Continuation of the lecture: Fluctuations in the differential of work and the equipartition theorem
I will upload the whole lecture notes to the blog. There, starting from page 42, the fluctuations of certain thermodynamic variables is discussed. In Eq.(82) you find the formula for the variance of the internal energy, which we have seen in one of our last classes. Following that, there is an intent to obtain a similar formula for the coeficients of the work differential. That is to say, for
DW(T, x1, x2, ... ) = Psi_1 dx1 + Psi_2 dx2 + ...
the coefficients Psi_1, Psi_2, ... are thermodynamic variables, which may show fluctuations. For instance, in the case of a gas,
DW = p dV , and the coefficient is p which shows fluctuations.
The whole part about fluctuations is still written in red color, because it is not terminated. But please go through the calculation and tell me via the comment function what you understand and what not. May be you even spot some mistakes.
Next comes a very small section about the Equipartition theorem. Again, please read it carefully, think about it and publish any doubts and questions. Apply these formulas to the different thermodynamic systems we know: ideal gas, real gas, atoms trapped in a harmonic potential, etc.
DW(T, x1, x2, ... ) = Psi_1 dx1 + Psi_2 dx2 + ...
the coefficients Psi_1, Psi_2, ... are thermodynamic variables, which may show fluctuations. For instance, in the case of a gas,
DW = p dV , and the coefficient is p which shows fluctuations.
The whole part about fluctuations is still written in red color, because it is not terminated. But please go through the calculation and tell me via the comment function what you understand and what not. May be you even spot some mistakes.
Next comes a very small section about the Equipartition theorem. Again, please read it carefully, think about it and publish any doubts and questions. Apply these formulas to the different thermodynamic systems we know: ideal gas, real gas, atoms trapped in a harmonic potential, etc.
Good morning. I do not understand why do we use the equipartition theorem, and whay the partition function depends on time.
ResponderBorrarwhy*
ResponderBorrarNo, sorry, the partition function does not depend on time. I don't know what happened. I will correct that as soon as possible.
ResponderBorrarAlso may be I should say something about d\Gamma which is an abbreviation for the measure of the integral: For instance in the case of N indistinguishable particles in one dimension:
d\Gamma(\vec p, \vec q) = \frac{\rmd^N\vec p \rmd^N\vec q}{\hbar^N N!}
El estúpido blog no permite agregar graficas en la sección de comentarios ...
In eq(90), isn't the result Nk_BT/2?
ResponderBorrar