Adiabatic Processes for an Ideal Gas

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SUMMARY

The discussion centers on deriving the equations for adiabatic processes of an ideal gas, specifically focusing on the relationships represented in the p-V, p-T, and v-T planes. The key equations derived include P Vγ = Constant, P1-γ Tγ = Constant, and T Vγ-1 = Constant. Participants express confusion regarding whether all three curves can be plotted on a single graph or if they should be represented in their respective planes. The First Law of Thermodynamics and properties of ideal gases are foundational to these derivations.

PREREQUISITES
  • Understanding of the First Law of Thermodynamics
  • Familiarity with properties of ideal gases
  • Knowledge of adiabatic processes and their characteristics
  • Ability to interpret and plot graphs in thermodynamic contexts
NEXT STEPS
  • Study the derivation of the adiabatic process equations for ideal gases
  • Learn how to plot p-V, p-T, and v-T diagrams for thermodynamic processes
  • Explore the implications of γ (gamma) in thermodynamic equations
  • Investigate the relationship between internal energy, enthalpy, and temperature for ideal gases
USEFUL FOR

This discussion is beneficial for students and professionals in thermodynamics, particularly those studying ideal gas behavior and adiabatic processes. It is especially useful for physics and engineering students tackling related homework problems.

splitringtail
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Homework Statement



The problem is derive the adiabatic processes for an ideal gas going through a point (v,p) on the p-V plane. Also, in terms of p,T and v,T. Draw the curves.

Homework Equations



First Law of Thermo

Properties of an Ideal Gas

Properties of Adiabatic Processes


The Attempt at a Solution



I derived the transformations, but I am getting the impression from the wording that I have to draw all three curves on the p-V diagram. Yet, I don't know. I figure I have to plot the other two in their respective planes.
 
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splitringtail said:

Homework Statement



The problem is derive the adiabatic processes for an ideal gas going through a point (v,p) on the p-V plane. Also, in terms of p,T and v,T. Draw the curves.

Homework Equations



First Law of Thermo

Properties of an Ideal Gas

Properties of Adiabatic Processes


The Attempt at a Solution



I derived the transformations, but I am getting the impression from the wording that I have to draw all three curves on the p-V diagram. Yet, I don't know. I figure I have to plot the other two in their respective planes.
The question is not clear. Can you provide the actual wording of the question?

AM
 
That is the problem wording.

I have to derive you know

P V^{gamma} = Constant

P^{1-gamma} T^{gamma} = Constant

T V^{gamma-1} = Constant

Which I have, from like the 1st Law of Thermodynamics and some empirical facts regarding the internal energy and enthalpy of an ideal gas.

My problem is I am confused whether it is possible to plot them on the same graph. It just talks about a point in the P-V planes. I would think I have to plot each on in their respective plane.
 

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