Write Maxwell's four Thermodynamic Relations.

ANSWER : The Maxwell's four thermodynamic relations are named after James Clerk Maxwell, a Scottish physicist who formulated them in the mid-19th century. He made significant contributions to various fields of physics, including electromagnetism and statistical mechanics, and his work in thermodynamics led to the establishment of these essential relations. The four Thermodynamic Relations are a set of four equations derived from the fundamental thermodynamic properties, these are :

1. Maxwell's First Relation :

This relation links changes in pressure and temperature with respect to volume. It is given as:

\[ \left( \dfrac{\partial T}{\partial V} \right)_P = -\left( \dfrac{\partial P}{\partial V} \right)_T \]

This equation shows that the rate of change of temperature with respect to volume at constant pressure is equal to the negative rate of change of pressure with respect to volume at constant temperature.

2. Maxwell's Second Relation :

This relation connects changes in pressure and temperature with respect to entropy. It is expressed as:

\[ \left( \dfrac{\partial T}{\partial P} \right)_S = \left( \dfrac{\partial V}{\partial S} \right)_P \]

This equation indicates that the rate of change of temperature with respect to pressure at constant entropy is equal to the rate of change of volume with respect to entropy at constant pressure.

3. Maxwell's Third Relation :

This relation correlates changes in volume and temperature with respect to pressure. It is represented as:

\[ \left( \dfrac{\partial V}{\partial T} \right)_P = \left( \dfrac{\partial S}{\partial P} \right)_T \]

This equation demonstrates that the rate of change of volume with respect to temperature at constant pressure is equivalent to the rate of change of entropy with respect to pressure at constant temperature.

4. Maxwell's Fourth Relation :

This relation relates changes in volume and pressure with respect to temperature. It can be written as:

\[ \left( \dfrac{\partial V}{\partial P} \right)_T = -\left( \dfrac{\partial S}{\partial T} \right)_P \]

This equation shows that the rate of change of volume with respect to pressure at constant temperature is equal to the negative rate of change of entropy with respect to temperature at constant pressure.

These four Maxwell relations are essential in thermodynamics and can help in solving various problems and understanding the behaviour of systems under different conditions.

Also Read : Write solution of Schrodinger's Equation for H-atom.

Also Read : Define Probability Current Density. Derive Equation of Continuity.

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