How Do You Calculate the Average Kinetic Energy of Multiple Helium Atoms?

AI Thread Summary
The average kinetic energy of multiple helium atoms can be expressed using the Boltzmann constant as E = (3/2)kT, where k is the Boltzmann constant and T is the temperature. The discussion highlights the relationship between pressure, volume, and the kinetic energy of gas particles, emphasizing the need to consider the translational motion of helium atoms. The Equipartition Principle is referenced, indicating that each degree of freedom contributes (1/2)kT to the energy. The challenge lies in correctly interpreting the total mass and number of atoms in the context of the ideal gas laws. Ultimately, the average kinetic energy formula for helium atoms is confirmed as 3/2 kT.
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Homework Statement


Write an expression E for the average kinetic energy of Helium atoms using the Boltzmann constant.

Homework Equations


PV = nRT

PV = \frac{1}{3}mN\overline{c^2}

k = \frac{R}{N_A}

[P - Pressure ; V - Volume ; m - Mass of an atom ; N - Number of atoms ; others have their general meanings.]

The Attempt at a Solution


My problem is they're asking for an expression for the average kinetic energy of Helium atoms. It's plural. I can build an expression for the kinetic energy of a single atom.

nRT = \frac{1}{3}mN\bar{c^2}

\frac{3}{2}nRT = \frac{1}{2}mnNA\overline{c^2}

\frac{3}{2}RT = \frac{1}{2}mNA\overline{c^2}

\frac{3}{2}kT = \frac{1}{2}m\overline{c^2} = E (Kinetic Energy of an atom)

Rest of the question is easy if this is the expression they're asking.
Do I have to take mN as the total mass of the gas and calculate it from there taking R as kNA? That way it's making the sum a bit difficult because they haven't defined the constant NA in the question, giving out a hint that it's not involving in this, may be.
 
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The average kinetic energy of an atom is the sum of the KE of the individual atoms divided by the number of the atoms KEav=ƩKEi/N

You certainly know the Equipartition Principle. The average energy of a particle in an ideal gas is (f/2)kT where f is the degrees of freedom. http://hyperphysics.phy-astr.gsu.edu/hbase/kinetic/eqpar.html. A He atom can only translate, its kinetic energy is translational energy with three degrees of freedom. Your final formula is the answer to the problem: The average kinetic energy of the He atoms (of a He atom in the He gas) is 3/2 kT, expressed with the Boltzmann constant k.

ehild
 
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Thanks for the help and the link! :D
 
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