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?
[Physics] isothermal compression of water and definition of temperature
phase-transitionpressuretemperaturethermodynamics
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Imagine a container containing just ice at $-1^\circ \rm C$. When you heat it, the energy goes into kinetic motion of the molecules, and its temperature increases. Similarly, if the container is filled with liquid water at $1^\circ \rm C$ its temperature will increase for the same reason.
But now imagine the container is filled with 90% ice and 10% water at $0^\circ \rm C$. If you heat the water part up, it's temperature will temporarily increase a little. But now the water is hotter than the ice, so heat will be transferred from the water to the ice. When the ice is heated above $0^\circ \rm C$ it melts, and this uses up some energy, cooling the water. This will continue until the ice and the water are the same temperature again, so you'll end up back at $0^\circ \rm C$, but with a higher proportion of liquid water and less ice.
This is why, if you heat a mixture of the two phases slowly enough, all the energy will go into melting the solid rather than increasing the temperature. It continues until all the solid has melted, which is when the temperature starts increasing again. The same thing happens in reverse if you decrease the temperature.
I'll give brief answers to your questions. If you need more detail, you should ask your questions separately.
What's the difference between heat and work at the atomic level? Isn't heat simply work between particles colliding with different momentum against each other?
Treating a substance semi-classically, one can say that at the atomic level, the atoms have a certain position and momentum. Quantum mechanically, even that's dubious because position and momentum are conjugate variables. With regard to heat and work, these don't exist at the atomic level.
Heat and work are processes, not states. Atoms don't contain heat or work. Neither do individual collections of atoms. Heat and work are measures of quantities transferred amongst objects. Objects don't contain heat or work.
Does an increase of pressure also increases the temperature of the gas?
For an ideal gas being compressed adiabatically, the answer is an emphatic yes. For anything else, the answer is sometimes yes, sometimes no. The answer depends on how much heat is being transferred into or out of the gas and on the nature of the gas. If the gas is right at the triple point (ideal gases don't have a triple point), all that compressing the gas adiabatically is going to do is cause some of the gas to turn into liquid or solid.
Excluding water and other special materials, why does a increase of pressure over a solid rises is melting point?
What your teacher told you is nonsense. Increased pressure does not decrease the molecule's motion. What increasing the pressure does do is to decrease the intermolecular distance.
The reason most substances contract when they freeze is because the bonding forces that make a substance become a crystalline solid hold the atoms/molecules closer together than the intermolecular distance at the same temperature in the liquid phase. Increasing the pressure in these substances decreases the intermolecular distance, thereby making it easier for those intermolecular bonding forces that make a substance a solid to take hold.
Water is different. It expands upon freezing. The structure of ice (ice Ih) is very open thanks to the hydrogen-hydrogen bonds in ice. Because ice expands upon freezing at normal pressures, increasing the pressure reduces the freezing point. Increase the pressure beyond about 100 atmospheres and water/ice starts behaving like most other substances. Increase the pressure beyond 3000 atmospheres and something even weirder happens. Now the freezing point drops markedly with increasing pressure. Increase the pressure beyond that and something even weirder happens: The freezing point increases again, this time very sharply increasing with rising pressure. The freezing point is over 600K at a pressure of 100,000 atmospheres.
If the pressure reduces the motion of the particles, how can the inner core have material with higher temperatures (i.e. particles with higher average kinetic energy)?
What your teacher told you was wrong.
Best Answer
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.