First, we get a set of formulas from the first law:

Defined by entropy

Get the first basic formula:

According to the definition of enthalpy

Get the second basic formula:

Definition of Gibbs free energy:

difference

Helmholtz free energy;

& ltfont size = 1 & gt； (In fact, we can find that these two free energies are very close. It is speculated that one is under adiabatic condition and the other is under isobaric condition. (This is convenient for calculation))

Do the same differential:

The four formulas are the basic thermodynamic relations. Next, discuss Maxwell relation. Finally, we will study the memory skills of these relationships.

Maxwell mainly uses the independence of derivative order of second-order mixed partial derivatives. Details are as follows:

therefore

We will find the partial derivative of the former formula and the partial derivative of the latter formula. Because the derivative order does not change the value, they are equal:

Similarly, for other equations, the following relationship exists:

In fact, in the end, we found that all the quantities in thermodynamics actually boil down to only four quantities. In other words, we can write any thermodynamic quantity and then transform it.

It is worth mentioning that due to

For an ideal gas, the internal energy is only related to temperature. Therefore, for an ideal gas, only three quantities are needed to describe all its behaviors. In fact, the ideal gas equation does include only these three quantities.

It is worth mentioning that if external differentiation is used, all the above equations can be directly derived. However, I am so stupid that I will stop here later.