Some Fatal Warnings about Thermodynamics

When we learn Thermodynamics, there are some thing rather confusing and error prone. here, I will list some of them, and to eliminate some misunderstandings.

Fatal Warning 1: The relation between Enthalpy and isobar heat

Some textbooks address that the change of Enthalpy equals the heat while the system undergoes an isobaric process.

However, the conclusion only holds for reversible isobaric processes and there mustn't be any non-PV work. In other words, If the system pressure and the environment pressure is different, this conclusion is false.

below is the deduction.

Since , we have:

Since the process is isobaric, , so:

Therefore, only when , namely, the process is reversible, we have .

In fact, the reversible process is a special case of the general process, and the relation between Enthalpy and heat is more complicated than that. So, we should be careful when we use this relation, and we should always check the conditions before applying it.

Fatal Warning 2: Gibbs and Helmholtz Free Energies.

The core idea of Gibbs and Helmholtz free energy is to consider the system and environment as a isolated system, so that the criteria of spontaneous process is the change of the total entropy of the isolated system.

However, during the deduction of deriving free energies, some assumptions was involved, which makes the free energy criteria have some limitations, which is often neglected by textbooks and courses.

Consider the environment is big enough so that its temperature is constant. Then, the change of the total entropy of the isolated system is:

isochoric process

For an isochoric process, we have: so that:

Since , we can deduce from

If system temperature and surrounding temperature are identical, we have:

So, we can define a state function whose decrease can indicate the increase of total entropy:

For a isothermo process, and the negative indicates a positive

As you saw, a lot of assumptions was introduced into the deduction. So, the criteria of Helmholtz free energy is only valid for isothermal process, and the system temperature must be identical to the surrounding temperature.

isobaric process

For an isobaric processwhere system pressure equals surrounding pressure, we have: so that:

If system temperature and surrounding temperature are identical, we have:

So, we can define a state function whose decrease can indicate the increase of total entropy:

For a isothermo process, and the negative indicates a positive

As you saw, a lot of assumptions was introduced into the deduction. So, the criteria of Gibbs free energy is only valid for isothermal process, and the system temperature must be identical to the surrounding temperature.

In conclusion, the criteria of free energies are only valid for isothermal processes, and the system temperature must be identical to the surrounding temperature. So, we should be careful when we use these criteria, and we should always check the conditions before applying them.