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Thermodynamic Relations Notes | Study Mechanical Engineering SSC JE (Technical) - Mechanical Engineering

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THERMODYNAMIC RELATIONS EQUILIBRIUM AND STABILITY

Thermodynamic Relations Notes | Study Mechanical Engineering SSC JE (Technical) - Mechanical Engineering

Thermodynamic Relations Notes | Study Mechanical Engineering SSC JE (Technical) - Mechanical Engineering

Thermodynamic Relations Notes | Study Mechanical Engineering SSC JE (Technical) - Mechanical Engineering

Thermodynamic Relations Notes | Study Mechanical Engineering SSC JE (Technical) - Mechanical Engineering

where
g is Gibbs function

  •  Maxwell's equations

Thermodynamic Relations Notes | Study Mechanical Engineering SSC JE (Technical) - Mechanical Engineering
Thermodynamic Relations Notes | Study Mechanical Engineering SSC JE (Technical) - Mechanical Engineering

Thermodynamic Relations Notes | Study Mechanical Engineering SSC JE (Technical) - Mechanical Engineering

Thermodynamic Relations Notes | Study Mechanical Engineering SSC JE (Technical) - Mechanical Engineering

Thermodynamic Relations Notes | Study Mechanical Engineering SSC JE (Technical) - Mechanical Engineering

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.

Thermodynamic Relations Notes | Study Mechanical Engineering SSC JE (Technical) - Mechanical Engineering

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

Thermodynamic Relations Notes | Study Mechanical Engineering SSC JE (Technical) - Mechanical Engineering

  • For ideal gas μj = 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.

Thermodynamic Relations Notes | Study Mechanical Engineering SSC JE (Technical) - Mechanical Engineering

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

Thermodynamic Relations Notes | Study Mechanical Engineering SSC JE (Technical) - Mechanical Engineering

Thermodynamic Relations Notes | Study Mechanical Engineering SSC JE (Technical) - Mechanical Engineering

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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