Say there is a vessel with constant volume

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SUMMARY

This discussion focuses on designing an experiment to measure the entropy change with respect to pressure, (dS/dP), in a vessel of constant volume. Participants suggest transforming (dS/dP)v into a function of heat capacity (Cp), volume (V), pressure (P), and temperature (T). The method involves varying pressure and measuring entropy to plot S vs. P, ultimately determining the slope. The conversation emphasizes starting with the enthalpy equation and manipulating it to isolate relevant variables for the experiment.

PREREQUISITES
  • Understanding of thermodynamic concepts, particularly entropy and enthalpy.
  • Familiarity with the equation of state (EOS) for gases.
  • Knowledge of heat capacity (Cp) and its implications in thermodynamic processes.
  • Experience with experimental design and data analysis in thermodynamics.
NEXT STEPS
  • Study the derivation of the enthalpy equation in thermodynamics.
  • Learn about the relationship between entropy and pressure in constant volume systems.
  • Explore experimental techniques for measuring entropy changes in gases.
  • Investigate the implications of the equation of state (EOS) on thermodynamic properties.
USEFUL FOR

This discussion is beneficial for thermodynamic researchers, experimental physicists, and engineers involved in designing experiments related to gas behavior and entropy measurement.

GGdog0818
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Say there is a vessel with constant volume. We know the EOS, moles and Cp of the vapor in it. How can we design an experiment to measure the (dS/dP) at constant V?

I think the idea is to transform (dS/dP)v into something that consists of Cp, V,P,T only. Then we can measure the small difference in T or P to substitute into equation and get (dS/dP)v.

But how? Anyone has an opinion?

THX
 
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Welcome to PF;
Directly: dS/dP is the slope of the S vs P graph isn't it?

Well, you could find a way to vary the pressure and measure the entropy - plot S vs P and take the slope.
How you do that, and cope with the complications, determines the experiment.
 
Start with the equation for dH expressed in terms of dT and dP, and set this equal to TdS + VdP. Then eliminate VdP from both sides, and you will see what to do next.
 

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