Definition of thermal equilibrium?

[Arham]

Hello

In Zemansky's book there is this definition of thermal equilibrium:

"Thermal equilibrium exists when there is no spontaneous change in the
coordinates of a system in mechanical and chemical equilibrium when it is
separated from its surroundings by diathermic walls. In other words, there is
no exchange of heat between the system and its surroundings."

This is vague for me. Consider a thermodynamic system in thermal contact with two heat reservoirs at different temperatures. When the system reaches steady state then there will be no change in the coordinates of system. We have a gradient of T in that case. And there will be no net exchange of heat.

What is your opinion?

Sorry for bad english. :shy:

 

[Llewlyn]

Two bodies are in thermal equilibrium if they have the same temperature and if that isn't going to change.

Ll.

 

[Arijit Dutta]

You are having a confusion between Thermal Eqb. and Steady State.
Thermal Eqb.: Ṫ = 0 = ∇T
Steady State: ∂T/∂t = 0; where T = T(r,t) is the temperature of the system.

 

[Arham]

Two bodies are in thermal equilibrium if they have the same temperature and if that isn't going to change.

Ll.

Thanks. But I think definition of temperature is based on definition of thermal equilibrium. In other words I think at first we must define thermal equilibrium, and then temperature.

 

[Arham]

You are having a confusion between Thermal Eqb. and Steady State.
Thermal Eqb.: Ṫ = 0 = ∇T
Steady State: ∂T/∂t = 0; where T = T(r,t) is the temperature of the system.

Thanks. I know this. Look! When can we assign a temperature field to a system? When there is local thermal equilibrium in the system. But what is the exact definition of thermal equilibrium?

 

[Arijit Dutta]

2 systems are said to be in thermal equilibrium with each other if there is no change in co- ordinates of either system when they are separated by a diathermal wall.

 

[Arham]

2 systems are said to be in thermal equilibrium with each other if there is no change in co- ordinates of either system when they are separated by a diathermal wall.

Coordinates of a system in steady state don't change with time either.

 

[Arijit Dutta]

I should have added- both the systems must be separated from their surroundings by adiabatic wall.

 

[Arham]

I should have added- both the systems must be separated from their surroundings by adiabatic wall.

Consider just these two systems: 1. The under study system which is in steady state, and 2. the rest of the world.