Entropy is a measure of possibilities. A messy room has high entropy because there are many possibly ways to be messy. Toys and clothes can be laying around anywhere within the room. A neat room has low entropy because there are few ways to be neat. All toys and clothes must be in their proper places.
A process can be driven, or forced to happen, only by increasing the entropy of the universe. A driven process is said to be "spontaneous". A few spontaneous processes are a falling brick, a bouncing ball, a crashing car, a melting ice cube on a warm day, a freezing lake on a cold day, or the chemical transformations of a burning match. The entropy of the universe increases during each of these spontaneous processes:
The change in entropy of the universe is separable into two parts. Part one is the change in the entropy of the "system". Part two is the change in entropy of the "surroundings".
The change in entropy of the surroundings (DSsur) is caused by dissipation of heat. Dissipation of heat drives many processes in our daily lives. A basketball might spontaneously roll off a table, bounce a couple of times, and come to rest on the floor. During this process the initial potential energy of the basketball is converted to kinetic energy, then to thermal energy (heat). The heat is dissipated. That heat dissipation is what drives the process in one direction, and keeps it from going in the reverse direction. Once a basket ball is at rest on the floor, it will not spontaneously gather heat from the surroundings, make the conversion from thermal to kinetic energy and bounce back onto the table.
Temperature matters. The change in entropy of the surroundings (DSsur) is the heat evolved (q) divided by the temperature (T).
This equation says that the entropy gain when heat is dissipated is greater at low temperature than at high temperature. To help understand this concept use money is an analogy for heat. Dissipating ten dollars (by spending it) buys a lot when money is dear (before inflation) but buys very little when money is cheap (after inflation). In the same way, dissipating a given amount of heat generates a lot of entropy when heat is dear (when it is cold) but generates less entropy when heat is cheap (when it is hot).
The temperature dependence of the entropy gain during heat dissipation is subtle but extremely important. It explains why the direction of a spontaneous process can change. At high temperature duplex DNA spontaneously melts, proteins spontaneously unfold, ice spontaneously melts. At low temperature DNA spontaneously anneals, proteins spontaneously fold, water spontaneously freezes. Let's think carefully about liquid water and ice. At all temperatures, the entropy of water molecules (the system) decreases upon freezing because water molecules are more ordered in the crystalline state than in the liquid. Water molecules have more rotational and translational freedom in liquid than in the solid. So DSsys always pushes ice to water. But when water freezes, the heat of fusion is released to the surroundings. So DSsur always pushes water to ice. The DSsur is greater at low temperature (T down => q/T up) than at high temperature (T up => q/T down) . (Here we assume that the heat of fusion doesn't change much with temperature.) So the increase in the entropy of the surroundings is greater at low temperature than at high temperature. At low temperature (<O°C) DSsur > -DSsys and water spontaneously freezes. At high temperature (<O°C) DSsur < -DSsys and ice spontaneously melts.
At constant pressure the heat evolved is equivalent to the negative of the enthalpy change of the system.
The condition for a spontaneous process is -TDSuniv < 0.
Let's invent a new function, the Gibbs Free Energy, G: DG=-TDSuniv
The condition for a spontaneous process is DG < 0, still an increasing entropy of the universe. In general we leave off the sys and write