Deriving the equation for lines of constant enthelpy

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SUMMARY

The discussion focuses on deriving the equation for the partial derivative (dP/dV)H, which represents the change in pressure with respect to volume while holding enthalpy constant. Participants emphasize the necessity of starting with the equation of state and utilizing the differential form dT=(∂T/∂P)V dP + (∂T/∂V)P dV. Additionally, they highlight the importance of combining this with the enthalpy equation dH=C_P dT + (V - T(∂V/∂T)P)dP to achieve the desired derivation.

PREREQUISITES
  • Understanding of thermodynamic concepts, specifically enthalpy and its derivatives.
  • Familiarity with the equation of state in thermodynamics.
  • Knowledge of Maxwell's relations and their applications.
  • Proficiency in calculus, particularly in handling partial derivatives.
NEXT STEPS
  • Study the derivation of Maxwell's relations in thermodynamics.
  • Learn about the implications of the equation of state for different thermodynamic systems.
  • Explore the application of the triple product rule in thermodynamic equations.
  • Investigate the relationship between enthalpy and temperature changes in various processes.
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Students and professionals in thermodynamics, chemical engineering, and physical chemistry who are looking to deepen their understanding of enthalpy and its mathematical representations.

djkuehlos14
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How would one derive the equation for (dP/dV)H? That is the partial of P over the partial of V, holding H constant. I've tried many different things, triple product rule, maxwell relationships, and nothing seems to work. I appreciate any advice.
 
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djkuehlos14 said:
How would one derive the equation for (dP/dV)H? That is the partial of P over the partial of V, holding H constant. I've tried many different things, triple product rule, maxwell relationships, and nothing seems to work. I appreciate any advice.

You need to start with the equation of state, and write
dT=(\frac{\partial T}{\partial P})_VdP+(\frac{\partial T}{\partial V})_PdV

You need to combine this with the equation:

dH=C_PdT+(V-T(\frac{\partial V}{\partial T})_P)dP
 

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