2nd Law of Thermodynamics

What is the Second Law of Thermodynamics?

Hint
Entropy is nature's tendency to proceed in a direction that increases the randomness of a system.
Entropy is nature's tendency to proceed in a direction that increases the randomness of a system.

There exists for every thermodynamic system in equilibrium an extensive scalar property called the entropy, $$S$$ , such that in an infinitesimal reversible change of state of the system, $$dS=dQ/T$$ , where $$T$$ is the absolute temperature, $$dS$$ is the change in entropy, and $$dQ$$ is the amount of heat received by the system (heat transfer). The entropy of a thermally insulated system cannot decrease and is constant if and only if all processes are reversible.

An example of a reversible process is ideally forcing a flow through a constricted pipe. Ideal means no boundary layer losses. As the flow moves through the constriction, the pressure, temperature and velocity change, but these variables return to their original values downstream of the constriction. The state of the gas returns to its original conditions and the change of entropy of the system is zero. Engineers call such a process an isentropic process. Isentropic means constant entropy. The second law states that if the physical process is irreversible, the combined entropy of the system and the environment must increase. The final entropy must be greater than the initial entropy for an irreversible process. An example of an irreversible process is when a hot object is put in contact with a cold object, like putting ice into fresh coffee to make ice coffee. Eventually, they both achieve the same equilibrium temperature. If we then separate the objects they remain at the equilibrium temperature and do not naturally return to their original temperatures. The process of bringing them to the same temperature is irreversible.
There exists for every thermodynamic system in equilibrium an extensive scalar property called the entropy, $$S$$ , such that in an infinitesimal reversible change of state of the system, $$dS=dQ/T$$ , where $$T$$ is the absolute temperature, $$dS$$ is the change in entropy, and $$dQ$$ is the amount of heat received by the system (heat transfer).