modphysnoob said:Homework Statement
a) Use Planck’s radiation law to derive the Stefan-Boltzmann law for the case of zero background
temperature (i.e., T0 = 0).
Homework Equations
http://csep10.phys.utk.edu/astr162/lect/light/plancklaw.gif
The Attempt at a Solution
So I know we are suppose to integrate over all wavelength but I dont' know what should the limit be
Planck's radiation law is a fundamental law of physics that describes the distribution of energy emitted by a black body at a given temperature. It states that the energy of electromagnetic radiation is quantized, meaning it can only exist in discrete packets of energy called photons.
The Stefan-Boltzmann law is a physical law that relates the total energy emitted by a black body to its temperature. It states that the total energy radiated per unit surface area of a black body is proportional to the fourth power of its absolute temperature.
To derive the Stefan-Boltzmann law, we start with Planck's radiation law and integrate it over all frequencies to get the total energy emitted by a black body. Then, we substitute the expression for the energy density from Planck's law into the total energy equation and solve for the temperature. This results in the Stefan-Boltzmann law.
The Stefan-Boltzmann law has many applications in physics and engineering. It is used to calculate the energy output of stars, determine the temperature of objects in space, and design efficient thermal systems. It is also used in climate science to study the Earth's energy budget and understand the effects of greenhouse gases on the planet's temperature.
The Stefan-Boltzmann law is applicable to all objects that behave like black bodies, meaning they absorb and emit all radiation that falls on them. Real-world objects may not behave exactly like black bodies, but they can be approximated using the Stefan-Boltzmann law. This is why the law is often used in practical applications, even if the objects are not perfect black bodies.