An Introduction to Thermal Physics · Problem 2.28

The Second Law — Daniel Schroeder

Physics — Statistical Mechanics · entropy-cards

Problem

How many possible arrangements are there for a deck of 52 playing cards? (For simplicity, consider only the order of the cards, not whether they are turned upside-down, etc.) Suppose you start with a sorted deck and shuffle it repeatedly, so that all arrangements become ``accessible.'' How much entropy do you create in the process? Express your answer both as a pure number (neglecting the factor of kk) and in SI units. Is this entropy significant compared to the entropy associated with arranging thermal energy among the molecules in the cards?

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