Fundamental Thermodynamics Relation

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SUMMARY

The discussion centers on the fundamental thermodynamic relation expressed by the equation dU = TdS - PdV. The user seeks clarification on calculating partial derivatives, specifically ∂U/∂P and ∂P/∂T, after successfully deriving ∂U/∂V = -P. The response emphasizes the necessity of specifying constant variables when determining these derivatives, highlighting the importance of understanding the conditions under which thermodynamic properties are evaluated.

PREREQUISITES
  • Understanding of thermodynamic concepts such as internal energy (U) and entropy (S).
  • Familiarity with partial derivatives in the context of multivariable calculus.
  • Knowledge of the thermodynamic variables pressure (P) and volume (V).
  • Basic grasp of the laws of thermodynamics and their mathematical formulations.
NEXT STEPS
  • Study the implications of holding variables constant in thermodynamic equations.
  • Learn about Maxwell's relations and their applications in thermodynamics.
  • Explore the derivation and significance of the Helmholtz and Gibbs free energies.
  • Investigate the relationships between thermodynamic properties using the Clapeyron equation.
USEFUL FOR

Students and professionals in physics and engineering, particularly those focused on thermodynamics and physical chemistry, will benefit from this discussion.

Silviu
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Hello! I am a bit confused by the formula ##dU = TdS - PdV##. If I want to compute for example ##\frac{\partial U}{\partial V}## I obtain ##-P##, but how should I proceed to obtain, for example ##\frac{\partial U}{\partial P}## or ##\frac{\partial P}{\partial T}## which are not obvious from the equation? Thank you!
 
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For those partial derivatives you mention, you need to specify what is being held constant.
 

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