)pirhor^(3))(C)xx10^(-6))/(3xx8xx5.67xx10^(-8)xx4pir^(2))=1.71rhorc`