Over the internet, I found many resources that explain very well what entropy represents. However, the dimensions still appear hard for me to make sense of: energy, simply put, is the ability to do work. Temperature is a measure of the average kinetic energy of the particles inside the system. How can one then make intuitive sense of entropy being one over the other?
Intuitively, if I think of a system that has different temperatures across, I realize that energy (heat) tends to spread out as temperature becomes more uniform throughout the system. But if we assume the system to be isolated and that the entropy increases as the process happens (which it must), then by the law of conservation of energy the only possibility for entropy to increase is that the average temperature of the system decreases. So it should be that the energy is distributed more "evenly" across the molecules, i.e. first "only a few molecules were very excited", now "more molecules are somewhat excited" where by excited I mean high in kinetic energy.
At a physical level, is this what we mean by "there is more heat for every unit of temperature"?
Best Answer
I have an analogy that is helpul (at least to me).
Replace the world energy by income, and energy levels by income ranges. In a country with no restriction for minimum or maximum incomes, and where luck to be born rich and/or gifted is the major factor to get money, there is an income distribution of equilibrium.
In that analogy, temperature is related to how spread is the curve, how big is the inequality. Supposing that the degree of inequality is the same (due to the randomic hypothesis), countries with higher average incomes have bigger absolute differences between top and bottom ranges. For example to be considered rich in a poor country means less income than in a rich country. So, higher energy correlates with higher temperature.
If for any historical reason, two regions were artificially separated, and had different average incomes, sometime after joining, instead of two different distributions there will be one. Supposing no increase of the total income (what means: keeping the same total energy), natural competition in the market leads the average income of the poorer region to increase and that of the richer region to decrease. In the process, if we divide the income increase of each year of the poorer region by the spread of its curve, the quotient is greater than to divide the decrease of income (same magnitude) of the richer region by its (bigger) curve spread. The conclusion is that the natural process of contacting 2 regions of different average incomes (energies) and range of inequality (temperatures) results in an increase of entropy, when the total income (energy) is conserved.