P-v-T diagrams

[Engineers] vs [Physicists]
[Ideal gas law plus real substances]

The equations of state we've seen so far are models which capture some common features of many substances, but are not necessarily exact for any particular substance. Chemical engineers typically depend on tables of thermodynamic properties of particular substances, tabulated at various $T$, $P$, and $v$ values more than an equation of state.

  • Connection of symmetry and critical point.
  • Note that we can have $P(v,T)$, $v(P,T)$, or $T(P,v)$.


  • CP$\equiv$ "Critical Point" @ 374.2 C, 207 atm.
  • Triple point @ 0.01 C, $6 \times 10^{-3}$ atm.
  • expands on freezing.
  • Volume change: at 100 C, 1 cc water $\rightarrow$ 1600 cc steam.

Which substance expands on freezing?