# A sphere with diameter of 80 cm is held at a temperature of 250°C and is radiating energy…

Q: A sphere with diameter of 80 cm is held at a temperature of 250°C and is radiating energy. If the intensity of the radiation detected at a distance of 2.0 m from the sphere’s centre is 102 W/m², What is the emissivity of the sphere?

Sol: From inverse square law $\large I \propto \frac{1}{r^2}$

$\large \frac{I_2}{I_1} = \frac{r_1^2}{r_2^2}$

$\large I_2 = I_1 (\frac{r_2^2}{r_1^2}) = 102 (\frac{2}{0.4})^2$

= 2.55 × 103 W/m2

The power at the surface of the sphere

P = I2 (4π r22 ) = 2.55 × 103 × 4π(0.4)2

and , P = e σ A T4

2.55 × 103 × 4π(0.4)2 = e × 5.67 × 10-8 × 4 π(0.4)2 ×(523)4

e = 0.61