Find the temperature at which the number of photons in a chamber of volume 25 litres is equal to

step 1 Okay, so we are given a laser of 0 .1 watt, which is approximately equal to 0 .1 jule per second

Find the temperature at which the number of photons in a...

Key Concepts

Photon Gas

A photon gas is a collection of photons in thermal equilibrium that behaves as a gas. Unlike particles with rest mass, photons are massless and their distribution is governed by quantum statistics. They exhibit unique properties, such as having no chemical potential, and their behavior in thermal equilibrium is described by the principles of statistical mechanics.

Blackbody Radiation

Blackbody radiation refers to the electromagnetic radiation emitted by an idealized object that absorbs all incident radiation. The radiation spectrum is solely a function of the temperature, with its energy distribution described by the Planck distribution. This concept is fundamental in understanding how a photon gas behaves inside a cavity at a given temperature.

Photon Number Density

Photon number density is the number of photons per unit volume in a system. In blackbody radiation, this density is a function of the temperature, typically exhibiting a cubic dependence. Utilizing the statistical mechanics of the photon gas, one can derive an expression for the number density in terms of temperature and fundamental constants.

Molar Quantity and Avogadro's Number

In thermodynamics, a mole is a unit that represents a specific number of particles, known as Avogadro's number. By equating the total number of photons in a given volume (obtained by multiplying the photon number density by the volume) to one mole, one can determine the temperature corresponding to that quantity. This concept bridges microscopic quantities (individual photons) with macroscopic measurements.

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