What does it mean when we state that a system is in an equilibrium state?
What happens to the intrinsic and extrinsic variables at equilibrium?
How can we characterise the state of the system when it is at equilibrium?
Which thermodynamic variables must be minimised/maximised at equilibrium
In general why does the state of a system change?
Explain what is meant by the term reservoir when it is used in thermodynamics?
Explain why new thermodynamic potentials are required
A system is said to be in equilibrium if it doesn't change over macroscopic timescales. For example, the liquid inside a medical thermometer expands when it is first put into a persons mouth because at that point it is NOT in equilibrium. However, after a short period of time, the liquid stops expanding as the thermometer reaches equilibrium with the person (heat bath) with which it has been put into contact. Once this equilibrium has been reached the volume of the liquid inside the thermometer does not change any further it settles down to a constant value. At equilibrium, the intensive variables are uniform (homogenous) in that that they have the same value for all parts of the system (in our thermometer example the temperature of the liquid in the thermometer and the temperature of the persons mouth are the same). The extensive variables, meanwhile, do not change in time. When a system is at equilibrium its "state" is completely characterised the values of a small set of thermodynamic variables.
When a system is at equilibrium the entropy must be maximised and the internal energy must be minimised. When this is not the case it is possible to extract energy as work thereby lowering the internal energy. The internal energy extracted can then be returned as heat thereby increasing the entropy. The same argument can be made the opposite way around
In general, when a system moves from one thermodynamic state to another, it does so because it is no longer in equilibrium. When this is the case the values of the various thermodynamic quantities change in order to attain a new equilibrium. For example, when I boil a pan full of water I place the pan in contact with a hot stove (a heat bath). The system here is the pan of water and the stove. Obviously, there is no equilibrium here as one of the intensive variables (the temperature) is not homogenous - the stove will be considerably hotter than the water. Consequently, in this out of equilibrium system the water heats up so as to ensure that the intensive variables (the temperature) take on a uniform, single value across the entire system. This sort of change in the values of the thermodynamic variables is said to be irreversible. In classical thermodynamics we prefer, for reasons of mathematical convenience, to think about reversible changes. I have never really found a satisfactory and simple way of explaining what distinguishes reversible transitions from irreversible ones. Oftentimes what is written in textbooks is either so vague as to be meaningless (for example in some places you read that reversible transitions take place infinitely slowly) or clearly wrong as it is straightforward to think of processes that are reversible that do not have the properties ascribed to reversible transitions in the book. The essential point though is that when the transition takes place reversibly all the various processes that absorb or release energy are described mathematically in the model. When the transition takes place irreversibly there are hidden processes (such as friction) that absorb/release energy. As there is no mathematical description of these processes appears in the model it thus appears as if the model does not conserve energy. Obviously, energy must be conserved in reality, however, so this distinction between reversible and irreversible transitions must be a feature of the model.
We often talk about systems placed in contact with a very large reservoir. We do this because when we do so we can assume that the reservoir is so large that the exchange of extensive variables with the system does not affect the values of the reservoirs intensive quantities. In other words, when a system is placed in contact with a reservoir it will have equilibrated with the reservoir once all its intensive thermodynamic variables are equal to values of the intensive thermodynamic variables of the reservoir. We use the thermodynamic potentials to describe systems in contact with various reservoirs. In particular, enthalpy is used to describe systems surrounded by adiabatic walls that are in contact with a volume reservoir. Helmholtz free energy is used to describe closed systems surrounded by diabatic walls that in contact with an internal energy reservoir (or heat bath). Gibbs free energy is used to describe closed systems surrounded by walls that can exchange both heat and work with the reservoir but that cannot exchange material. The reservoir for the Gibbs free energy is both a volume reservoir and an energy reservoir (or heat bath).
<aside> 📌 SUMMARY: A system is said to be at equilibrium if it does not change over macroscopic timescales. At equilibrium extensive variables do not change in time and intensive variables take on a single, uniform value across the whole system. Equilibrium states are completely characterised by a small set of thermodynamic variables
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