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?

Question

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Answer 1

Textbook Question

Chapter 2.6, 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?

Expert Solution & Answer

To determine

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

52!=8.06×1067, 2.16×10−21J/K

Explanation of Solution

Given:

A deck of 52 cards.

Formula Used:

S=NklnΩ

Calculation:

The possibility of a card to be on 1^s^t position =52

The possibility of a card to be on 2ⁿ^d position =51

The possibility of a card to be on 3^r^d position =50

Similarly

The possibility of a card to be on 52ⁿ^dposition =1

The total number of possible ways of arranging the card is

52!=8.06×1067

As all the arrangements are accessible.

Entropy while shuffling the card is

Sk=ln52!=156;S=156k=2.16×10−21J/K

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 52!=8.06×1067, 2.16×10−21J/K respectively.

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01:51

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Answer 2

Textbook Question

Chapter 2.6, 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?

Expert Solution & Answer

To determine

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

52!=8.06×1067, 2.16×10−21J/K

Explanation of Solution

Given:

A deck of 52 cards.

Formula Used:

S=NklnΩ

Calculation:

The possibility of a card to be on 1^s^t position =52

The possibility of a card to be on 2ⁿ^d position =51

The possibility of a card to be on 3^r^d position =50

Similarly

The possibility of a card to be on 52ⁿ^dposition =1

The total number of possible ways of arranging the card is

52!=8.06×1067

As all the arrangements are accessible.

Entropy while shuffling the card is

Sk=ln52!=156;S=156k=2.16×10−21J/K

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 52!=8.06×1067, 2.16×10−21J/K respectively.

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01:51

Answer 3

Textbook Question

Chapter 2.6, 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?

Expert Solution & Answer

To determine

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

52!=8.06×1067, 2.16×10−21J/K

Explanation of Solution

Given:

A deck of 52 cards.

Formula Used:

S=NklnΩ

Calculation:

The possibility of a card to be on 1^s^t position =52

The possibility of a card to be on 2ⁿ^d position =51

The possibility of a card to be on 3^r^d position =50

Similarly

The possibility of a card to be on 52ⁿ^dposition =1

The total number of possible ways of arranging the card is

52!=8.06×1067

As all the arrangements are accessible.

Entropy while shuffling the card is

Sk=ln52!=156;S=156k=2.16×10−21J/K

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 52!=8.06×1067, 2.16×10−21J/K respectively.

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01:51

Answer 4

Textbook Question

Chapter 2.6, 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?

Expert Solution & Answer

To determine

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

52!=8.06×1067, 2.16×10−21J/K

Explanation of Solution

Given:

A deck of 52 cards.

Formula Used:

S=NklnΩ

Calculation:

The possibility of a card to be on 1^s^t position =52

The possibility of a card to be on 2ⁿ^d position =51

The possibility of a card to be on 3^r^d position =50

Similarly

The possibility of a card to be on 52ⁿ^dposition =1

The total number of possible ways of arranging the card is

52!=8.06×1067

As all the arrangements are accessible.

Entropy while shuffling the card is

Sk=ln52!=156;S=156k=2.16×10−21J/K

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 52!=8.06×1067, 2.16×10−21J/K respectively.

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Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!

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Answer 5

Textbook Question

Answer 6

Textbook Question

Answer 7

Expert Solution & Answer

To determine

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

52!=8.06×1067, 2.16×10−21J/K

Explanation of Solution

Given:

A deck of 52 cards.

Formula Used:

S=NklnΩ

Calculation:

The possibility of a card to be on 1^s^t position =52

The possibility of a card to be on 2ⁿ^d position =51

The possibility of a card to be on 3^r^d position =50

Similarly

The possibility of a card to be on 52ⁿ^dposition =1

The total number of possible ways of arranging the card is

52!=8.06×1067

As all the arrangements are accessible.

Entropy while shuffling the card is

Sk=ln52!=156;S=156k=2.16×10−21J/K

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 52!=8.06×1067, 2.16×10−21J/K respectively.

Answer 8

Expert Solution & Answer

To determine

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

52!=8.06×1067, 2.16×10−21J/K

Explanation of Solution

Given:

A deck of 52 cards.

Formula Used:

S=NklnΩ

Calculation:

The possibility of a card to be on 1^s^t position =52

The possibility of a card to be on 2ⁿ^d position =51

The possibility of a card to be on 3^r^d position =50

Similarly

The possibility of a card to be on 52ⁿ^dposition =1

The total number of possible ways of arranging the card is

52!=8.06×1067

As all the arrangements are accessible.

Entropy while shuffling the card is

Sk=ln52!=156;S=156k=2.16×10−21J/K

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 52!=8.06×1067, 2.16×10−21J/K respectively.

Answer 9

Expert Solution & Answer

Answer 10

Expert Solution & Answer

Answer 11

To determine

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.