What Equations Calculate Thermal Radiation and Wavelength Peak Intensity?

[Gh0stman]

Homework Statement

Consider a 5.50×10 (to the 4th power) object that emits thermal radiation.

Homework Equations

How much power does it emit per square meter? W
What is its wavelength of peak intensity? nm

The Attempt at a Solution

i am looking for the equations to calculate this thing

 

[Kurdt]

Homework Statement

Consider a 5.50×10 (to the 4th power) object that emits thermal radiation.

What does this number describe about the object? I.e what are the units?

Homework Equations

How much power does it emit per square meter? W
What is its wavelength of peak intensity? nm

The Attempt at a Solution

i am looking for the equations to calculate this thing

I would guess you have been learning about the Stefan-Boltzman law and Wien's displacement law.

 

[m2003]

Hello,

The thermal radiation law, also known as the Stefan-Boltzmann law, states that the power emitted per unit area by a black body is proportional to the fourth power of its absolute temperature. The equation for this law is given by P = σAT^4, where P is the power emitted, σ is the Stefan-Boltzmann constant (5.67 x 10^-8 W/m^2K^4), A is the surface area of the object, and T is the absolute temperature in Kelvin.

To calculate the power emitted per square meter, you can use the above equation and plug in the values given in the problem. So, P = (5.67 x 10^-8 W/m^2K^4) x (5.50 x 10^4 K)^4 = 2.78 x 10^14 W/m^2.

To find the wavelength of peak intensity, you can use Wien's displacement law, which states that the wavelength of maximum intensity (λmax) is inversely proportional to the absolute temperature. The equation for this law is given by λmax = b/T, where b is the Wien displacement constant (2.90 x 10^-3 mK). So, in this case, λmax = (2.90 x 10^-3 mK)/(5.50 x 10^4 K) = 5.27 x 10^-8 m = 52.7 nm.

I hope this helps you with your homework. Let me know if you have any further questions. Good luck!