ANS:C - Maxwell's

Maxwell's equations, in the context of thermodynamics, are a set of four partial differential equations that describe the relationships between the thermodynamic properties of a system. These equations were formulated by the Scottish physicist James Clerk Maxwell in the 19th century. They provide fundamental insights into the behavior of thermodynamic systems and are derived from the laws of conservation of energy and mass, along with other principles of thermodynamics. The four Maxwell's equations are as follows:

1. Maxwell's First Equation (or Maxwell's reciprocal theorem): (∂𝑇∂𝑉)𝑆=−(∂𝑃∂𝑆)𝑉(∂V∂T​)S​=−(∂S∂P​)V​ This equation relates the rate of change of temperature with respect to volume at constant entropy to the rate of change of pressure with respect to entropy at constant volume.
2. Maxwell's Second Equation: (∂𝑇∂𝑃)𝑆=(∂𝑉∂𝑆)𝑃(∂P∂T​)S​=(∂S∂V​)P​ This equation relates the rate of change of temperature with respect to pressure at constant entropy to the rate of change of volume with respect to entropy at constant pressure.
3. Maxwell's Third Equation: (∂𝑃∂𝑇)𝑉=(∂𝑆∂𝑉)𝑇(∂T∂P​)V​=(∂V∂S​)T​ This equation relates the rate of change of pressure with respect to temperature at constant volume to the rate of change of entropy with respect to volume at constant temperature.
4. Maxwell's Fourth Equation (or Maxwell's relations): (∂𝑆∂𝑇)𝑉=(∂𝑃∂𝑉)𝑇(∂T∂S​)V​=(∂V∂P​)T​ This equation relates the rate of change of entropy with respect to temperature at constant volume to the rate of change of pressure with respect to volume at constant temperature.

Maxwell's equations are powerful tools in thermodynamics as they allow one to express partial derivatives of thermodynamic variables in terms of other measurable properties. They provide additional relationships between properties beyond those explicitly defined by the fundamental thermodynamic equations, such as the first and second laws of thermodynamics. These equations are widely used in the analysis and understanding of thermodynamic systems and processes.