Notes

They could measure pressure, they could measure temperature, they could measure volume.

the first law of thermodynamics is that energy cannot be created or destroyed

energy can only be transformed

internal energy as literally all the energy that's in a system.

Intuitively, enthalpy can be said to be the internal energy of a system as well as the energy it takes that system to establish itself in differentiation or displacement from its environment. For example, when considering the enthalpy of a puddle, it is the amount of internal energy in the puddle, as well as the amount of energy required for that puddle to establish its pressure and volume in relation to the air above it and the earth around and beneath it.

Assume the temperature of the tea was T1 before you shake it. The internal energy before you shake it will depend (mostly) on the mass of the tea and the temperature. When you shake it you inject a lot more kinetic energy into the tea, but initially, that kinetic energy is not molecular level, random, kinetic energy. It is represented by complex and chaotic and turbulent flow patterns in the tea that will subside when you set the flask down. Until it subsides, it is not part of what is called the internal energy. Until it subsides, it is kinetic energy of macroscopic motion. Once it subsides, it will have become randomized molecular motion and will add to the internal energy. This will be manifested in an increase in the temperature to T2 > T1. The longer and more vigorously you shake it, the greater the final value of T2 and the greater the increase in the internal energy.

Potential energy comes from interaction with a charge, be it mass (gravity), electric charge (electric potential), weak or strong nuclear forces... by reducing intermolecular interaction to 0, and recognizing that the mass of a gas molecule is so tiny as to render gravity negligble (by mgh), the molecules have no potential energy.

Internal energy is NOT all the energy in the system, it is the kinetic and potential energy associated with the random motion of the molecules of an object. If you heat an object, you will increase its internal energy. As the object cools, its internal energy will decrease.

Conservation of energy is always true, but energy moves from one place to another and can also change forms. In a closed system, energy is conserved. Whenever it seems energy is not conserved you have to broaden your view of what the system is. A hot pot of water cools off. Its energy is not conserved, but it is not a closed system, either The energy is transferred to the surroundings, and if I take a big enough view of "the system" I will see that energy is conserved