Helmholtz Free Energy

#Physics
Related to Gibb's Free Energy

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

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

$\displaystyle F=-\tau \ln Z$

• $\displaystyle Z$ is the [partition function]

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

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