In the case of energy, the scientific meaning is not far from your everyday notion. The images one gets from the word; oil, coal, nuclear power plants, solar panels, and so on; all provide energy in the scientific sense. One of the many kinds of energy is called "kinetic energy." It is the energy a moving object has because of its motion. The kinetic energy of a moving object depends on its mass (think "weight") and its speed. The molecules in a glass of water or an ice cube are all in continual motion, and so each molecule has a tiny amount of kinetic energy. The temperature of an object is a reflection of the kinetic energy of the atoms or molecules that make it up. To sum up, fast molecules = high kinetic energy = high temperature.
For example, water is warmer than ice, which means that the molecules in water generally have more kinetic energy (and are thus moving faster) than the ones in ice. When we place an ice cube in a glass of water, the slow moving molecules in the ice are bombarded by the faster molecules in the water. In the resulting collisions, the molecules in the ice usually end up faster while the molecules in the water end up slower. Hence the ice gets warmer and the water gets colder! This transfer of energy from the warmer substance to the colder substance is called "heat."
Now what does all this have to do with entropy? Well, there's only so much energy in a glass of water. If we start from scratch and pass out all the energy in very small doses to all the molecules in a glass of water, how is the energy likely to distribute itself? Well, just as the air molecules in a box tend to distribute themselves evenly throughout the box, the kinetic energy in a glass of water tends to distribute itself evenly among all the molecules in the water. The many different ways to distribute the energy in a glass of water are microstates of the system. Macrostates in which the energy is evenly distributed have the highest entropy, and so are the most likely.
When we place the ice cube in the water, the energy is unevenly distributed. The entropy is low. The system continually changes its state, and since most of the microstates belong to high entropy macrostates, the entropy naturally increases. It doesn't have to do this, since all microstates are equally likely, but an increase in entropy is overwhelmingly likely, as we saw with the box of gas.
And so heat flows from the warm substance to the cold substance. You already knew this, but perhaps not from this perspective.
All this is summed up in the second law of thermodynamics.
The Second Law of Thermodynamics
The Page of EntRoPy
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