Undergrad Questions about my Understanding of Thermodynamics and Statistical Mechanics

[Yseult]

Good afternoon all,

I have two questions to check my understanding/understand better those questions.

Why is heat capacity an important quantity in thermodynamics and statistical mechanics?
From my understanding, heat capacity is an extensible property so any change in the system would result in a change in the heat capacity. It also works with constant pressure and volume, making it ideal. Works with different types of molecules (monatomic, diatomic ...).
Is there more to it that I am missing?

The specific heat capacity contribution from the electrons in a metal at RTP differs from the equipartition for electron gas, why?
I understand that electrons have no contribution to heat capacity and only a few are excited by the Pauli exclusions principle. In a metal, electrons are delocalised but in a gas electrons would vibrate more so would have more energy. There is also the idea of the Fermi energy and at lower temperatures, they would have the maximum Fermi energy. But how does the fermi energy relate to the heat capacity?
How would the equipartition be related in this case for electrons? I understand for molecules but not for electrons.

If I could get some help to understand those better that would be great :D

 

[Chestermiller]

Good afternoon all,

I have two questions to check my understanding/understand better those questions.

Why is heat capacity an important quantity in thermodynamics and statistical mechanics?
From my understanding, heat capacity is an extensible property so any change in the system would result in a change in the heat capacity. It also works with constant pressure and volume, making it ideal. Works with different types of molecules (monatomic, diatomic ...).
Is there more to it that I am missing?

Specific heat capacity is an intensive property, and changes in other intensive properties will affect specific heat capacity. What you are missing is the "how" of "how is heat capacity applied in practice to analyze thermodynamics changes in physical systems." Without knowing how it can be applied in practice, understanding what it represent is useless.

 

[Yseult]

Specific heat capacity is an intensive property, and changes in other intensive properties will affect specific heat capacity. What you are missing is the "how" of "how is heat capacity applied in practice to analyze thermodynamics changes in physical systems." Without knowing how it can be applied in practice, understanding what it represent is useless.

Thank you for the answer! I will look more into it.