Lesson 13 · Superheated enthalpy
Two coordinates, one cell
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Two coordinates, one cell

On the saturation line, pressure alone fixes everything: name the pressure and the table hands you the temperature and every enthalpy. Above the line that stops being true. Superheated steam at 2,000 kPa can be at 300 °C or at 500 °C, and its enthalpy is different at each. So the superheated table has two coordinates, and we write h=h(p,T)h = h(p,\,T), read aloud h equals h of p and T. hh is the specific enthalpy in kJ/kg, pp the absolute pressure in kPa, and TT the steam temperature in °C. Pressure picks the block. Temperature picks the entry inside it.

There is no short formula behind those entries. The printed table is generated from the IAPWS-IF97 industrial standard, a long polynomial fit that nobody evaluates by hand. Your job is to read it correctly, and then to subtract. Enthalpy has an arbitrary zero, so a single value means little. Every use of this table ends in a difference.

The first difference is the heat added per kilogram between two states at one pressure: q=h2h1q = h_2 - h_1, q equals h-two minus h-one, where h1h_1 is the inlet enthalpy, h2h_2 the outlet enthalpy and qq the heat added, all in kJ/kg. Scale it by the steam rate and it is a duty: Q˙=m˙(h2h1)\dot Q = \dot m\,(h_2 - h_1), Q-dot equals m-dot times h-two minus h-one, with m˙\dot m in kg/s and Q˙\dot Q in kW. The subscripts follow the steam: 1 is where it enters the section, 2 is where it leaves.

Two nuggets. At the same temperature, steam at a HIGHER pressure carries LESS enthalpy: 3,052 kJ/kg at 1,000 kPa and 300 °C, but 2,962 at 4,000 kPa. Read the wrong block and the error is silent. And the same 50-degree rise costs about 106 kJ/kg in one corner of the table and 131 in another, so a constant specific heat is a guess. The table exists because that number moves.

h=RTτ(γτ+γτr),τ=540 KTh = R\,T\,\tau\left(\gamma^{\circ}_{\tau} + \gamma^{r}_{\tau}\right), \quad \tau = \frac{540\ \mathrm{K}}{T}

  • hh= Specific enthalpy (specific latent heat)
  • pp= Pressure (absolute) (pressure)
  • TT= Steam temperature (temperature)
Superheated Steam Enthalpy h(p, T) solver →