Internal energy and the first law of thermodynamics

  In previous posts, we've covered how molecules move randomly, and they have kinetic energy with it. This is called the internal energy. In ideal gas, molecules have different kinetic energy due to different speed but sum of KE are constant, when the gas is kept at a constant temperature.

  In real gas, because molecules exerts force to each other, making potential energy at any rate, at any instant. Random motion also varies potential energy randomly. For the real gas, internal energy is given by sum of potential energies and the kinetic energies.
However, If two objects with different temperature impacts together, temperature will flow from higher point to lower point, not by any difference in internal energies.

First law of thermodynamics

  The increase in internal energy of a system is equal to
the sum of the heat added to the system and the work done on it

In mathematical form, ΔU = Q + W
Be careful with the sign,
+ΔU means an increase in internal energy.
+Q means that heat has been added to the system.

+W means the work is done on the system.