1.2.1 Possible basic quantities

What do we need to describe a - simple - fluid locally?

• Macroscopic bulk velocity $\ensuremath{\mathchoice{\mbox{\boldmath$\displaystyle v$}} {\mbox{\boldmath$\te... ...}} {\mbox{\boldmath$\scriptstyle v$}} {\mbox{\boldmath$\scriptscriptstyle v$}}}$ (or momentum $\rho\ensuremath{\mathchoice{\mbox{\boldmath$\displaystyle v$}} {\mbox{\boldmath... ...}} {\mbox{\boldmath$\scriptstyle v$}} {\mbox{\boldmath$\scriptscriptstyle v$}}}$)
• Two thermodynamic quantities, e.g.
  • temperature $T$ and pressure $P$
  • or mass density $\rho$ and internal energy $e_{\rm i}$

All quantities depend on space $\ensuremath{\mathchoice{\mbox{\boldmath$\displaystyle x$... ...ox{\boldmath$\scriptstyle x$}} {\mbox{\boldmath$\scriptscriptstyle x$}}}$ and time $t$. We assume

• LTE: two thermodynamic quantities are sufficient to describe the local microscopic state of the fluid completely: element composition, ionization, occupation numbers, microscopic velocity distribution,
• we do not need to look at the atomic level: we have a continuous fluid.