Question

Modern Physics Question --> Topic: Thermal Radiation & Blackbodies

Q: A 2.30 cm diameter tungsten sphere is heated to a temperature of 2000 degree C. At this temperature tungsten radiates only 30% of the energy radiated by a blackbody of the same size and temperature.

(a) Determine the temperature of a perfectly black spherical body of the same size that radiates at the same rate as the tungsten sphere.

(b) calculate the diameter of a perfectly black spherical body at the same temperature as the tungsten that radiates at the same rate.

Answer 1

Here .

as the rate of radiation of power = 0.30 * rate of radiation of blackbody at this temperature

a) for the same size body ,

let the temperature is T

sigma * 0.30 * Area * (2000 + 273)^4 = sigma * Area * T^4

0.30 * 2273^4 = T^4

solving for T

T = 1682 K = 1409 degree C

the temperature of same sized black body is 1409 degree C

b)

for tha body at the same temperatre ,

let the diameter is d

sigma * T^4 * 0.30 * 4pi * 2.3^2 = sigma * T^4 * 4pi * d^2

0.30 * 4pi * 2.3^2 = 4pi * d^2

solving for d

d = 1.26 cm

the diameter of the spherical body will be 1.26 cm