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Superheated Steam Enthalpy h(p, T)

Also known as superheated steam enthalpy · steam table enthalpy · h from pressure and temperature · IAPWS-IF97 region 2 · superheated steam table · enthalpy of superheated steam · steam enthalpy calculator · temperature from enthalpy superheated

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

Worked example: R7-97 Table 15: 0.0035 MPa, 300 K → 2549.9114 kJ/kg — press Try an example to run it live, then adjust anything.

Enter your known values, leave one input blank, and solves for the missing one. Tap a variable’s symbol to see what it means, with a typical value. Try different units for next level excitement!

Constant used — built into this formula, no need to enter
T0=273.15 KT_0 = 273.15\ \text{K}Ice point (0 °C in kelvin) · exact
See also
Degrees of Superheat — How far above the saturation line the state point on this page actually sits.Saturation Temperature and Pressure of Steam — The line this region ends at, and the boundary this page refuses to cross.Steam Turbine Specific Work — The usual reason to want an inlet enthalpy: subtract the exhaust one and you have the work.Desuperheater Water Injection Rate — Turning a target temperature into the target enthalpy that station has to spray to.

Learning zone

Once steam is dry, pressure and temperature stop being the same fact and become two independent ones, and a single number no longer describes the state. That is what makes the superheated table two-dimensional: a grid of pressures down the side, temperatures across the top, and a small block of properties in every cell. This page is that grid without the grid — it evaluates IAPWS-IF97 Region 2 directly at whatever pressure and temperature you give it, so there is no interpolating between a 250 °C row and a 300 °C row and no wondering whether the interpolation should have been linear.

It is worth being clear about what IF97 is. It is the INDUSTRIAL formulation, released in 1997 by the International Association for the Properties of Water and Steam and adopted by ASME, and it is the equation the printed tables are generated from rather than an approximation of them. Region 2 covers superheated vapour from 0 °C to 800 °C and from vacuum up to 100 MPa, and its Gibbs function is written in two halves: an ideal-gas part of nine terms, and a residual part of forty-three that carries everything real gases do that ideal ones do not. The enthalpy is (h = RT au(gamma^{circ}_{ au} + gamma^{r}_{ au})) with ( au = 540,mathrm{K}/T), and the split is visible in the numbers: at 0.0035 MPa and 700 K the ideal half gives 3335.73 kJ/kg and the true answer is 3335.68, so the whole residual is worth 15 parts per million. At 30 MPa and the same temperature the residual drags that 3335.7 down to 2631.5. Low-pressure steam really is nearly an ideal gas; boiler steam really is not.

Two boundaries and the page stops rather than guesses. Below the saturation temperature at your pressure there is no superheated steam to have an enthalpy — the sample is wet, its temperature is pinned to the saturation line whatever its enthalpy, and the thing to solve for is quality rather than temperature. Above 800 °C IF97 hands over to Region 5, and at high pressure and moderate temperature it hands over to Region 3, the near-critical region where the standard switches from a Gibbs function in (p, T) to a Helmholtz function in (ρ, T) because the isotherms there are too flat in pressure for anything else to work. Both hand-overs are honest ends of a fitted range, not physics.

The enthalpy zero is arbitrary, so only differences mean anything. IAPWS fixes it at the triple point, where the internal energy and entropy of saturated liquid water are both defined as zero. That is a convention, and every other steam table shares it, which is why the numbers agree — but it also means an absolute enthalpy is not a quantity you can do anything with on its own. Every real use of this page ends in a subtraction: inlet minus exhaust across a turbine, before minus after across a desuperheater, superheated minus saturated to find how much heat the superheater added. The page also refuses to run backwards to a pressure, and the reason is instructive rather than a limitation of the software. At 300 °C the enthalpy falls only from 3076.95 kJ/kg at 1 kPa to 3051.70 kJ/kg at 1 MPa — a thousandfold change in pressure for eight-tenths of a percent in enthalpy. Read that backwards and an enthalpy known to a tenth of a kJ/kg pins the pressure to within a factor of several, which is a way of saying it does not pin it at all. Pressure is the easy thing to measure; measure it.

Superheated Steam Enthalpy h(p, T)
h=R T τ(γτ∘+γτr),τ=540 KTh = R\,T\,\tau\left(\gamma^{\circ}_{\tau} + \gamma^{r}_{\tau}\right), \quad \tau = \frac{540\ \mathrm{K}}{T}
Where
  • hh= Specific enthalpy (J/kg)
  • pp= Pressure (absolute) (kPa)
  • TT= Steam temperature (°C)
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