Relation between kinetic energy and temperature for hydrogen

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SUMMARY

The relationship between kinetic energy and temperature for hydrogen is defined by the equation (1/2)m*(v^2) = (3/2)K*T, where m represents mass, K is the Boltzmann constant, and T is the temperature in Kelvin. The discussion clarifies that the professor's note, which states (1/2)m*(v^2) = (1/2)K*T, is incorrect. The correct formulation applies specifically to ideal gases and accounts for the mean kinetic energy of particles. The distinction between components of velocity is also noted, emphasizing the importance of context in these equations.

PREREQUISITES
  • Understanding of kinetic energy equations
  • Familiarity with the Boltzmann constant (K)
  • Basic knowledge of ideal gas laws
  • Concept of temperature in Kelvin
NEXT STEPS
  • Study the derivation of the mean kinetic energy of particles in ideal gases
  • Learn about the implications of the ideal gas law on kinetic theory
  • Explore the role of temperature in thermodynamics
  • Investigate the differences between translational and rotational kinetic energy
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Students of physics, researchers in thermodynamics, and anyone interested in the principles of kinetic theory and gas behavior will benefit from this discussion.

magodiafano
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Hello
I have a question about the relationship between kinetic energy and temperature for the hydrogen.

In my professor's note, there is written that:

(1/2)m*(v^2) = (1/2)*K*T

where m is the mass, K the costant and T the temperature in Kelvin.

My doubt is in the fact that on internet I discovered that the relation is:

(1/2)m*(v^2) = (3/2)*K*T

so are my professor's notes wrong?
 
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There is a rather long, but simple derivation of the mean kinetic energy of a particle related to temperature (see http://en.wikipedia.org/wiki/Kinetic_theory). As you can see, your professor made a mistake and it is indeed (3/2)KT. Take into account however, that this is only applicable for an ideal gas.
 
he ain't wrong he was talking about one component of velocity
 

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