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thermodynamics explained

phase diagram explained

The P-T phase diagram splits solid, liquid, gas; plus the P-v saturation dome, triple and critical points

Ice, water, and steam are not different substances. They are the same H2O sitting in a different form according to pressure and temperature. Drag the point on the phase diagram and the same substance moves from solid to liquid and from liquid to gas when you raise the temperature or lower the pressure. This map is the phase diagram. The horizontal axis is temperature, the vertical axis is pressure, and the plane is divided into regions of solid, liquid, and gas. On the boundary that splits region from region the two phases exist together, and there is a place where the three regions meet at one point. This one map holds when a substance freezes and when it boils.

A phase diagram is a map of two axes, temperature across and pressure up. Drag the point around the plane and the region it sits in tells you which phase the substance is in under that condition. The cold high-pressure side at the upper left is solid, the middle is liquid, and the hot low-pressure side at the lower right is gas. Raising only the temperature can melt a solid, and lowering only the pressure can boil a liquid, so what matters is that phase depends on the condition, not on the kind of substance. The same water boils before it reaches 100 degrees on a high mountain, because the low pressure up there has moved the boiling boundary on the diagram. A pressure cooker, the other way, shuts the lid tight and raises the pressure inside so the water has to pass 100 degrees before it boils, and the hotter water cooks food faster.

Now look at the boundaries that split the regions. Pick the boundaries one at a time with the buttons. On the fusion line between solid and liquid, ice and water are together, and on the vaporization line between liquid and gas, water and steam are together. There is also a sublimation line where solid meets gas directly, and dry ice turning straight to vapor without melting is that. On a boundary the two phases coexist in equilibrium, and the place where the three boundaries meet at one point is the triple point, where solid, liquid, and gas coexist together. For each substance the temperature and pressure of this triple point are fixed as one. The triple point of water comes out the same whenever and wherever you measure it, so a sealed cell that reproduces the triple point is used as the reference for calibrating a thermometer.

Now the P-v diagram drawn with pressure and volume. A dome rises in the middle, and the inside of this dome is the saturation region, the stretch where liquid and gas are mixed. Increase the volume with the slider and the outside to the left of the dome is compressed liquid, the inside is a mixture of liquid and vapor together, and the outside to the right is superheated vapor. Inside the dome the fraction the vapor occupies is called the quality. The left end is quality 0, saturated liquid just starting to boil, and the right end is quality 1, saturated vapor fully evaporated. The top where the left curve and the right curve of the dome meet is the critical point, and that is handled in the last scene. This dome and the quality matter especially in a power plant, because wet vapor with liquid drops left has a low quality and eats the turbine blades, so engineers watch this quality closely.

See what happens while something boils. When water boils in a pot, no matter how high you turn the fire the temperature of the water does not rise past 100 degrees, and dragging how far the evaporation has gone shows the liquid turning into vapor while the temperature and the pressure stay the same. The heat you add is not spent raising the temperature. It is spent entirely pulling molecules out of the liquid and making them gas, and this is called latent heat. So while the phase changes the process is isothermal and isobaric and only the volume grows a lot, and on the P-v diagram this process shows as a flat line crossing the inside of the dome. This is why a thermometer does not move until the boiling water has all evaporated. Latent heat also cools you, because sweat takes that much latent heat from the skin as it evaporates and you feel cool.

Last is the top of the dome, the critical point. Raise the temperature with the slider and the higher the temperature, the shorter the flat stretch that crosses the dome, the stretch where liquid and gas are distinct, until at the critical temperature it shrinks to one point. This point is the critical point. Past this temperature and pressure something striking happens. The distinction between liquid and gas disappears altogether. There is no boiling boundary, and you cannot say where liquid ends and gas begins. This state is called a supercritical fluid, dense like a liquid and free to spread like a gas. So the critical point is also where the boiling boundary ends on the phase diagram. This supercritical state is used in practice. Supercritical carbon dioxide slips into a coffee bean like a gas and dissolves caffeine like a liquid, and it is used to take the caffeine out of coffee.

In PracticeTo sum up, the phase of a substance is set by pressure and temperature, not by its kind, and a phase diagram is a map that divides the plane of temperature and pressure into regions of solid, liquid, and gas. On the fusion line, the vaporization line, and the sublimation line that split the regions, two phases coexist, and at the triple point where the three meet at one point the three phases are together. On the P-v diagram drawn with pressure and volume, the inside of the saturation dome is the mixed stretch of liquid and vapor, and that fraction is the quality. While boiling, the temperature and the pressure stay the same and the heat is spent entirely on the phase change, so the process is isothermal and isobaric, and past the critical point at the top of the dome the distinction between liquid and gas disappears. The next lesson looks at the work a gas does when the volume changes like this, the boundary work, as the area on a P-V diagram.
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