Thermodynamics and intertial frame

In summary, there is no generally accepted version of relativistic thermodynamics, and classically, defining temperature is done in several equivalent ways. However, in the relativistic case, these definitions are no longer the same. Temperature is considered Lorentz invariant, but pressure is not, as it depends on the motion of the observer and the concept of simultaneity. Material properties are also generally considered Lorentz invariant. The speed of sound, on the other hand, is not Lorentz invariant as it is derived from a specific dynamic problem and is not a fundamental thermodynamic property. The concept of entropy is considered Lorentz scalar, while temperature is considered Lorentz invariant. However, there are differing opinions on the Lorentz
  • #1
duri
16
0
Is thermodynamics states like temperature, pressure and material properties like specific heat, thermal conductivity etc. invariant with inertial reference frame?.
 
Science news on Phys.org
  • #2
There is no generally accepted version of relativistic thermodynamics. Classically, there are several equivalent ways tp define temperature. Relativistically, they are no longer the same.
 
  • #3
Yes, classily they are invariant with respect to the motion of the observer.

Chet
 
  • #4
Chestermiller said:
Yes, classily they are invariant with respect to the motion of the observer.

Chet

Then sqrt(gamma*R*T) should be invariant with respect to inertial frame. (At least for speed in order of 100). Then can I claim speed of sound is invariant in all inertial frame of reference. I expect reply to be NO, but why it is no?
 
  • #5
I think temperature is Lorentz invariant. Invariance under spatial rotation is trivial.About the boosts, when you change coordinates from one inertial one to another, you're actually changing the energy of each particle by a constant amount which doesn't contribute to the temperature.
But pressure doesn't seem to be Lorentz invariant to me. Because it depends on the average number of particles hitting the container's wall in a given amount of time. That definition has a concept of simultaneity hidden in it! and in addition it depends on time and space intervals which are not Lorentz invariant.
About material properties, I'm not sure but I think they're Lorentz invariant.
I should also say that its not trivial to say [itex] \sqrt{\gamma R T} [/itex] is Lorentz invariant.
As far as I remember, people replace things with other things in that formula to get speed of sound in terms of different things. So you should go to the actual derivation of this formula and see whether there is an assumption of taking a particular reference frame or not in between of the derivation. Because people aren't careful about SR when they talk about things as classical as speed of sound!
 
Last edited:
  • #6
duri said:
Then sqrt(gamma*R*T) should be invariant with respect to inertial frame. (At least for speed in order of 100). Then can I claim speed of sound is invariant in all inertial frame of reference. I expect reply to be NO, but why it is no?
The speed of sound is a quantity that is inherently derived for a specific dynamic problem that assumes that the gas is stationary relative to the observer, and the wave is traveling through the gas. If the observer were moving at the speed of sound relative to the gas when he passed the point at which a pulse was applied, he would observe that the wave would be stationary, but the gas would be moving backwards. This would not be consistent with the premise that the observer is stationary relative to the gas. So the speed of sound is the solution to a dynamic problem with a specific set of boundary conditions. On the other hand, transport and intensive thermodynamic properties such as temperature, pressure, heat capacity, thermal conductivity, and viscosity are more fundamental, and are not tied to the solution of any specific dynalmic problem.

Chet
 
  • #7
In my opinion, the main problem is that two thermodynamic systems which move at different speed cannot be in thermal equilibrium as e.g. their blackbody radiation spectrum will be blue or redshifted which will tend to equalize their velocity. So it is not possible to define relative temperature via the zeroth law for systems of different speed.
 
  • #8
In my opinion entropy is scalar under Lorentz transformation.
Energy has coefficient [tex]\gamma[/tex] in Lorentz transformation.
So temperature dE/dS has coefficient [tex]\gamma[/tex] in Lorentz transformation as well.
 
  • #9
duri said:
Is thermodynamics states like temperature, pressure and material properties like specific heat, thermal conductivity etc. invariant with inertial reference frame?.

I may be misunderstanding the question. When the wind blows, pressure becomes a function of the wind direction and velocity. Equilibrium gaseous equations of state are invalid under non-equilibrium conditions (wind, evaporation, condensation, etc.).

This is a common concern in the atmospheric sciences, since the global atmosphere is never in a state of equilibrium. Even small volumes of the free atmosphere are rarely (if ever) in a state of equilibrium.
 
  • #10
sweet springs said:
In my opinion entropy is scalar under Lorentz transformation.
Energy has coefficient [tex]\gamma[/tex] in Lorentz transformation.
So temperature dE/dS has coefficient [tex]\gamma[/tex] in Lorentz transformation as well.
Ok, but dE/dS isn't a scalar quantity as T is.
 
  • #11
DrDu said:
Ok, but dE/dS isn't a scalar quantity as T is.

Thanks. I am almost sure S is scalar but not sure T is. Could you tell me proof or reason ?
 
  • #12
temperature is defined by the zeroth law of thermodynamics, i.e. the transitivity of thermal equilibrium. Two systems are in thermal equilibrium if they have the same temperature. So temperature is a scalar. But E is part of the energy momentum four vector, so if S is scalar, dE/dS can't be a scalar.
 
  • #13
DrDu said:
temperature is defined by the zeroth law of thermodynamics, i.e. the transitivity of thermal equilibrium. Two systems are in thermal equilibrium if they have the same temperature. So temperature is a scalar.

Thanks. Scalar is number that does not change under Lorentz transformation. Two system A and B are in thermal equilibrium. In IFR #0
[tex]T_{0A}=T_{0B}[/tex]
In IFR #1
[tex]T_{1A}=T_{1B}[/tex]
How can we conclude that
[tex]T_{0A}=T_{1A}[/tex]
in order T to be a scalar?
 
  • #14
PS I consider
[tex]T_{1A}=T_{0A},\\T_{1A}=\gamma T_{0A},\\T_{1A}=\frac{T_{0A}}{\gamma}[/tex]
are the three major controverse ideas.
 

1. What is thermodynamics?

Thermodynamics is the branch of physics that deals with the relationship between heat, energy, and work. It studies how energy is transferred and transformed between different forms, and how it affects the properties of matter.

2. What is an inertial frame?

An inertial frame is a reference frame in which a body at rest remains at rest and a body in motion continues to move with constant velocity, unless acted upon by an external force. This concept is important in understanding the laws of motion and the principles of relativity.

3. What is the first law of thermodynamics?

The first law of thermodynamics is the law of conservation of energy, which states that energy cannot be created or destroyed, only transferred or converted from one form to another. This means that the total energy of a closed system remains constant over time.

4. How is thermodynamics related to entropy?

Entropy is a measure of the disorder or randomness in a system. The second law of thermodynamics states that the total entropy of a closed system will always increase over time. This means that in any natural process, energy will always flow from a more ordered state to a less ordered state, increasing the overall entropy of the system.

5. How does thermodynamics apply to everyday life?

Thermodynamics has many practical applications in our daily lives, from the design of engines and refrigerators to understanding the behavior of gases and the properties of materials. It also helps us understand natural phenomena such as weather patterns and the functioning of the human body. Overall, thermodynamics is essential in understanding and manipulating energy in our world.

Similar threads

  • Thermodynamics
Replies
3
Views
951
  • Thermodynamics
Replies
3
Views
788
Replies
1
Views
619
Replies
5
Views
1K
Replies
4
Views
901
  • Thermodynamics
Replies
2
Views
906
  • Thermodynamics
Replies
33
Views
1K
Replies
2
Views
386
  • Thermodynamics
Replies
10
Views
2K
Replies
15
Views
1K
Back
Top