How is the kinetic energy related to the temperature?
With a very large number of particles it makes sense to use statistical methods to study nature. When describing the molecular velocities in a gas, one expects the most probable distribution, since these are particle numbers in the order of magnitude of the Avogadro number. This most probable distribution (the Maxwell-Boltzmann distribution) assumes that the number of particles and the total energy are constant (conservation of energy). The adaptation of the probability distribution to these constraints is generally not a simple mathematical problem (see e.g. Richtmyer, et al.). A simpler way to get the solution is to look at the barometric altitude formula from atmospheric physics. The following derivation from Rohlf.
This derivation makes use of the fact that the mean kinetic energy of the molecules can be expressed in terms of the kinetic temperature. The conservation of energy in this case simply means that the kinetic energy is to be balanced with the potential (gravitational) energy, if one regards the atmosphere as an ideal gas.
From the expression for the kinetic temperature
this results in an experimentally verified expression for the kinetic energy of the molecules. The barometric altitude formula:
provides the description of an ideal gas system and can be used to derive a plausibility argument for Maxwell's velocity distribution. The following steps are necessary for this:
In one dimension of space this results in the expression:
If one includes all directions of the speed, the result is Maxwell's speed distribution:
It should be noted that a formula that depends on gravity was used for the velocity distribution, but "g" no longer appears in the end. The barometric formula was only used to link the conservation of particles and energy with the velocity distribution.
- How do molluscs excrete
- Who is Gareth in The Walking Dead
- What's the best Wally West Feats
- Who started the ASMR trend on YouTube
- What is a TIFF file versus JPEG
- Which countries produce matcha tea?
- Can emotions of girls be modeled through graphics
- What are your favorite Disney sequels
- How do I plan to move states
- How do different Python IDEs compare
- How can I live without marriage
- Is automotive engineering a good major?
- How does mental stress affect physical health?
- What is the best movie database API
- Women like double anal sex
- What are some really amazing facts
- Will cheating ever stop
- What are conservatory designs
- How can I play U19 cricket
- What are the solutions of cotx x
- How great is Schubert's unfinished symphony
- Will GitHub stay free
- Cray 1 was the first supercomputer
- Can you get Imovie for a PC?
- How important are investment horizons for investors
- How to say handshaking in French
- Helps Vanish remove dried stains
- The tenants pay for the sewage disposal
- What is the deontological ethical theory
- How do fishing tournaments work
- Why are no more Whodunnit films made
- What is your favorite site
- How can a student contribute to society