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)` .

Explanation

To solve the problem of calculating the initial rate of rise of temperature of a solid copper sphere placed in an enclosure, we can follow these steps:

### Step 1: Understand the Problem
We have a solid copper sphere with a diameter of 10 mm, cooled to a temperature of 150 K, and placed in an enclosure at 290 K. We need to calculate the initial rate of rise of temperature of the sphere, assuming heat exchange occurs only through radiation.

### Step 2: Use Stefan-Boltzmann Law
The rate of heat transfer by radiation can be expressed using the Stefan-Boltzmann law:
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