Siemens
An oceanographer lowers a probe over the side and measures not salt but current. An alternating current flows between the electrodes of the probe, and from its strength the instrument tells how much salt is in the water. Seawater conducts current millions of times better than water from a laboratory purifier. Since 1978 this is exactly how the salinity of the ocean is determined.
Conductance is the reciprocal of resistance. Resistance shows how much a conductor hinders current; conductance shows how easily current passes through it. One siemens is the conductance at which a voltage of 1 V drives a current of 1 A. Lord Kelvin proposed calling this unit the “mho”: the word “ohm” read backwards.
| Notation | S |
| Definition | ampere per volt · A/V · Ω⁻¹ · kg⁻¹·m⁻²·s³·A² |
| Reference values | conductance quantum 2e²/h — 77.480 917 µS · KCl solution 0.01 mol/L — 1413 µS/cm at 25 °C · 1 S = 1 ℧ |
| Introduced | mho, ℧ — since 1883 · siemens in the SI since 1971, 14th General Conference |
| Standards | ISO 80000-6 · ISO 7888 · IEC 60746-3 · SI Brochure 9th ed. |
| Typical values | 5.5 µS/m — ultrapure water · 5.3 S/m — seawater · 60 MS/m — copper |
01 · Definition
An ampere for every volt
Conductance G equals the current that flows through a conductor at a voltage of one volt. It is the reciprocal of resistance: a 1 kΩ conductor is 1 mS, a 1 Ω conductor is 1 S. Siemens are handy wherever current takes several paths at once. The conductances of parallel branches simply add up.
In a metal current is carried by electrons, in water by the ions of dissolved salts. Pure water barely conducts, but every pinch of salt adds ions. That is why the conductance of water tells how much salt it contains. For this, conductivity is used: the conductance of a cube of the substance, referred to its length and area.
Why siemens add up in parallel, not ohms
A 10 V battery feeds four resistors connected in parallel. Each branch can be switched on and off. The red dots are the current in a branch; they run faster the higher its conductance. The current of each branch equals its conductance times 10 V, and the currents add up. So the conductances add up too, while the total resistance has to be found through fractions.
A water meter measures the conductance between two electrodes but displays conductivity. To do this it divides siemens by the cell constant: the ratio of the gap between the electrodes to their area. In a cell with 1 cm² electrodes 1 cm apart the numbers are the same, only the units differ: µS and µS/cm. If the electrodes are moved twice as far apart, the conductance halves while the conductivity stays the same.
Why salt conducts current and sugar does not
On the left is a conductivity meter; its sensor is lowered into a 200 mL glass. The instrument applies an alternating voltage between two platinum electrodes and measures the current. Red dots are ions of sodium and other metals, blue ones are ions of chlorine and acid residues. Every time the voltage changes sign, the ions turn towards the other electrode. With the spoon above you can add salt or sugar. The hot plate under the glass heats or cools the water. The magnifier on the right shows that an ion drags a shell of water molecules along with it. The alternating voltage on the scene is slowed down a thousand times.
Choose the water and add salt to it.
02 · Conversion
| Unit | Value | Where it is met |
|---|---|---|
| {n} | {v} | {note} |
The mho, ℧, equals exactly one siemens. It is still found in American technical literature.
For water, µS/cm is written. 1 µS/cm = 0.1 mS/m = 100 µS/m — it is the same conductivity.
TDS meters show TDS in mg/L. It is not a measurement but a conversion: the conductivity is multiplied by 0.5—0.7.
03 · Orders of magnitude
04 · Measuring instruments
05 · Writing rules
06 · Neighbouring units
07 · Historical section
Since 1978 the salinity of the ocean has been determined on the PSS-78 scale. It is the ratio of two conductivities: of the sample and of a potassium chloride solution, 32.4356 g per kilogram of water, at 15 °C. If the ratio equals one, the salinity is 35. To check salinometers all over the world, sealed ampoules of standard seawater are shipped. Each batch is labelled with its K₁₅ ratio.
Ordinary conductivity meters are checked against KCl solutions. A 0.01 mol/L solution gives 1413 µS/cm at 25 °C. The conductivity of water rises by about 2 % per degree. That is why the instrument converts the reading to 25 °C, and the report gives both figures: the reading and the temperature.
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