Understanding Internal Energy: Kinetic Theory and the Law of Equipartition

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Discussion Overview

The discussion revolves around the concept of internal energy, particularly in the context of kinetic theory of gases and the law of equipartition of energy. Participants explore the relationship between internal energy, temperature, and the challenges in determining absolute internal energy at a specific state.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • Some participants assert that internal energy at a specific state cannot be calculated, emphasizing that calculations typically focus on changes in internal energy rather than absolute values.
  • There is a question about the significance of determining absolute internal energy, with some arguing that it is not meaningful unless considering general relativity.
  • Participants discuss the equation U=(f/2)RT from the law of equipartition of energy, questioning why it cannot be used to determine absolute internal energy.
  • Some participants suggest that internal energy is relative to a reference point defined as zero internal energy, prompting inquiries about what this reference point is.
  • Leela raises concerns about whether the equation for internal energy accounts for chemical bond energies, latent heat effects, and the impact of temperature on heat capacity.
  • There is a distinction made between ideal gases and real gases, with some participants noting that internal energy for real gases depends on additional variables such as volume and entropy.
  • One participant expresses confusion about the core issue being discussed, asking for clarification on the specific question being posed.

Areas of Agreement / Disagreement

Participants express differing views on the ability to calculate absolute internal energy and the relevance of such calculations. There is no consensus on the significance of the reference point for internal energy or the implications of ideal versus real gases.

Contextual Notes

Participants highlight limitations in the discussion, such as the dependence on definitions of internal energy and the assumptions made regarding ideal versus real gases. The role of molecular interactions and other thermodynamic variables remains unresolved.

LEELA PRATHAP KUMAR
Internal energy at a specific state can't be calculated but by kinetic theory of gases and law of equipartition of energy Average kinetic energy is directly proportional to temperature.And for an ideal gas internal energy is due to kinetic energy only for an ideal gas potential energy can be neglected It means internal energy is a function of temperature only. It gives equation
KE=(3/2)RT it is for monoatomic gas (from kinetic theory of gases)
U=(f/2)RT from law of equipartition of energy
Here f is no. Of degrees of freedom
so why can't we find internal energy at a particular state?
 
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LEELA PRATHAP KUMAR said:
Internal energy at a specific state can't be calculated
Why do you think that?
 
mfb said:
Why do you think that?
Because what we calculate the most is change in internal energy but not internal energy at a specific state
 
Are you asking why one can't determine the absolute internal energy of a material?
 
LEELA PRATHAP KUMAR said:
Because what we calculate the most is change in internal energy but not internal energy at a specific state
The total energy does not matter (unless you consider general relativity). You can calculate it, but there is no point in it.
 
Chestermiller said:
Are you asking why one can't determine the absolute internal energy of a material?
Yes
And we always talk only change in internal energy
But U=(f/2)RT from law of equipartition of energy so why can't we determine absolute internal energy
 
mfb said:
The total energy does not matter (unless you consider general relativity). You can calculate it, but there is no point in it.
Can't we calculate internal energy at a state by using law of equipartition of energy U=(f/2)RT
 
LEELA PRATHAP KUMAR said:
Can't we calculate internal energy at a state by using law of equipartition of energy U=(f/2)RT
That is the internal energy relative to some reference point which gets defined as 0 internal energy.
 
mfb said:
That is the internal energy relative to some reference point which gets defined as 0 internal energy.
What is that reference point ?
 
  • #10
U=0 corresponds to T=0 in your equation.
 
  • #11
Leela:

Does your equation for internal energy include chemical bond energies of polyatomic molecules? How about latent heat effects of fusion and vaporization? What about the effect of temperature on heat capacity?
 
  • #12
mfb said:
U=0 corresponds to T=0 in your equation.
But in kinetic theory of gases we took absolute terms only like temperature , pressure
Where this reference point is considered in kinetic theory of gases and law of equipartition of energy
 
  • #13
Chestermiller said:
Leela:

Does your equation for internal energy include chemical bond energies of polyatomic molecules? How about latent heat effects of fusion and vaporization? What about the effect of temperature on heat capacity?
But in kinetic theory of gases we don't consider molecular interactions
 
  • #14
LEELA PRATHAP KUMAR said:
But in kinetic theory of gases we don't consider molecular interactions
But that is a feature of real gases.
 
  • #15
Chestermiller said:
But that is a feature of real gases.
Yes but kinetic theory of gases strictly defined for ideal gases
And internal energy for real gases are different from ideal gases.I mean it is not only a function of temperature but with some variables like volume ,entropy
 
  • #16
LEELA PRATHAP KUMAR said:
Yes but kinetic theory of gases strictly defined for ideal gases
And internal energy for real gases are different from ideal gases.I mean it is not only a function of temperature but with some variables like volume ,entropy
Yes. So? What exactly are you asking? As a PF expert on thermo, I'm having trouble understanding your issue. Can you please restate it more precisely?
 

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