1
$\begingroup$

In my statistical mechanics course, I'm deriving the entropy for an ideal gas and I've come across a statement in the book by Pathria where it states that in the case of an ideal gas, the Hamiltonian is strictly a function of the momenta ($p_{i}$).

Are there general conditions that hold for this to be true? Or is this just a result of the particular system being considered?

$\endgroup$
1
$\begingroup$

I don't know what is the general conditions for only a momentum dependence. But an example of only momentum dependence is the case of non-interacting particles. Consider the case where the only energy a particle has is its kinetic energy, and it does not interact with anything, not gravity, not a container, not other particles, not anything. In that case you just get $\frac{1}{2} \frac{p^2}{m}$ per particle.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.