Drawing constant property lines on p-v/T-s/u-s diagrams

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Discussion Overview

The discussion revolves around predicting the shapes of constant property lines (such as isenthalpic, isothermal, isentropic, and isobaric lines) on various thermodynamic diagrams, including T-s and P-v diagrams. Participants explore the theoretical and practical aspects of these diagrams, particularly in the context of pure substances.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • One participant inquires about rules for predicting the shapes of constant property lines on T-s and P-v diagrams.
  • Another participant suggests using the equation of state, specifically the ideal gas law, to understand the shapes of isotherms and other lines, noting that isotherms have a 1/V shape when temperature is constant.
  • A participant questions the ability to extrapolate from the ideal gas law to other constant property lines in pure substance models, particularly within the vapor dome where no specific constitutive relation exists.
  • It is mentioned that at low pressures relative to critical pressure, the behavior of gas phases can be approximated accurately using heat capacities and other thermodynamic properties, but this becomes more complex at higher pressures requiring additional equation of state data.

Areas of Agreement / Disagreement

Participants express differing views on the applicability of the ideal gas law and the feasibility of extrapolating its implications to other constant property lines in pure substance models. The discussion remains unresolved regarding the best approach to predict these shapes.

Contextual Notes

Participants highlight limitations in applying the ideal gas law to pure substances in the vapor dome and note that the complexity increases at higher pressures, which may affect the accuracy of predictions.

Urmi Roy
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Hi All,

I'm really curious to know how we can predict the shapes of constant property lines (isenthalpic/constant internal energy/isotherms/isentropes/isobars) on any given plot, such as T-s and P-v or even u-s diagrams. Is there a rule to do so? Usually in practice we deal with p-v and T-s diagrams, but other types of plots also exist.
 
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You use the equation of state.
Take the PV diagram: can you see why a constant volume line will be vertical ad the constant pressure line will be horizontal?

The equation of state is (probably) the ideal gas law: PV=nRT ... if temperature is a constant for an isotherm, then P=<constant>/V ... so the isotherm has to have a 1/V shape.

Now extrapolate for the others you are interested in.
 
Simon Bridge said:
You use the equation of state.
Take the PV diagram: can you see why a constant volume line will be vertical ad the constant pressure line will be horizontal?

The equation of state is (probably) the ideal gas law: PV=nRT ... if temperature is a constant for an isotherm, then P=<constant>/V ... so the isotherm has to have a 1/V shape.

Now extrapolate for the others you are interested in.

I'm referring to pure substance P-v/T-s diagrams. Therefore in the vapor dome, no particular constitutive relation exists.

I don't see how can simply extrapolate (again considering the pure substance model) to get things such as constant enthalpy/entropy/internal energy etc lines.
 
Urmi Roy said:
I'm referring to pure substance P-v/T-s diagrams. Therefore in the vapor dome, no particular constitutive relation exists.

I don't see how can simply extrapolate (again considering the pure substance model) to get things such as constant enthalpy/entropy/internal energy etc lines.
At pressures that are low compared to the critical pressure (so that the gas phase behavior approximates an ideal gas), this portion of the diagrams can be approximated very accurately from scratch. All you need to know are the heat capacities of the liquid and the gas as a function of temperature, the heat of vaporization at one temperature, the equilibrium vapor pressure at one temperature, and the specific volume of the liquid as a function of temperature. At higher pressures, filling in these diagrams is more complicated, and requires equation of state data.

Chet
 

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