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The triple point

Heat and matter · level 6, lesson 4 of 6

A question to start

Lower the pressure, and water boils at a lower temperature. Keep lowering it, and the boiling point drops to the freezing point. What happens below that?

The idea

At one special pressure and temperature, ice, liquid water and water vapour can all exist together. This is water's triple point:

\[611.657 \text{ Pa and } 0.01\ °\text{C}.\]

Below 611.657 Pa, water cannot be liquid at any temperature. Warm the ice and it turns straight into vapour: it sublimes. That is what Phoenix's ice lumps did.

Pressure and the triple point Mars Earth
Average surface pressure 636 Pa 101,400 Pa
Compared with 611.7 Pa just 4% above 166 times above
Olympus Mons86 PaEverest33 kPaEarth101 kPa triple point612 PaMars average636 Pa ice sublimesliquid water possible 100 Pa1 kPa10 kPa100 kPa air pressure: each tick is 10 times the one before

Mars's average pressure is only just above the triple point. Pressure falls with height, so on high ground it drops below it, and liquid water is impossible there.

Worked examples

1. How high? Mars's pressure falls by a factor \(e\) (to 37%) every 11.0 km of height, its scale height: \(p = p_0 e^{-h/H}\). It falls from 636 Pa to 611.7 Pa when \(e^{-h/11} = 611.7/636 = 0.962\), so \(h = -11 \ln 0.962 = 0.43\) km. At average pressure, anywhere more than about 0.4 km above the average level is too high for liquid water.

2. Olympus Mons. Its top is about 22 km up: \(p = 636\,e^{-22/11} = 636 \times 0.135 = 86\) Pa, far below the triple point.

3. On Earth. Even at the top of Everest, about 33 kPa, the pressure is 50 times the triple point. Liquid water is possible anywhere on Earth's surface.

Try it

  1. What can exist together at the triple point?
  2. What happens to ice warmed at a pressure below 611.7 Pa?
  3. Using the scale height, find the pressure 5.5 km above the average level on Mars.
  4. Why is liquid water so rare on Mars?
Answers
  1. Ice, liquid water and water vapour.
  2. It sublimes: it turns straight into vapour without melting.
  3. \(636 \times e^{-0.5} = 636 \times 0.61 = 386\) Pa.
  4. The pressure is close to, or below, the triple point, so liquid water can last only in a narrow range of temperature, if at all.

Common mistake

"The triple point is 0 °C." It is 0.01 °C, and only at 611.657 Pa. At Earth's air pressure, ice melts at 0 °C.

Where it leads