Properties and state: two numbers fix the fluid

The state is a point

• The running case is a boiler feed line: before any law is applied, the water must be pinned down. A state 状态 is the fluid's condition at an instant, and two independent intensive properties fix it - on a property diagram 状态图 the state is a point, and everything else follows.
• A simple compressible substance obeys a two-variable equation of state $p = p(v, T)$, so any other equilibrium property is a function of the same pair. Pick any two independent ones and the rest are determined.

Walking the dome with quality

• Under the saturation dome 饱和线 lies the two-phase region, and quality 干度 $x$ - the vapour mass fraction - walks across it: $v = v_f + x(v_g - v_f)$, likewise $u$, $h$, $s$. Dome arithmetic is linear in $x$ because the two phases sit at the same $p$ and $T$.
• Saturated water 饱和水 at $100^\circ\mathrm{C}$: $p_{sat} = 101.35\ \mathrm{kPa}$, $v_f = 0.001044$, $v_g = 1.6729\ \mathrm{m^3/kg}$, $h_f = 419.04$, $h_{fg} = 2257.0\ \mathrm{kJ/kg}$. At $x = 0.5$: $v = \mathbf{0.837}\ \mathrm{m^3/kg}$ and $h = 419.04 + 0.5 \times 2257.0 = \mathbf{1547.5}\ \mathrm{kJ/kg}$ - one row of the table, one multiplication.

Outside the dome: the ideal gas

• Far from condensation, air obeys $pv = RT$ with $R = 0.287\ \mathrm{kJ/(kg\,K)}$. At $300\ \mathrm{K}$ and $101.325\ \mathrm{kPa}$: $v = RT/p = \mathbf{0.8497}\ \mathrm{m^3/kg}$; double the pressure at the same $T$ and $v = \mathbf{0.4248}$ - exactly half.
• The isotherm is a hyperbola because $T$ fixes the product $pv$; the ideal gas 理想气体 ends where condensation begins, and above the critical point the dome closes and there is no boiling at all.

Three property slips

Recap