An Introduction to Thermal Physics · Problem 2.36

The Second Law — Daniel Schroeder

Physics — Statistical Mechanics · entropy-order-of-magnitude

Problem

For either a monatomic ideal gas or a high-temperature Einstein solid, the entropy is given by NkNk times some logarithm. The logarithm is never large, so if all you want is an order-of-magnitude estimate, you can neglect it and just say S∼NkS \sim Nk. That is, the entropy in fundamental units is of the order of the number of particles in the system. This conclusion turns out to be true for most systems (with some important exceptions at low temperatures where the particles are behaving in an orderly way). So just for fun, make a very rough estimate of the entropy of each of the following: this book (a kilogram of carbon compounds); a moose (400 kg of water); the sun (2×10302 \times 10^{30} kg of ionized hydrogen).

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