# isothermal compression of water and definition of temperature

During isothermal compression of water vapor (below critical temperature), the pressure increases initially, and then remains constant up to certain point, and then steeply increases with small decrease in volume. This means that initially water is in the form of vapor, and finally it becomes liquid. But temperature is the measure of kinetic energy of the molecules. But liquids have less kinetic energy compared to gases. Then how can both liquid and solid phases exist at the same temperature?

• Temperature is not a measure of the average kinetic energy of the molecules. This is only true for an ideal gas. – march Feb 16 '16 at 5:08
• Then how can we define it for real gases – nayana v Feb 17 '16 at 5:00
• Temperature has various more precise definitions, but in thermal equilibrium we have the equipartition theorem which says that the amount of energy per degree of freedom is $k T/2$, so it is fair to say that $T$ does give a measure of the average kinetic energy, whether in a gas or a liquid or solid. The mistake here is the assertion "liquids have less kinetic energy compared to gases". That is not true. – Andrew Steane Nov 7 '18 at 13:13

Why do you think that liquids have less kinetic energy compared to gasses?

Equipartition theorem (https://en.wikipedia.org/wiki/Equipartition_theorem) states that average kinetic energy is the same per degree of freedom and is 1/2 * k * T. The motion of a molecule of water inside a liquid is jittery, but still the molecule has 6 degrees of freedom so the kinetic energy should be the same.

This may look counter-intuitive. We heat water, water evaporates, energy consumed => molecules in gas should move faster. Isn't it? Actually the energy goes to breaking the attractive forces between molecules in liquid.

For the process to be isothermic, heat must be removed at a rate that will hold the temperature constant. Starting with vapor, as heat is removed, there is a phase change from vapor to liquid as the volume decreases, until there is only liquid. Further attempts at compression result in a VERY large pressure increase for a very tiny volume decrease. This means that the "missing" kinetic energy of the vapor was transferred out of the container as heat as the water vapor was condensed.