A small blackened metal sphere of radius is kept in an evacuated enclosure whose wall…

PHYSICS · Subjective · CBSE · Physics · Thermal Properties of Matter · Thermal Properties of Matter

Problem

A small blackened metal sphere of radius

2.0\,\text{cm}

is kept in an evacuated enclosure whose wall temperature is maintained at

500\,\text{K}

. The sphere itself reaches a steady temperature of

800\,\text{K}

. Take the Stefan–Boltzmann constant

\sigma = 5.67\times10^{-8}\,\text{W}\,\text{m}^{-2}\,\text{K}^{-4}

. (i) Calculate the net rate at which the sphere loses energy by thermal radiation. (ii) Verify by dimensional analysis that the quantity

\sigma A T^{4}

has the dimensions of power. (iii) Convert the surface area used in part (i) from

\text{cm}^2

\text{m}^2

before substitution and state why this conversion is essential.