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Test prep for ap courses
A piston is resting halfway into a cylinder containing gas in thermal equilibrium. The layer of molecules next to the closed end of the cylinder is suddenly flash-heated to a very high temperature. Which best describes what happens next?
- The high temperature molecules push out the piston until their energy is reduced enough that the system is in equilibrium.
- The molecules with the highest temperature bounce off their neighbors, losing energy to them, and so on until the system is at a new equilibrium with the piston moved out.
- The molecules with the highest temperature bounce off their neighbors, losing energy to them, and so on until the system is at a new equilibrium with the piston where it started.
- The high temperature molecules push out the piston until their energy is reduced enough that the system is in equilibrium, and then the piston gets sucked back in.
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Design a macroscopic simulation using reasonably common materials to represent one very high energy particle gradually transferring energy to a bunch of lower energy particles, and determine if you end up with some sort of equilibrium.
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Section summary
- Disorder is far more likely than order, which can be seen statistically.
- The entropy of a system in a given state (a macrostate) can be written as
where
is Boltzmann's constant, and
is the natural logarithm of the number of microstates
corresponding to the given macrostate.
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
years; calculate the time to two-digit accuracy.
It should happen twice in every
or once in every
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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
. (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)
(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)
(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
it is the relatively stable flow of income
what is circular flow of income
branches of macroeconomics
what is Flexible exchang rate?
is gdp a reliable measurement of wealth
introduction to econometrics
Why is unemployment rate never zero at full employment?
bcoz of existence of frictional unemployment in our economy.
Umashankar
what is flexible exchang rate?
poudel
due to existence of the pple with disabilities
Abdulraufu
the demand of a good rises, causing the demand for another good to fall
is it possible to leave every good at the same level
Joseph
I don't think so. because check it, if the demand for chicken increases, people will no longer consume fish like they used to causing a fall in the demand for fish
Anuolu
is not really possible to let the value of a goods to be same at the same time.....
Salome
Suppose the inflation rate is 6%, does it mean that all the goods you purchase will cost
6% more than previous year? Provide with reasoning.
Not necessarily. To measure the inflation rate economists normally use an averaged price index of a basket of certain goods. So if you purchase goods included in the basket, you will notice that you pay 6% more, otherwise not necessarily.
Waeth
discus major problems of macroeconomics
what is the problem of macroeconomics
Yoal
Economic growth
Stable prices
and low unemployment
Ephraim
explain inflationcause and itis degre
increase in general price levels
WEETO
Good day
How do I calculate this question: C= 100+5yd G= 2000 T= 2000 I(planned)=200.
Suppose the actual output is 3000. What is the level of planned expenditures at this level of output?
how to calculate actual output?
Chisomo
how to calculate the equilibrium income
Beshir
Criteria for determining money supply
who we can define macroeconomics in one line
Muhammad
Aggregate demand
Mohammed
C=k100 +9y and i=k50.calculate the equilibrium level of output
nawalparasi district
from belatari
Amisha
I am Camara from Guinea west Africa... happy to meet you guys here
Sekou
ahile becheclor ho
Amisha
hjr ktm bta ho
ani k kaam grnu hunxa tw
Amisha
money as unit of account means what?
Kalombe
A unit of account is something that can be used to value goods and services and make calculations
Jim
all of you please speak in English I can't understand you're language
Muhammad
I want to know how can we define macroeconomics in one line
Muhammad
it must be .9 or 0.9
no Mpc is greater than 1
Y=100+.9Y+50
Y-.9Y=150
0.1Y/0.1=150/0.1
Y=1500
Kalombe
Mercy is it clear?😋
Kalombe
hi can someone help me on this question
If a negative shocks shifts the IS curve to the left, what type of policy do you suggest so as to stabilize the level of output?
discuss your answer using appropriate graph.
if interest rate is increased this will will reduce the level of income shifting the curve to the left ◀️
Kalombe
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Source:
OpenStax, College physics for ap® courses. OpenStax CNX. Nov 04, 2016 Download for free at https://legacy.cnx.org/content/col11844/1.14
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