A sphere of ice at `0^(@)C` having initial radius `R` is placed in an environment having ambient temperature `gt 0^(@)C`. The ice melts uniformly, such that shape remains spherical. After a time 't' the radius of the sphere has reduced to r. which graph best depicts r(t)

Options

A.
B.
C.
D.

Answer

B

Explanation

Heat lost
=`sigmaA(T^(4)- T_(0)^(4)) = -sigma4pir^(2)(T_(0)^(4) - T^(4))`
= `(d(mL))/(dt) = rhoL (dv)/(dt) = rhoL4pir^(2)(dr)/(dt)`
`implies -sigma4pir^(2) (T_(0)^(4) - T^(4)) = sigmaL4pir^(2) (dr)/(dt)`
`implies` radius decreases with time