Question

A black marble has a diameter of 1 cm and an emissivity of 0.8. If the marble is at a temperature of 20 oC, how much thermal radiation (in Joules) does it emit in 1 hour?

Answer 1

Stefan boltzmann constant = $\sigma$ = 5.67 x 10^-8 W/m²K⁴

Diameter of the marble = D = 1 cm = 0.01 m

Emissivity = e = 0.8

Temperature of the black marble = T = 20 ^oC = 293 K

Area of the black marble = A

A = 4$\pi$R² = $\pi$D²

A = $\pi$(0.01)²

A = 3.141 x 10^-4 m²

Power radiated by the black marble = P

P = Ae$\sigma$T⁴

P = (3.141x10^-4)(0.8)(5.67x10^-8)(293)⁴

P = 0.105 W

Time period = T = 1 hour = 3600 sec

Energy radiated by the black marble in 1 hour = E

E = PT

E = (0.105)(3600)

E = 378 J

Thermal radiation emitted by the black marble in 1 hour = 378 J