Is Mass Dependent on Temperature According to Mass-Energy Equivalence?

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Discussion Overview

The discussion revolves around the relationship between mass and temperature, particularly in the context of mass-energy equivalence. Participants explore whether atomic mass units are temperature-dependent and how kinetic energy influences the apparent mass of a system. The scope includes theoretical considerations, conceptual clarifications, and some mathematical reasoning.

Discussion Character

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

Main Points Raised

  • One participant questions if atomic mass units are defined at a specific temperature, suggesting that the number of atoms in a mass X could vary inversely with temperature.
  • Another participant asserts that while energy is temperature-dependent, rest mass is not, emphasizing the distinction between rest mass and energy.
  • A participant elaborates that internal motions of atoms can lead to a very small increase in the total rest mass of a solid object due to increased kinetic energy, but this does not affect the number of atoms or their individual rest masses.
  • Some participants agree that while the rest mass of a solid object may increase with energy, this does not imply a change in the number of atoms required to achieve a specific mass.
  • One participant presents calculations to illustrate that the contribution of temperature (300 K) to the rest mass of an atomic mass unit is negligible, suggesting that any changes in mass due to temperature are effectively non-existent.
  • Another participant highlights that even a negligible change in rest mass could imply a significant reduction in the number of atoms in a typical sample, raising questions about the implications of such changes.

Areas of Agreement / Disagreement

Participants express differing views on the relationship between mass and temperature. While some argue that rest mass remains constant regardless of temperature, others suggest that kinetic energy can lead to small changes in rest mass. The discussion remains unresolved, with multiple competing perspectives present.

Contextual Notes

There are limitations in the discussion regarding the assumptions made about the relationship between kinetic energy and rest mass, as well as the definitions of mass and temperature. The mathematical steps presented by participants may also depend on specific interpretations of mass-energy equivalence.

  • #91
xox said:
The individual particles have different "gammas". I already pointed out this mistake.

The particles have different gammas because they have different velocities. I do not see the problem.
 
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  • #92
xox said:
m_{0i}=m_p+\gamma_{ei}(v_e) m_e-u_i (for ONE atom)

From the above, it DOES NOT follow that, for a system of atoms:

M=\Sigma{\gamma'_i m_i}-U

I think part of this is simply definition of U, independent of any pairwise model, such that it can even apply to non-linear interactions. You have a system of particles 'at infinity'. As they come together and bind, radiation is released. The mass of the system is reduced by the radiation released/c^2 (else conservation violated). We call this released energy = mass deficit * c^2 = binding energy = U by convention. U is generically a function of the system as a whole, with a maximum value defining the ground state of the system.
 
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