Phase Equilibrium

About

One chemical changes state — heated, cooled, compressed, expanded or throttled. Give the amount as a quantity for a sealed vessel or as a rate for a flowing stream; finds the final state and the heat and work.

What This Models

A substance moving from one state to another, either as a fixed amount in a vessel or piston, or as a steady stream through a device. Both are the same equation of state answering the same question; what separates them is whether you have a quantity or a rate.

Inputs

Component and Name or Formula choose the chemical, or a mixture of up to 6, exactly as on the Property tab. The default is Nitrogen.

Amount as is the one dropdown that decides everything else. Its seven choices are Mass, Moles and Volume (a quantity, for a vessel) and Mass flow, Molar flow, Volumetric flow and Normal Volumetric Flow (a rate, for a stream). Type the value beside it, in the unit chosen on the Units tab. Switching between a quantity and a rate carries the chemical and the starting temperature and pressure across, so the form does not reset.

Initial Temperature and Initial Pressure (inlet, for a stream) start at 20 °C and 1 bar.

Specify pins down the final state. On a quantity basis you can give the final temperature, pressure or volume; on a rate basis only the outlet temperature or pressure, since a stream has no volume of its own. The default is a final pressure of 10 bar.

Calculation type (labelled Device / process for a stream) is the path taken: Constant Volume, Constant Temperature, Constant Pressure, Adiabatic (Isentropic) or Isenthalpic (Throttle). Constant Volume is offered for a quantity only. A type that contradicts what you pinned down is greyed out rather than removed, so it stays visible why it is unavailable: a specified final temperature rules out Constant Temperature and Isenthalpic, a specified final pressure rules out Constant Pressure, and a specified final volume rules out Constant Volume. If your current choice becomes unavailable, it is cleared and a hint explains why.

Isentropic efficiency (%) appears only for Adiabatic. 100 % is the reversible ideal; a real compressor or turbine is lower.

Press Calculate to solve. Editing any input, or changing a unit, clears the result.

The Amount Decides Which

Enter a mass, a number of moles or a volume and this is a closed system: a fixed amount in a vessel, where the work is n times the change in internal energy. Enter a mass flow, molar flow, volumetric flow or normal flow and it is an open system: a stream through a compressor, turbine, exchanger or valve, where the shaft work is the molar flow times the change in enthalpy. You do not choose between them separately — the amount you have already says which one you mean.

What Changes With It

Constant volume is offered only for a quantity. A flowing stream has no volume of its own, only a rate, so holding it constant means nothing — and for the same reason a final volume can only be asked for on a quantity basis. Everything else is common to both: constant pressure, constant temperature, adiabatic with an isentropic efficiency, and isenthalpic throttling.

The normal-flow reference defaults to 20 °C and 1 atm and is editable on the Units tab. Check it against your instrument: "normal" conditions are not standardised, and a 0 °C reference reads about 7 % higher in mass terms.

Method

Given the initial state and the path, the final state is solved directly from the equation of state, and the energy follows from the first law, with the sign convention that positive means energy added to the fluid.

Key Relations

n·(U₂ − U₁) = Q + W        quantity basis (closed system)
ṅ·(h₂ − h₁) = Q̇ + Ẇ        rate basis (open, steady flow)

n is the fixed amount; ṅ the flow rate. U is internal energy, h is enthalpy — the open-system form carries h rather than U because a flowing stream does flow work on its surroundings just by moving, and h = U + Pv already accounts for it. Isenthalpic (a throttle) is the special case h₂ = h₁: no work, no heat, and the temperature still changes — the Joule–Thomson effect. Combinations that contradict each other — isenthalpic against a specified final temperature, say — are greyed out rather than silently answered.

What comes back

The answer is a grid of cards under a heading naming the calculation type and the chemical.

For a quantity (a vessel):

For a stream:

A blue banner repeats the path, "From 20 °C, 1 bar to …". A single-phase state reads 100 % / 0 % or 0 % / 100 % for its liquid/vapour split. Anything in between means the state sits under the saturation dome, where temperature and pressure are no longer independent. A supercritical fluid reads N/A, because above the critical point there is no liquid-vapour boundary to be either side of.

The equation of state is CoolProp's reference equation where one exists for the fluid, and Peng-Robinson where none does, which is a general cubic and less accurate, especially for liquid densities. Amber banners flag an extrapolated range or a mixture-model caveat, and a note under the result names the mixture model used.

Solids And Solutions

Neither equation of state models a solid, so a chemical that is solid at your conditions is treated separately: heating or cooling it needs no equation of state, only the integral of its heat capacity. Only a final temperature can be asked for. A target pressure or volume is refused, because compressing a solid is a mechanical process this mode does not model. If the range would cross a melting point, or a sublimation or decomposition point, the calculation is refused rather than under-reporting the energy, because a latent heat would be needed that this mode has no data for. Use the Heater case, which does include melting and boiling.

Water plus dissolved solutes with fitted data is treated as an aqueous solution, from fitted density and heat capacity rather than an equation of state. It carries no phase equilibrium, so the same final-temperature-only rule applies.

Limitations

One substance or one mixture at a time, with its chemical identity fixed: nothing reacts here. For species turning into one another use Chemical Equilibrium or Reaction. Large excursions can push the fluid outside the equation of state's fitted range.