Physics EM Waves

Question

A rectangular metal plate measures 0.14 m long and 0.3 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

We can use Stefan-Boltzmann law, which relates the radiated power of a blackbody to its temperature with the following equation

P = σ A ε T^4

where P is the power radiated,

σ is the Stefan-Boltzmann constant (5.67 x 10^-8 W/m^2K^4),

A is the surface area of the plate,

ε is its emissivity (which we assume to be 1 for a blackbody),

T: temperature in Kelvin.

First, we need to convert the dimensions of the plate to meters:

length = 0.14 m

width = 0.3 m

The surface area is:

A = length x width = 0.14 m x 0.3 m = 0.042 m^2

T = 1333 K

Now the power radiated:

P = σ A ε T^4 = (5.67 x 10^-8 W/m^2K^4) x (0.042 m^2) x (1) x (1333 K)^4 ≈ 1226.5 W

Hence, the metal plate will radiate approximately 1226.5 watts of power when heated to a temperature of 1333 K