Thermodynamics Maxwell relation

In summary, the conversation discussed the use of the relation (\frac{\partial S}{\partial V})=\frac{P}{T} and its connection to the first law of thermodynamics. It was noted that this relation can be obtained by setting dE = 0 and keeping the number of particles and energy constant in the system. This relation was also represented in subscript form as a reminder to keep E and N constant. It was questioned if this relation could be derived without using the first law of thermodynamics.
  • #1
LagrangeEuler
717
20
When can be used
[tex](\frac{\partial S}{\partial V})=\frac{P}{T}[/tex]?
 
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  • #2
The fundamental relation is, if I recall correctly,
##\mathrm dE = T \, \mathrm dS - p \, \mathrm dV + \mu \, \mathrm dN##

So setting dE = 0, you obtain P/T = dS/dV when dN = 0, so if the number of particles and the energy in the system don't change.
For convenience you can put this in the subscript:
##\left( \frac{\partial S}{\partial V} \right)_{E, N} = \frac{P}{T},##
as a reminder that E and N should be kept constant.
 
  • #3
And could you get this relation without using first law of thermodynamics?
 

Related to Thermodynamics Maxwell relation

1. What is the Thermodynamics Maxwell relation?

The Thermodynamics Maxwell relation is a mathematical expression that relates the partial derivatives of thermodynamic state variables, such as temperature, pressure, and volume. It is derived from the first and second laws of thermodynamics and plays an important role in understanding the relationships between different thermodynamic properties.

2. How is the Thermodynamics Maxwell relation used in thermodynamic calculations?

The Thermodynamics Maxwell relation is used in thermodynamic calculations to find relationships between different thermodynamic properties, such as the change in entropy with respect to temperature or the change in volume with respect to pressure. These relationships can be used to solve complex thermodynamic problems and make predictions about the behavior of a system.

3. What are the limitations of the Thermodynamics Maxwell relation?

The Thermodynamics Maxwell relation is based on certain assumptions, such as the system being in equilibrium and the working substance being a perfect gas. These assumptions may not hold true in all systems, leading to limitations in the applicability of the relation. Additionally, the Thermodynamics Maxwell relation may not be accurate for systems with phase transitions or non-ideal behavior.

4. How is the Thermodynamics Maxwell relation derived?

The Thermodynamics Maxwell relation is derived from the first and second laws of thermodynamics, which state that energy is conserved and that the total entropy of a closed system always increases. By applying these laws to infinitesimal changes in state variables, such as temperature and pressure, and using mathematical relationships, the Thermodynamics Maxwell relation can be derived.

5. What are some practical applications of the Thermodynamics Maxwell relation?

The Thermodynamics Maxwell relation has many practical applications, such as in the design and operation of heat engines, refrigeration systems, and power plants. It is also used in chemical engineering to optimize processes and in materials science to understand the behavior of materials under different conditions. Additionally, the relation is used in the development of thermodynamic models and equations of state for various substances.

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