1. MEL140
Lectures 4 and 5

2. State Condition of the system as described by its properties.
Usually only a subset of properties need to be specified to identify the state of a system.
Some difficulties in specifying “state” of a system.
State of the world
State of the “hot potato”
The idea of equilibrium comes to rescue.

3. Thermodynamic equilibrium (TE)
A system is in (a) thermodynamic equilibrium (state) if it undergoes no changes when isolated from its surroundings.
Given unchanging surroundings, the system will remain unchanging if it is in equilibrium.
Equilibrium correspond to a state of balance; the system is “at peace” with all its parts and with its surroundings.
Intuitively, non-equilibrium is identified from the existence of “currents” or “flows” or “fluxes” such as heat flow, chemical diffusion, electric currents etc. arising from certain “driving forces” corresponding to the “imbalances” discussed above.
Thermodynamics studies the passage of system from one equilibrium state to another
equilibrium state. Often the passage itself is idealized using the concept of thermodynamic
Equilibrium (see later).

4. More on thermodynamic equilibrium (TE)
Types of thermodynamic equilibrium:
Mechanical equilibrium: balance of forces
Thermal equilibrium: see later
Chemical equilibrium: system does not change due to diffusion, phase change processes or chemical reactions occurring between its parts.
Intuitively, non-equilibrium is identified from the existence of “currents” or “flows” or “fluxes” such as heat flow, chemical diffusion, electric currents etc. arising from certain “driving forces” corresponding to the “imbalances” discussed above.

5. Thermal equilibrium
When a “hot” body is placed in contact with a “cold” body through a part of their boundary that allows passage of heat, the properties of the body change initially due to heat transfer between them. Eventually the heat transfer stops and the properties no longer change with time. The two bodies have reached thermal equilibrium.

6. Properties corresponding to different types of thermodynamic equilibrium
Mechanical equilibrium: balance of forces: pressure.
Thermal equilibrium: ?

7. Zeroth Law of Thermodynamics
If, of three systems A, B and C:
system A is in thermal equilibrium with system C,
system B is in thermal equilibrium with system C,
Then:
systems A and B are in thermal equilibrium with each other.
Reminder: “is in thermal equilibrium” “no changes occur when interaction is allowed between the systems through a shared diathermal no-work boundary”

8. Zeroth Law of Thermodynamics: implications
In particular, system C may be as shown in figure and have an easily measurable property such as “mercury level” which changes only in response to energy interactions through diathermal no-work walls.
Zeroth law can be restated:
“two systems A and B must be in thermal equilibrium if they have
resulted in the same mercury level on thermal contact with a standard
body C of the type shown in the figure”

9. Zeroth Law of Thermodynamics: implications
Zeroth law can be restated:
“two systems A and B must be in thermal equilibrium if they have resulted in the same mercury level on thermal contact with a standard
body C of the type shown in the figure” C
“mercury level, as recorded by C” is a variable characterizing thermal equilibrium just in the same way pressure of a simple compressible system is a variable of “mechanical equilibrium”.
To make sure that C does not significantly affect states of A/B, C may be made “small enough” in size compared to A/B. Then the mercury level variable can be given the fancy name temperature and considered the property of A/B responsible for thermal equilibrium.
More generally, we can infer the existence of temperature
as a new property from the third law and concept of thermal
equilibrium, when both are expressed mathematically.

10. There exists a property called empirical temperature
To find the common characteristic: (on board)
Express A-C, B-C and A-B thermal interaction mathematically as a relation among their properties.