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**THERMODYNAMIC RELATIONS EQUILIBRIUM AND STABILITY**

where

g is Gibbs function

**Maxwell's equations**

__Joule-Thompson Effect__

When a gas is throttled then first its temperature increase (heating) as the pressure decrease but after a particular pressure, temperature decrease (cooling) as pressure decrease. At different initial temperature different such pressure exist.

- The curve connecting all transition point is inversion curve.
- The Joule-Thompson Coefficient is:

- For ideal gas μ
_{j}= 0 i.e. in throttling process temperature of ideal gas remains constant. - If initial temperature and pressure are within inversion curve, i.e. below maximum inversion temperature, cooling happens.
- Except Hydrogen and Helium the maximum inversion temperature of all the other gases is more than atmospheric temperature so cooling occurs in throttling of those gases.
- For Hydrogen and Helium maximum inversion temperature is below atmospheric temperature so heating occurs after throttling.
- For cooling of Hydrogen and Helium after throttling, they should initially be cooled below their maximum inversion temperature.
- There is no change in Temperature when an ideal gas is made to under go a Joule-Thompson expansion

__Clausius-Clapeyron equation__

- Clausis-Clayperon equation is a way of characterizing a discontinuous phase transition between two phases of matter of a single constituent.
- On a P-T diagram, the line separating two phases is known as the coexistence curve.

where dp/dT is the slope of the tangent to the co-existence curve at any point, l is the specific latent heat, T is the temperature and V is the specific volume change and S stands for specific entropy.

where,

Sf = entropy of the final phase

Si = entropy of the initial phase

Vf = volume of the final phase

Vi = volume of the initial phase

__Triple Point__

Phase diagram for water and any other substance on p–T coordinates.

- Slope of sublimation curve at the triple point is greater than that of the vaporization curve.

i.e. (dy/dx)_{sublimation}_{ }> (dy/dx)_{vaporization}

- Gibbs phase rule for non reactive system

Degree of freedom:

f = c – p + 2

c — no. of components

p — no. of phases

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