1. Internal Energy
Internal energy (also called thermal energy) is the energy an object or substance has due to the kinetic and potential energies associated with the random motions of all the particles that make it up. The kinetic energy is, of course, due to the motion of the particles. To understand the potential energy, imagine a solid in which all of its molecules are bound to its neighbors by springs. As the molecules vibrate, the springs are compressed and stretched. (Liquids and gases are not locked in a lattice structure like this.)
The hotter something is, the faster its molecules are moving or vibrating, and the higher its temperature.

2. Internal Energy vs. Heat
The term heat refers is the energy that is transferred from one body or location due to a difference in temperature. Heat is internal energy when it is transferred between bodies.
Technically, a hot potato does not possess heat; rather it possesses a good deal of internal energy on account of the motion of its molecules. If that potato is dropped in a bowl of cold water, we can talk about heat: There is a heat flow (energy transfer) from the hot potato to the cold water; the potato’s internal energy is decreased, while the water’s is increased by the same amount.

3. Temperature Equilibrium
Heat is defined as the transfer of thermal energy that is due to a difference in temperature.
Thermal Equilibrium
Hot Coals
Insulated Container
Two objects are in thermal equilibrium if and only if they have the same temperature.
Cool Water
Same Temperature

4. First Law of Thermodynamics
Energy loss is equal to energy gain.

5. Second Law of Thermodynamics

6. The Zeroth Law of Thermodynamics
We have already discussed the zeroth law, and include it here for completeness:
If object A is in thermal equilibrium with object C, and object B is separately in thermal equilibrium with object C, then objects A and B will be in thermal equilibrium if they are placed in thermal contact.

7. Entropy To generalize:
The total entropy of the universe increases whenever an irreversible process occurs.
The total entropy of the universe is unchanged whenever a reversible process occurs.
Since all real processes are irreversible, the entropy of the universe continually increases. If entropy decreases in a system due to work being done on it, a greater increase in entropy occurs outside the system.