Helmholtz Free Energy

Related to Gibb’s Free Energy

$F(\tau ,V)\equiv U-\tau \sigma \Rightarrow \mathrm{d}F=-\sigma d\tau -P\mathrm{d}V+\mu \mathrm{d}N$

• $F$ is the Helmholtz free energy
• $U$ is the internal energy
• $\tau$ is the [fundamental temperature]
• $P$ is [pressure]
• $V$ is the volume of the gas
• $\mu$ is the [chemical potential]
• $N$ is the number of particles

$F=-\tau \ln Z$

• $Z$ is the [partition function]

$F=N\tau \left(\ln \left(\frac{n}{n_Q}\right)-1\right)$

• For monatomic (unsure whether it needs to be monatomic) ideal gas