Derivation of Thermodynamic Relations

Context: Engineering
Thread starter lohboys
Start date Oct 19, 2019
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Derivation Relations Thermodynamic

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SUMMARY

The forum discussion focuses on the derivation of thermodynamic relations, specifically the equation dG = -SdT + VdP. The key transformation involves dividing by dV while holding temperature constant, leading to the expression (dG/dV)T = V (dP/dV)T. The cancellation of dT at constant temperature is confirmed, validating the mathematical steps taken in the derivation.

PREREQUISITES

Understanding of thermodynamic potentials, specifically Gibbs free energy (G).
Familiarity with partial derivatives in thermodynamics.
Knowledge of the first and second laws of thermodynamics.
Basic calculus, particularly differentiation techniques.

NEXT STEPS

Study the implications of Gibbs free energy in chemical reactions.
Learn about the Maxwell relations in thermodynamics.
Explore the relationship between thermodynamic properties and phase transitions.
Investigate the applications of partial derivatives in thermodynamic systems.

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Students and professionals in physics and chemistry, particularly those focusing on thermodynamics and physical chemistry principles.

Oct 19, 2019

lohboys

Homework Statement: I'm trying to derive a thermodynamic relation in terms of P,V,T,Cp,Cv and was wondering if my working was correct. I am trying to derive (dG/dV) at constant temperature

Relevant Equations: dG= -SdT + VdP

dG= -SdT + VdP ... now dividing by dV holding temperature constant
(dG/dV)T = -S (dT/dV)T + V (dP/dV)T ... now dT and constant temperature cancel out
final answer:
(dG/dV)T = V (dP/dV)T