The formula, in words

The amount in an offer is its absolute pressure times its volume, divided by its departure factor, its absolute temperature and the molar gas constant. A gauge reading becomes absolute by adding the pressure of the air where it was taken. An absolute reading is used as it stands. Celsius becomes kelvin by adding 273.15. Dividing by price gives the amount for a unit of money. The gas constant cancels out of the comparison. The amount is exactly proportional to absolute pressure, which is why the moving offer is a straight line.

A worked example

1. Large volume absolute pressure: $900 + 100 = 1{,}000.000000$ kPa.
2. $P_s = 1{,}200.000000$ kPa, where $P_s$ is the smaller volume absolute pressure.
3. Large volume absolute temperature: $40 + 273.15 = 313.150000$ K.
4. Smaller volume absolute temperature: $20 + 273.15 = 293.150000$ K.
5. Large volume amount: $\frac{110{,}000}{2{,}603.673968874687}=42.247993149$ kmol.
6. Smaller volume amount: $\frac{120{,}000}{2{,}437.384716511622}=49.233097749$ kmol.
7. At equal prices of 1,000.00, Large volume gives 0.042247993149 and Smaller volume gives 0.049233097749 kmol per unit of money.
8. The exact comparison changes between 1,065.335772 and 1,065.335773 kPa gauge.

The neighbouring question

“Reference state: two property tables, one hidden offset” is about one stream read against two references whose zero points differ. This page reads two offers against each other on the conditions each one wrote down. It holds no reference state, no standard condition and no conversion factor, and it never converts a stream.

What this does not model

It compares two quotes on the conditions you typed. It does not price gas, verify a composition, supply a condition a quote left out, or decide whether either offer is acceptable. It assumes both quotes concern the same gas on the same quantity basis with the same included content and the same commercial scope, and it has no way to check that. It takes your departure factor as a declaration about your own conditions.

This page has no reachable refusal

Every value the calculation would refuse is kept inside its domain by the control before the calculation sees it, and the two basis choices are closed sets. The one thing that looks like a refusal is a tie, and a tie is an answer this page prints.

Check it yourself

Set the sweep to run from 1,000 to 1,100 in steps of 10. Eleven values are checked. The answer holds through 1,060 and changes at 1,070. Then choose the second record, which turns the departure factor on and sets the sweep from 600 to 900 in steps of 50. The crossing sits at a lower pressure, with nothing in the two quotes changed.

The calculation domain

Exactly two offers. Volume ranges from 0.000001 to 1,000,000 m³ and temperature from −100 to 500 °C; pressure runs up to the maximum you set. These values allow six decimal places, the factor ranges from 0.01 to 10, price has two decimal places, and atmospheric pressure runs up to 200 kPa.

Source anchors

IUPAC Gold Book, compression factor. NIST reference on fundamental physical constants. The published entry defines the compression factor this page applies, and the published reference carries the molar gas constant it uses. Every condition on this page comes from your own typing.

Boundary

It says which of two quotes holds more of the same gas for a unit of money on the conditions written down and typed here. It does not price the gas, verify its composition, or decide whether either offer is one you should accept.

Calculation version

1.0.0