# 15.7 Statistical interpretation of entropy and the second law of  (Page 2/8)

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The two most orderly possibilities are 5 heads or 5 tails. (They are more structured than the others.) They are also the least likely, only 2 out of 32 possibilities. The most disorderly possibilities are 3 heads and 2 tails and its reverse. (They are the least structured.) The most disorderly possibilities are also the most likely, with 20 out of 32 possibilities for the 3 heads and 2 tails and its reverse. If we start with an orderly array like 5 heads and toss the coins, it is very likely that we will get a less orderly array as a result, since 30 out of the 32 possibilities are less orderly. So even if you start with an orderly state, there is a strong tendency to go from order to disorder, from low entropy to high entropy. The reverse can happen, but it is unlikely.

100-coin toss
Macrostate Number of microstates
Heads Tails ( W )
100 0 1
99 1 $1\text{.}0×{\text{10}}^{2}$
95 5 $7\text{.}5×{\text{10}}^{7}$
90 10 $1\text{.}7×{\text{10}}^{\text{13}}$
75 25 $2\text{.}4×{\text{10}}^{\text{23}}$
60 40 $1\text{.}4×{\text{10}}^{\text{28}}$
55 45 $6\text{.}1×{\text{10}}^{\text{28}}$
51 49 $9\text{.}9×{\text{10}}^{\text{28}}$
50 50 $1\text{.}0×{\text{10}}^{\text{29}}$
49 51 $9\text{.}9×{\text{10}}^{\text{28}}$
45 55 $6\text{.}1×{\text{10}}^{\text{28}}$
40 60 $1\text{.}4×{\text{10}}^{\text{28}}$
25 75 $2\text{.}4×{\text{10}}^{\text{23}}$
10 90 $1\text{.}7×{\text{10}}^{\text{13}}$
5 95 $7\text{.}5×{\text{10}}^{7}$
1 99 $1\text{.}0×{\text{10}}^{2}$
0 100 1
Total: $1\text{.}\text{27}×{\text{10}}^{\text{30}}$

This result becomes dramatic for larger systems. Consider what happens if you have 100 coins instead of just 5. The most orderly arrangements (most structured) are 100 heads or 100 tails. The least orderly (least structured) is that of 50 heads and 50 tails. There is only 1 way (1 microstate) to get the most orderly arrangement of 100 heads. There are 100 ways (100 microstates) to get the next most orderly arrangement of 99 heads and 1 tail (also 100 to get its reverse). And there are $1.0×{\text{10}}^{\text{29}}$ ways to get 50 heads and 50 tails, the least orderly arrangement. [link] is an abbreviated list of the various macrostates and the number of microstates for each macrostate. The total number of microstates—the total number of different ways 100 coins can be tossed—is an impressively large $1\text{.}\text{27}×{\text{10}}^{\text{30}}$ . Now, if we start with an orderly macrostate like 100 heads and toss the coins, there is a virtual certainty that we will get a less orderly macrostate. If we keep tossing the coins, it is possible, but exceedingly unlikely, that we will ever get back to the most orderly macrostate. If you tossed the coins once each second, you could expect to get either 100 heads or 100 tails once in $2×{\text{10}}^{\text{22}}$ years! This period is 1 trillion ( ${\text{10}}^{\text{12}}$ ) times longer than the age of the universe, and so the chances are essentially zero. In contrast, there is an 8% chance of getting 50 heads, a 73% chance of getting from 45 to 55 heads, and a 96% chance of getting from 40 to 60 heads. Disorder is highly likely.

