- #1
Dario SLC
My doubt it is simply if have other reason to don't use this principle for the specific heat of diatomic gases.
$$U=NkT=nRT$$
$$u_n=\frac{U}{n}=RT\text{ molar energy}$$
$$u_N=\frac{U}{N}=kT\text{ average energy}$$
$$Z=\sum{e^{-\omega_i/kT}}\text{ with $\omega_i$ particular energy}$$ partition function
I believe (better said, in the Sears book, Thermodynamics) that the equipartition energy is not valid because, for the energies relative to the vibrational motion and rotational motion, it has quantized.
If was valid the principle of equipartition energy, this say:
$$U_t=\frac3{2}kT$$
when ##U_t## is relative at the translation motion, and the factor three is for the degree of freedom, ie:
$$\frac{1}{2}kT+\frac{1}{2}kT+\frac{1}{2}kT$$ for each degree of freedom.
In the vibrational motion, like in the solid if we are model like oscillator and it have the quadratic coordinate for the velocity (kinetic energy) and quadratic coordinate for the position (potential energy), only (since classical point of view), therefore the energy of vibration is ##\frac{1}{2}kT+\frac{1}{2}kT=kT##, but it is not the real when ##T\Longrightarrow0## (then solved using quantized energy).
Here my question, ONLY because the energy of vibration is quantized, the principle of partition energy I can't use it?
(Similar to rotational motion)
Thanks!
Homework Equations
$$U=NkT=nRT$$
$$u_n=\frac{U}{n}=RT\text{ molar energy}$$
$$u_N=\frac{U}{N}=kT\text{ average energy}$$
$$Z=\sum{e^{-\omega_i/kT}}\text{ with $\omega_i$ particular energy}$$ partition function
The Attempt at a Solution
I believe (better said, in the Sears book, Thermodynamics) that the equipartition energy is not valid because, for the energies relative to the vibrational motion and rotational motion, it has quantized.
If was valid the principle of equipartition energy, this say:
$$U_t=\frac3{2}kT$$
when ##U_t## is relative at the translation motion, and the factor three is for the degree of freedom, ie:
$$\frac{1}{2}kT+\frac{1}{2}kT+\frac{1}{2}kT$$ for each degree of freedom.
In the vibrational motion, like in the solid if we are model like oscillator and it have the quadratic coordinate for the velocity (kinetic energy) and quadratic coordinate for the position (potential energy), only (since classical point of view), therefore the energy of vibration is ##\frac{1}{2}kT+\frac{1}{2}kT=kT##, but it is not the real when ##T\Longrightarrow0## (then solved using quantized energy).
Here my question, ONLY because the energy of vibration is quantized, the principle of partition energy I can't use it?
(Similar to rotational motion)
Thanks!