Question

A rectangular metal plate measures 0.24 m long and 0.5 m wide. The plate is heated to a temperature of 1,333 K by passing a current through it. Assuming that it behaves like a blackbody, how much power does the plate radiate under these conditions?

Answer 1

The total power P radiated from one square meter of black surface at temperature T goes as the fourth power of the absolute temperature:

Pf = σT^4

σ = Stefan-Boltzmann constant = 5.67 * 10^-8 W/m^2 .K^4
T = absolute temperature = 1,333 K
L = length of the plate = 0.24 m
W = width of the plate = 0.5 m
A = area of the plate
Pf = fractional power  
P = total radiated power  


A = L x W
A = (0.24 m)(0.5 m)
A = 0.12 m^2

Pf = 5.67 * 10^-8 W/m^2 .K^4 * (1333 K )^4
Pf = 1.79 * 10^5 W/m^2

P = A x Pf
P = (0.12) * 1.79 * 10^5
P = 2.15 * 10^4 W is the power radiated by the plate under given conditions.