Steam diagrams
The saturation dome, the Mollier h–s chart and the T–s diagram for water and steam, drawn from IAPWS-IF97. One diagram per sheet.
The steam tables tell you the number. These three pictures tell you the shape, which is the part a column of figures hides. The dome closing at the critical point, a turbine expansion running straight down the page and out of the dry steam into the wet, a boiler’s heat input standing as an area under a line: none of that is visible in a table, and all of it is obvious here.
Every curve is computed from IAPWS-IF97 when the page is built, the same engine and the same formulation as the tables. Nothing is traced from a published chart. The isobars stop where the standard stops rather than running on past it, and the saturation line is sampled hardest where it moves fastest, so the apex of the dome is a curve and not a corner.
| Saturation line | 0 °C to 373.946 °C, 22.064 MPa |
| Isobars | 0.01 to 100 bar absolute, ten of them |
| Superheat | up to 800 °C, the top of IF97 regions 1 to 4 |
| Worked expansion | 50 bar, 400 °C → 0.1 bar |
The saturation dome. Inside it water is liquid and vapour at once and the temperature cannot move until the boiling is finished; outside it the fluid is one phase and a temperature is free again. The two branches meet at the critical point, 373.946 °C and 22.064 MPa, where the gap between them — the latent heat — has closed to nothing.
- hf and hg — the two branches; the vertical gap between them is the latent heat
- x = 0.2 to 0.8 — dryness fraction inside the dome
Scroll the chart sideways to see all of it.
This is the picture the temperature table was describing in numbers. The lower branch is saturated water, hf, climbing the whole way. The upper branch is dry saturated steam, hg, which peaks at 2,803 kJ/kg around 234 °C and then turns back down. At any temperature the vertical gap between them is the latent heat, and you can watch it close: 2,256 kJ/kg at 100 °C, and zero at the apex.
The Mollier chart. Enthalpy up, entropy across, so an ideal turbine expansion is a VERTICAL line and the heat drop it produces is a distance you can measure with a ruler. The line drawn here starts at 50 bar and 400 °C and ends at 0.1 bar, crossing the saturation line on the way down and finishing inside the dome at a dryness fraction of 0.800.
- Saturation line — x = 1 to the right of the apex, x = 0 to the left
- Isobars — 0.01 to 100 bar absolute
- Isotherms — 200 to 700 °C, superheat region only
- Quality lines — x = 0.75 to 0.95, below the saturation line
- Ideal turbine expansion — 50 bar and 400 °C down to 0.1 bar, isentropic
Scroll the chart sideways to see all of it.
Enthalpy up the page and entropy across it, which is a strange pair of axes until you see what it buys: an ideal, adiabatic, reversible expansion holds entropy constant, so it runs straight DOWN this chart and the work it produces is a length you can measure. The line drawn here drops 1,091 kJ/kg and crosses the saturation line on the way, and the exhaust it lands on is one fifth liquid water.
The T–s diagram. Temperature up, entropy across, and the area under a reversible path is the heat that crossed the boundary — so the boiler’s heat in, the condenser’s heat out and the net work of a cycle are all areas on this one sheet. The cycle drawn on it is a plain Rankine: 50 bar and 400 °C at the throttle, condensing at 0.1 bar and 45.8 °C.
- Saturation dome — liquid branch left, vapour branch right
- Isobars — 0.01 to 100 bar absolute
- Quality lines — x = 0.2 to 0.8 inside the dome
- Rankine cycle — 50 bar and 400 °C into a 0.1 bar condenser
Scroll the chart sideways to see all of it.
Same dome, different axes, and this is the sheet a cycle gets drawn on. Each isobar runs flat across the dome — boiling at constant pressure is boiling at constant temperature — and climbs steeply once the water has run out. The Rankine cycle traced on it heats up the liquid branch, crosses the dome, carries on into superheat, drops vertically through the turbine and closes flat along the condenser.
Letter landscape, one diagram per sheet with its legend and letterhead. The wordmark is drawn inside the SVG, so it survives printing, saving and screenshots alike.
Learning zone
How to read the dome
Pick a temperature on the bottom axis and go straight up. The first line you meet is hf, the enthalpy of saturated water at that temperature; the second is hg, dry saturated steam. Between them you are inside the dome, where the fluid is a mixture and the dashed lines say what fraction of it is vapour. At 100 °C, x = 0.8 means a kilogram carrying 2,224 kJ, which is exactly what a trap ahead of a badly drained main is handing to a coil that was sized for 2,676.
The shape of the top branch surprises people. Dry saturated steam gets LESS energetic above about 234 °C, because past that point the latent heat is falling faster than the sensible heat is climbing. Raise boiler pressure for a hotter steam and each kilogram carries less than it did. That is the whole economics of a steam plant in one bend of one line.
