Question

A solid metal sphere is 15.0 cm in diameter and has surface of uniform color.When its surface is at 112°C, you measure that it radiates energy at a rate of71.3 W. What is the emissivity of the surface of this object

Answer 1

Answer:

The emissivity of the surface of this object is 0.809.

Explanation:

Given that,

Diameter = 15.0 cm

Temperature = 112°C

Power = 71.3 W

We need to calculate the area

Using formula of area

$A=4\pi r^2$

Put the value into the formula

$A=4\pi(\dfrac{15.0\times10^{-2})^2}{4}$

$A=0.0707\ m^2$

We need to calculate the emissivity of the surface of this object

Using formula of the  emissivity

$P=\epsilon \sigma AT^4$

$\epsilon=\dfrac{P}{\sigma AT^4}$

Where, A = area

T = temperature

$\sigma$ =Stefan Boltzmann constant

P = power

Put the value into the formula

$\epsilon=\dfrac{71.3}{5.670\times10^{-8}\times0.0707\times(112+273)^4}$

$\epsilon=0.809$

Hence, The emissivity of the surface of this object is 0.809.