# Thermodynamics/Thermal Properties Of Matter
## Phase Diagram

A Phase Diagram is graph between Pressure(P) and Temperature(T) showing their relation to a given substance's phases. It shows:
* A substance's phases (solid, liquid, gas)
* What phase is present for each Pressure-Temperature coordinate.
* What Phases can exist for certain ranges of Pressure(P) or Temperature(T)
* At most points on the diagram, only 1 phase can exist.
However, at points of phase change two (or three) phases exist in equilibrium. Such points are on the lines in the graph.
 If a substance is heated at constant P (line A), melting and boiling T are the T at which line A crosses the fusion and vaporization curves. The fusion curve is the line separating the solid and liquid regions. The vaporization curve separates the liquid and gas regions.
 Similarly, if a substance is compressed at constant T (line B), condensation and freezing T are the T at which line B crosses the vaporization and fusion curves.
 At a constant and low P, a material can be sublimated i.e. transformed from solid directly to vapor (line C).
Water phase diagram:
Water contracts on melting. Its fusion curve always slopes upwards to the left.
Melting point:
As P is reduced to p1, melting point of ice increases to TA’. Thus, ice melts at high T if P is reduced. Also, water freezes at lower T if P is increased. This is why skiers press on snow by weight of their body, to create a thin layer of water that helps in skiing.
Boiling point:
As P is reduced to p1, boiling point of water decreases to TB’. Thus, water boils at lower T if P is reduced. This is why a person living on high mountains cannot cook his food properly, because of the low boiling T of water. High pressure vessels are used to cook food in shorter time because the high P produced on water inside the vessel increases the boiling T of water.
Triple point and Critical Point
 Triple point = point at which the 3 phases exist together. There is thus only 1 P and T at which all the 3 phases can coexist.
 Critical point = end of vaporization curve, at which liquid and vapor has the same density.
 Above critical T, no liquid-vapor phase transition occurs for any P.
 Above critical P, no liquid-vapor phase transition occurs for any T. Thus, only 2 phases occur: crystalline solid phase and amorphous phase. As T is raised, the amorphous phase changes continuously from a state which behaves like a liquid to a state which behaves like a perfect gas.
 H and He have very low critical T, so it is hard to liquefy them.

## Thermal Expansion

 Increase in length (∆L) is directly prop. to increase in T (∆T) if ∆T is not too large: ∆L = α L0 ∆T
Where α = coefficient of linear expansion, characteristic for each material, unit = (°C$^{-1}$).
 For isotropic solids, change in length for a given ∆T is the same for all the lines in the solid. Thus, change in area is given by:
∆A = 2 α A0 ∆T = β A0 ∆T
Where β = coefficient of area expansion, unit = (°C$^{-1}$).
 Change in volume is given by
∆V = 3 α V0 ∆T = γ V0 ∆T
Where γ = coefficient of volume expansion, unit = (°C$^{-1}$).
 Fluids have no definite shape, so their volume expansion is large with the T rise.
 Liquids generally expand 10 times greater than solids with increasing T.
 As for water, and above 4°C, it expands as T rises. But when T is lowered from 4°C to 0°C, it expands instead of contracting. Density of water is thus maximum at 4°C.