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Conceptual questions

Explain why a building made of bricks has smaller entropy than the same bricks in a disorganized pile. Do this by considering the number of ways that each could be formed (the number of microstates in each macrostate).

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Problem exercises

Using [link] , verify the contention that if you toss 100 coins each second, you can expect to get 100 heads or 100 tails once in 2 × 10 22 size 12{2´"10" rSup { size 8{"22"} } } {} years; calculate the time to two-digit accuracy.

It should happen twice in every 1.27 × 10 30 s or once in every 6.35 × 10 29 s ( 6.35 × 10 29 s ) ( 1 h 3600 s ) ( 1 d 24 h ) ( 1 y 365.25 d ) = 2.0 × 10 22 y

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What percent of the time will you get something in the range from 60 heads and 40 tails through 40 heads and 60 tails when tossing 100 coins? The total number of microstates in that range is 1 . 22 × 10 30 size 12{1 "." "22"´"10" rSup { size 8{"30"} } } {} . (Consult [link] .)

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(a) If tossing 100 coins, how many ways (microstates) are there to get the three most likely macrostates of 49 heads and 51 tails, 50 heads and 50 tails, and 51 heads and 49 tails? (b) What percent of the total possibilities is this? (Consult [link] .)

(a) 3 . 0 × 10 29 size 12{3 "." 0 times "10" rSup { size 8{"29"} } } {}

(b) 24%

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(a) What is the change in entropy if you start with 100 coins in the 45 heads and 55 tails macrostate, toss them, and get 51 heads and 49 tails? (b) What if you get 75 heads and 25 tails? (c) How much more likely is 51 heads and 49 tails than 75 heads and 25 tails? (d) Does either outcome violate the second law of thermodynamics?

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(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.

(a) - 2 . 38 × 10 23 J/K size 12{ +- 2 "." "38"´"10" rSup { size 8{ +- "23"} } " J/K"} {}

(b) 5.6 times more likely

(c) If you were betting on two heads and 8 tails, the odds of breaking even are 252 to 45, so on average you would break even. So, no, you wouldn’t bet on odds of 252 to 45.

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10-coin toss
Macrostate Number of Microstates ( W )
Heads Tails
10 0 1
9 1 10
8 2 45
7 3 120
6 4 210
5 5 252
4 6 210
3 7 120
2 8 45
1 9 10
0 10 1
Total: 1024

(a) If you toss 10 coins, what percent of the time will you get the three most likely macrostates (6 heads and 4 tails, 5 heads and 5 tails, 4 heads and 6 tails)? (b) You can realistically toss 10 coins and count the number of heads and tails about twice a minute. At that rate, how long will it take on average to get either 10 heads and 0 tails or 0 heads and 10 tails?

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(a) Construct a table showing the macrostates and all of the individual microstates for tossing 6 coins. (Use [link] as a guide.) (b) How many macrostates are there? (c) What is the total number of microstates? (d) What percent chance is there of tossing 5 heads and 1 tail? (e) How much more likely are you to toss 3 heads and 3 tails than 5 heads and 1 tail? (Take the ratio of the number of microstates to find out.)

(b) 7

(c) 64

(d) 9.38%

(e) 3.33 times more likely (20 to 6)

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In an air conditioner, 12.65 MJ of heat transfer occurs from a cold environment in 1.00 h. (a) What mass of ice melting would involve the same heat transfer? (b) How many hours of operation would be equivalent to melting 900 kg of ice? (c) If ice costs 20 cents per kg, do you think the air conditioner could be operated more cheaply than by simply using ice? Describe in detail how you evaluate the relative costs.

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Questions & Answers

Water is flowing in a pipe with a varying cross-sectional area, and at all points the water completely fills the pipe. At point 1 the cross-sectional area of the pipe is 0.077 m2, and the magnitude of the fluid velocity is 3.50 m/s. (a) What is the fluid speed at points in the pipe where the cross
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what's the period of velocity 4cm/s at displacement 10cm
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What is physics
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the branch of science concerned with the nature and properties of matter and energy. The subject matter of physics includes mechanics, heat, light and other radiation, sound, electricity, magnetism, and the structure of atoms.
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and the word of matter is anything that have mass and occupied space
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1/v+1/u=1/f
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What type of experimental evidence indicates that light is a wave
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double slit experiment
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The S. L. Unit of sound energy is
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some sort of blatherring or mambo jambo you may say
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uchenna
ufff....this associated with physics ..so u can ask questions related to all topics of physics..
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what is upthrust
Olisa
Up thrust is a force
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upthrust is a upward force that acts vertical in the ground surface.
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what is centre of gravity?
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you think the human body could produce such Force
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the total amount of heat energy required to change the physical state of a unit mass of matter without a corresponding change in temperature.
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Practice Key Terms 3

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Source:  OpenStax, College physics. OpenStax CNX. Jul 27, 2015 Download for free at http://legacy.cnx.org/content/col11406/1.9
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