## Disorder in a gas

The fantastic growth in the odds favoring disorder that we see in going from 5 to 100 coins continues as the number of entities in the system increases. Let us now imagine applying this approach to perhaps a small sample of gas. Because counting microstates and macrostates involves statistics, this is called statistical analysis    . The macrostates of a gas correspond to its macroscopic properties, such as volume, temperature, and pressure; and its microstates correspond to the detailed description of the positions and velocities of its atoms. Even a small amount of gas has a huge number of atoms: of an ideal gas at 1.0 atm and $0º C$ has $2\text{.}7×{\text{10}}^{\text{19}}$ atoms. So each macrostate has an immense number of microstates. In plain language, this means that there are an immense number of ways in which the atoms in a gas can be arranged, while still having the same pressure, temperature, and so on.

#### Questions & Answers

What is physics?
physics is a branch of science in which we are dealing with the knowledge of our physical things. macroscopic as well as microscopic. we are going look inside the univers with the help of physics. you can learn nature with the help of physics. so many branches of physics you have to learn physics.
vijay
What are quarks?
6 type of quarks
Neyaz
what is candela
Candela is the unit for the measurement of light intensity.
Osei
any one can prove that 1hrpower= 746 watt
Newton second is the unit of ...............?
Neyaz
Impulse and momentum
Fauzia
force×time and mass× velocity
vijay
Good
Neyaz
What is the simple harmonic motion?
oscillatory motion under a retarding force proportional to the amount of displacement from an equilibrium position
Yuri
Straight out of google, you could do that to, I suppose.
Yuri
*too
Yuri
ok
Fauzia
Oscillatory motion under a regarding force proportional to the amount of displacement from an equilibrium position
Neyaz
examples of work done by load of gravity
What is ehrenfest theorem?
You can look it up, faster and more reliable answer.
Yuri
That isn't a question to ask on a forum and I also have no idea what that is.
Yuri
what is the work done by gravity on the load 87kj,11.684m,mass xkg[g=19m/s
Maureen
What is law of mass action?
rate of chemical reactions is proportional to concentration of reactants ...
ok thanks
Fauzia
what is lenses
lenses are two types
Fauzia
concave and convex
right
Fauzia
speed of light in space
in vacuum speed of light is 3×10^8 m/s
vijay
ok
Vikash
2.99×10^8m/s
Umair
2.8820^8m/s
Muhammed
which is correct answer
Vikash
he is correct but we can round up in simple terms
vijay
3×10^8m/s
vijay
is it correct
Fauzia
I mean 3*10^8 m/s ok
vijay
299792458 meter per second
babar
3*10^8m/s
Neyaz
how many Maxwell relations in thermodynamics
vijay
how we can do prove them?
vijay
What is second law of thermodynamics?
Neyaz
please who has a detailed solution to the first two professional application questions under conservation of momentum
I want to know more about pressure
Osei
I can help
Emeh
okay go on
True
I mean on pressure
Emeh
definition of Pressure
John
it is the force per unit area of a substance.S.I unit is Pascal 1pascal is defined as 1N acting on 1m² area i.e 1pa=1N/m²
Emeh
pls explain Doppler effect
Emmex
solve this an inverted differential manometer containing oil specific gravity 0.9 and manometer reading is 400mm find the difference of pressure
Einstine claim that nothing can go with the speed of light even its half (50%) but in to make antimatter they they hit the sub atomic particals 99.9%the speed of light how is it possible
nothing with physical properties. this doesn't include things like particles and gravitational waves
Mustafa
that particles are of very small mass.... near equals to massless
Aritra
but they exist
vijay
yes they exist but mass is too less
Aritra
ok
vijay
greet all
Abayomi
the unit of radioactivity is .....?
Neyaz
Great Sharukh ! Do you have question in physics?
book says that when wave enter from one medium to another its wavelenght changes but frequency not how ? and f is inversely related to wavelenth
Sharukh
yes but how comes
Sani
how are you?
World
what's the problem
Aritra
I really don't know physics.. I need help,in solving
Amara
me too
Ewulum
hii
Cheeru
I really don't know physics.. I need help,in solving
Cheeru
me too
True
I can teach u if u are ready
latunde
yes I am ready
True
hi
Emeh