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
Want to see more full solutions like this?
Chapter 2 Solutions
An Introduction to Thermal Physics
Additional Science Textbook Solutions
Physics for Scientists and Engineers: A Strategic Approach with Modern Physics (4th Edition)
University Physics (14th Edition)
Modern Physics
Physics for Scientists and Engineers with Modern Physics
Physics for Scientists and Engineers: A Strategic Approach, Vol. 1 (Chs 1-21) (4th Edition)
Conceptual Physics (12th Edition)
- One way to "derive" the thermodynamic definition for entropy is simply to recognize that its thermodynamic definition must be a state function, and all thermodynamic state functions are worthy of giving a special name and carry special meaning. a) Starting with the First Law of Thermodynamics (expressed either of 2 ways) AU = q + w du = dq + dw show all the steps and assumptions/conditions required to arrive at the new expression below, which includes the definition of entropy: AS - arev AU T T - nRln () arev must be state function. b) Using your result from part (a), explain why T To be explicit, explain why entropy must defined by (P, V, T) alone, and any change between the same 2 states, (P₁, V₁, T₁). and (P2, V2, T2), regardless of path, will give the same change in entropy.arrow_forwardImagine that you are rolling three typical six-sided dice. Each way that you can roll a particular outcome using these three dice represents a microstate for that outcome. How many ways can you roll a five with these three dice? That is, how many microstates exist for a roll of five with three dice? What is the entropy associated with an outcome of five in this situation?arrow_forwardHow many possible arrangements are there for a deck of 52 palying 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?arrow_forward
- (a) What is the change in entropy if you start with 10 coins in the 5 heads and 5 tails macrostate, toss them, and get 2 heads and 8 tails?(b) How much more likely is 5 heads and 5 tails than 2 heads and 8 tails? (Take the ratio of the number of microstates to find out.)(c) If you were betting on 2 heads and 8 tails would you accept odds of 252 to 45? Explain why or why not.arrow_forwardConsider a system of two Einstein solids, with NA = 300, NB = 200, and qtotal = 100 Compute the entropy of the most likely macrostate and of the least likely macrostate. Also compute the entropy over long time scales, assuming that all microstates are accessible. (Neglect the factor of Boltzmann's constant in the definition of entropy; for systems this small it is best to think of entropy as a pure number.)arrow_forwardThe entropy change of one mole of an ideal gas of vibrating diatomic molecules, as volume and temperature is changed is provided (image). Using the equation derived to demonstrate that for an ideal gas undergoing an adiabatic expansion from initial volume Vi to final volume Vf the change in entropy is zero.arrow_forward
- Problem #2 For heat exchange between a thermal reservoir at 300 K and a constant volume system containing one mole of monatomic ideal gas: a) Derive the equation for the total change in entropy for a designed initial system temperature Tj. b) Plot AStotal vs. Tsys for the initial system temperature ranging from 160 K to 500 K in increments of 10 K (i.e., Tsys = 160 K, 170 K, ... , 500 K). Use Matlab, Excel or similar plotting software for your plot. Label the plot axes and include units. %Darrow_forwardAn ideal monatomic gas is contained in a cylinder with a movable piston so that the gas can do work on the outside world, and heat can be added or removed as necessary. (Figure 1) shows various paths that the gas might take in expanding from an initial state whose pressure, volume, and temperature are po, Vo, and To respectively. The gas expands to a state with final volume 4V. For some answers it will be convenient to generalize your results by using the variable R₂ = Vfinal/Vinitial, which is the ratio of final to initial volumes (equal to 4 for the expansions shown in the figure.) The figure shows several possible paths of the system in the pV plane. Although there are an infinite number of paths possible, several of those shown are special because one of their state variables remains constant during the expansion. These have the following names: Adiabatic: No heat is added or removed during the expansion. • Isobaric: The pressure remains constant during the expansion. ● •…arrow_forwardAn ideal monatomic gas is contained in a cylinder with a movable piston so that the gas can do work on the outside world, and heat can be added or removed as necessary. (Figure 1) shows various paths that the gas might take in expanding from an initial state whose pressure, volume, and temperature are po, Vo, and To respectively. The gas expands to a state with final volume 4V. For some answers it will be convenient to generalize your results by using the variable R₂ = Vfinal/Vinitial, which is the ratio of final to initial volumes (equal to 4 for the expansions shown in the figure.) The figure shows several possible paths of the system in the pV plane. Although there are an infinite number of paths possible, several of those shown are special because one of their state variables remains constant during the expansion. These have the following names: Adiabatic: No heat is added or removed during the expansion. ● Isobaric: The pressure remains constant during the expansion. ● •…arrow_forward
- Please describe to me the laws of thermodynamics. There are a certain number of them and therefore you must have all of them. Each should be labeled with it's number. For instance "The First Law of thermodynamics says that..."arrow_forwardThe attached images have 3 parts, solve those 3 parts and also because of limited images to upload, this is the 4th part, iam typing here: Calculate the total change in entropy for entire system, in J/K.arrow_forwardI have answered b but I got 4.33 Kg for A and not correct (a) What is the entropy of an Einstein solid with 4 atoms and an energy of 18ε? Express your answer as a multiple of kB . The entropy of the solid is ______ kB.(b) What is the entropy of an Einstein solid in a macropartition that contains 9 ×10 e690 microstates? Express your answer as a multiple of kB. The entropy of the solid is 1590.92kB.arrow_forward
- College PhysicsPhysicsISBN:9781305952300Author:Raymond A. Serway, Chris VuillePublisher:Cengage LearningUniversity Physics (14th Edition)PhysicsISBN:9780133969290Author:Hugh D. Young, Roger A. FreedmanPublisher:PEARSONIntroduction To Quantum MechanicsPhysicsISBN:9781107189638Author:Griffiths, David J., Schroeter, Darrell F.Publisher:Cambridge University Press
- Physics for Scientists and EngineersPhysicsISBN:9781337553278Author:Raymond A. Serway, John W. JewettPublisher:Cengage LearningLecture- Tutorials for Introductory AstronomyPhysicsISBN:9780321820464Author:Edward E. Prather, Tim P. Slater, Jeff P. Adams, Gina BrissendenPublisher:Addison-WesleyCollege Physics: A Strategic Approach (4th Editio...PhysicsISBN:9780134609034Author:Randall D. Knight (Professor Emeritus), Brian Jones, Stuart FieldPublisher:PEARSON