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How many possible arrangements are there for a deck of 52
Chapter 2, Problem 28P(choose chapter or problem)
Problem 28P
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 k) and in SI units. Is this entropy significant compared to the entropy associated with arranging thermal energy among the molecules in the cards?
Questions & Answers
QUESTION:
Problem 28P
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 k) and in SI units. Is this entropy significant compared to the entropy associated with arranging thermal energy among the molecules in the cards?
ANSWER:
Step 1
Each card in this case is a micro state. Hence the total number of microstates is
Now we have to find out the possible number of arrangements and then we have to find the entropy of if we shuffle it completely.
Then we have to compare the entropy to the entropy of arranging the molecules in the card.