Does a hot coffee have bigger mass than a cold coffee?

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Discussion Overview

The discussion revolves around the question of whether a hot cup of coffee has a greater mass than a cold cup of coffee, exploring concepts of mass, energy, and temperature within the context of physics. Participants examine the implications of kinetic energy on mass, the nature of invariant mass, and the relationship between temperature and density.

Discussion Character

  • Debate/contested
  • Technical explanation
  • Conceptual clarification

Main Points Raised

  • Some participants argue that relativistic mass is a concept that does not reflect an increase in mass due to kinetic energy, suggesting that the mass of an object remains constant regardless of its speed.
  • Others propose that the mass of a system of particles is not simply the sum of their rest masses, and that kinetic energy contributes to the overall invariant mass of the system.
  • It is noted that the four-momentum of a system, which includes kinetic energy, affects the invariant mass, and that this mass is not additive in the way rest masses are.
  • Some participants highlight that the thermal expansion of hot coffee leads to lower density compared to cold coffee, which may overshadow any mass increase due to energy considerations.
  • Questions arise regarding the nature of kinetic energy in relation to the mass of the coffee and its particles, with some expressing confusion about why higher kinetic energy does not translate to increased mass.
  • There are discussions about the implications of gravitational potential energy and its relevance to the mass of the coffee, with clarifications that potential energy is a property of the system rather than the coffee alone.

Areas of Agreement / Disagreement

Participants generally express disagreement on the interpretation of mass in relation to energy and temperature. There is no consensus on whether the hot coffee is indeed heavier or how kinetic energy affects mass, with multiple competing views remaining throughout the discussion.

Contextual Notes

Limitations include the complexity of defining mass in relativistic contexts, the dependence on the frame of reference, and the challenge of measuring differences in mass due to temperature changes, which are suggested to be negligible compared to other factors like thermal expansion.

  • #91
cianfa72 said:
In this simple case we can think of binding energy as distributed/associated to the electric field.
Binding energy is a property of the bound system. It cannot be assigned to any particular part of it. The "electric field" isn't even a part of the bound system, properly speaking, since it extends to infinity.
 
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  • #92
I don't know if it actually makes sense or not: can we think of the bi-atomic molecule as a system of two particles with a spring attached to them? In this model the binding energy should be simply "stored" in spring's potential energy.
 
  • #93
cianfa72 said:
can we think of the bi-atomic molecule as a system of two particles with a spring attached to them?
You can capture some phenomenological features this way, but of course there is no actual spring.

cianfa72 said:
In this model the binding energy should be simply "stored" in spring's potential energy.
Yes, but as noted above, there is no actual spring so this model does not mean that the binding energy can actually be localized this way.
 
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  • #94
PeterDonis said:
Binding energy is a property of the bound system. It cannot be assigned to any particular part of it. The "electric field" isn't even a part of the bound system, properly speaking, since it extends to infinity.
It can be perfectly described by the energy difference of the electric field configuration of the bound system and the separated system. The energy density of the electric field being proportional to the field strength squared. The electric field is certainly an important part of the bound system, without it the system would not be bound.
 
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  • #95
Orodruin said:
It can be perfectly described by the energy difference of the electric field configuration of the bound system and the separated system.
Wouldn't this have to cover an unbounded region, since it would have to include radiation emitted to infinity during the process of forming the bound system?
 
  • #96
PeterDonis said:
Wouldn't this have to cover an unbounded region, since it would have to include radiation emitted to infinity during the process of forming the bound system?
The radiation is not part of the bound system. It is of course a matter of definition how you draw the boundary of your system (particularly as there is only one EM field - so separating different contributions is a bit arbitrary in the first place), but the bound state itself is stationary and electrically neutral so the bound state field is a dipole at worst - falling off as 1/r^3.
 
  • #97
Orodruin said:
The radiation is not part of the bound system. It is of course a matter of definition how you draw the boundary of your system (particularly as there is only one EM field - so separating different contributions is a bit arbitrary in the first place)
In this case the bound system is actually "two particles plus the electric field".
 
  • #98
cianfa72 said:
In this case the bound system is actually "two particles plus the electric field".
"two particles plus some of the electric field"
 
  • #99
Orodruin said:
"two particles plus some of the electric field"
Why some and not all of the electric field distributed over the space ?
 
  • #100
cianfa72 said:
Why some and not all of the electric field distributed over the space ?
Because the electric (and magnetic) field can have other sources than the particles in the bound state in addition to containing the radiation emitted when the bound state formed.
 
  • #101
Orodruin said:
Because the electric (and magnetic) field can have other sources than the particles in the bound state in addition to containing the radiation emitted when the bound state formed.
Sorry, I didn't get your point. Which are the other field's sources other than the 2 charged particles ?
 
  • #102
cianfa72 said:
Sorry, I didn't get your point. Which are the other field's sources other than the 2 charged particles ?
If you have only two particles in the entire universe and they have forever been in a bound state, none.
 
  • #103
Orodruin said:
If you have only two particles in the entire universe and they have forever been in a bound state, none.
You mean that in real universe where there are multiple particles, the current field distribution depends on the two particles in the bound system acting as sources as well on all other charged particles (not included in the two particle's bound system).
 
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