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I also know that for gases the formula is (3/2)kT, but is the same true for liquids? If not, then what is the formula?

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- Thread starter Alex319
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In summary, the formula for calculating the speed of atoms in a liquid due to thermal motion is (3/2)kT, as it is for gases. This is known as the equipartition theorem in classical statistical mechanics. However, this rule does not hold true in quantum analysis, as shown by the example of a quantum harmonic oscillator. Additionally, in liquids, the interactions between particles must also be taken into account when calculating average kinetic energy, making the classical method less accurate.

- #1

- 3

- 0

I also know that for gases the formula is (3/2)kT, but is the same true for liquids? If not, then what is the formula?

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- #2

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It's because the kinetic energy term is quadratic in momentum and can always be factored out of the total partition function- Q=Q(KE) * Q(PE)

Any quadratic degree of freedom has an energy of 1/2 k T, a result generally referred to as the equipartition theorem.

However, the 1/2 kT rule is only true in classical statistical mechanics. It is not true in a quantum analysis.

For example, a quantum harmonic oscillator in its ground state has energy E=1/2 hbar w0, with K.E.=1/4 hbar w0, which is not equal to 1/2 kT.

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