How to read a Mollier chart, and why a turbine engineer owns one
Find the throttle condition where its isobar crosses its isotherm: 50 bar and 400 °C put you at 3,197 kJ/kg and 6.648 kJ/(kg·K). An ideal expansion keeps entropy constant, so drop straight down to the exhaust pressure and read the enthalpy where you land. At 0.1 bar that is 2,105 kJ/kg, an ideal heat drop of 1,091 kJ/kg, and a real machine gets the isentropic efficiency times that.
Now look where the line ended: well below the saturation line, at a dryness fraction of 0.800. One kilogram in five leaving that turbine is liquid water travelling at the speed of the last-stage blades, and it erodes them. The usual limit is around 10 to 12 percent moisture at the exhaust. Getting there from 50 bar by superheat alone would mean a throttle temperature of about 596 °C, which is metallurgy most plants would rather not buy, and that is exactly why reheat exists: take the steam out half-expanded, warm it up again, and finish the expansion from a drier start.
Two more things this chart is good for. Throttling — a valve, an orifice, a leaking trap — is constant enthalpy, so it is a HORIZONTAL move to the right, and you can see at a glance that letting wet steam down in pressure dries it out. And a desuperheater is a vertical move down onto the saturation line at constant pressure, which is why the water it needs is easy to work out from the two enthalpies the chart shows.
How to read a T–s diagram, and why a cycle lives on it
The property that earns this diagram its place is that the area under a reversible path is the heat that crossed the boundary. So on the cycle drawn here, the area under the boiler leg is the fuel, the area under the condenser leg is what goes to the cooling tower, and the difference — the area enclosed — is net work. An efficiency is a picture of two areas, and every improvement a designer makes to a steam cycle is an attempt to make the enclosed area a bigger share of the one below it. This cycle’s ideal efficiency is 36.4 percent, and the Rankine solver does the same arithmetic with your own four states.
The pump leg is worth a sentence because it is nearly invisible. Raising a kilogram of water from 0.1 bar to 50 bar costs about 5.0 kJ against the turbine’s 1,091, so the feedwater leg disappears into the liquid branch of the dome. That tiny cost is the entire reason the Rankine cycle uses a condenser: compressing a liquid is almost free, compressing a gas is not.
Notice too how flat the boiling leg is and how far to the right the isobars lean once they leave the dome. Superheat adds temperature but it adds entropy with it, which is why the expansion from a higher throttle temperature lands further right and drier. The dome is not just scenery on this chart; it is the thing the exhaust has to avoid.
What a drawn chart is for, and where to take a number from instead
These are for understanding and for estimating, and I would rather say so plainly than let a reader trust a pixel. A millimetre of the printed enthalpy axis on the Mollier plate is roughly 28 kJ/kg and a millimetre of the entropy axis is roughly 0.03 kJ/(kg·K). Reading a state off it to better than about half a percent is not a skill, it is optimism, and that was just as true of the wall charts these are drawn in the tradition of.
When the number has to be right, take it from the tables or from the two panels above them, which call the same engine to full double precision and will give you the state at a pressure and temperature you actually have rather than the nearest gridline. Use the chart to see what the answer should look like, and the panel to get it. The chart is also the better tool for catching a mistake: a state that plots in the wrong region is obvious here and invisible in a column of digits.
Where the curves stop, and what has been left off
The isobars stop at 800 °C because that is the top of IF97’s regions 1 to 4, and past it the standard hands over to region 5, a separately fitted equation for combustion-gas temperatures. Nothing here extrapolates. The sampling breaks at the first state the engine refuses rather than drawing a polynomial outside the box it was fitted in, and points near the critical point that will not converge are dropped rather than faked.
Left off deliberately: constant-volume lines, which belong on a Mollier chart in principle and turn it into spaghetti in practice; the compressed-liquid isobars, which crowd onto the liquid branch so tightly that drawing ten of them draws one thick line; and the supercritical region above 22.064 MPa, which has no dome to cross and needs a different picture. The critical point itself is marked on all three sheets, at 373.946 °C, 22.064 MPa, 2,087.2 kJ/kg and 4.412 kJ/(kg·K) — the one state where hf and hg are the same number.
- The steam tables — the same engine, to the digit rather than to the gridline, plus the saturated and superheated panels.
- Rankine cycle efficiency — the cycle on plate 3, with your own four state points.
- Flash steam percentage — a horizontal move on the Mollier chart, worked as a number.
- Latent heat, Q = mL — the vertical gap across the dome, times a mass.
- Saturated steam as a fluid — viscosity, conductivity and specific heat, which none of these sheets carry.
IAPWS R7-97(2012), the Revised Release on the IAPWS Industrial Formulation 1997 for the Thermodynamic Properties of Water and Steam, implemented in full and sampled at page build. The saturation line is drawn from 201 points clustered towards the critical temperature, and 10 isobars carry 470 more between them, all from region 1, 2 and 3 equations, stopping at the standard’s own limits. No curve on this page was traced from a published chart, and no number in the text was typed in by hand.