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?
To Find: Possible arrangements of the deck of 52 cards. The entropy while shuffling the card. Significance of the entropy of the card and the thermal energy of the molecule of the card.
Answer to Problem 28P
Explanation of Solution
Given:
A deck of 52 cards.
Formula Used:
Calculation:
The possibility of a card to be on 1st position
The possibility of a card to be on 2nd position
The possibility of a card to be on 3rd position
Similarly
The possibility of a card to be on 52ndposition
The total number of possible ways of arranging the card is
As all the arrangements are accessible.
Entropy while shuffling the card is
As the entropy is very negligible if compared to the entropy of particles due to thermal motion of the card while shuffling the cards.
Conclusion:
Thus, possibility of arrangements of cards and entropy during that are
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