entropy physics 202 professor lee carkner lecture 17
Post on 18-Dec-2015
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PAL #16 Internal Energy 3 moles of gas, temperature raised from 300 to
400 K He gas, isochorically
Q = nCVT, CV = (f/2)R = (3/2) R Q = (3)(3/2)R(100) = 3740 J # 4 for heat, all in translational motion
He gas, isobarically Q = nCPT, CP = CV + R = (5/2) R Q = (3)(5/2)R(100) = 6333 J # 2 for heat, energy in translational and work
H2 gas, isochorically Q = nCVT, CV = (5/2) R, f = 5 for diatomic Q = (3)(5/2)R(100) = 6333 J # 2 for heat, energy into translational and rotational
motion H2 gas, isobarically
Q = nCPT, CP = CV + R = (7/2) R Q = (3)(7/2)R(100) = 8725 J # 1 for heat, energy, into translation, rotation and work
Randomness Classical thermodynamics is deterministic
Every time!
But the real world is probabilistic
It is possible that you could add heat to a system and the temperature could go down
The universe only seems deterministic because the number of molecules is so large that the chance of an improbable event happening is absurdly low
Reversible
Why? The smashing plate is an example of an
irreversible process, one that only happens in one direction
Examples: Heat transfer
Entropy
What do irreversible processes have in common?
The degree of randomness of system is called entropy
In any thermodynamic process that proceeds from an initial to a final point, the change in entropy depends on the heat and temperature, specifically:
S = Sf –Si = ∫ (dQ/T)
Isothermal Entropy In practice, the integral may be hard to compute
Let us consider the simplest case where the
process is isothermal (T is constant):S = (1/T) ∫ dQ
S = Q/T
Like heating something up by 1 degree
Entropy Change Imagine now a simple idealized system
consisting of a box of gas in contact with a heat reservoir
If the system loses heat –Q to the reservoir and the reservoir gains heat +Q from the system isothermally:Sbox = (-Q/Tbox) Sres = (+Q/Tres)
Second Law of Thermodynamics
(Entropy)
S>0 This is also the second law of thermodynamics Entropy always increases Why?
The 2nd law is based on statistics
State Function
Entropy is a property of system
Can relate S to Q and W and thus P, T and V
S = nRln(Vf/Vi) + nCVln(Tf/Ti)
Not how the system changes ln 1 = 0, so if V or T do not change, its
term drops out
Statistical Mechanics
We will use statistical mechanics to explore the reason why gas diffuses throughout a container
The box contains 4 indistinguishable molecules
Molecules in a Box There are 16 ways that the molecules can
be distributed in the box
Since the molecules are indistinguishable there are only 5 configurations
If all microstates are equally probable than the configuration with equal distribution is the most probable
Configurations and Microstates
Configuration I1 microstate
Probability = (1/16)
Configuration II4 microstates
Probability = (4/16)
Probability
There are more microstates for the configurations with roughly equal distributions
Gas diffuses throughout a room because the probability of a configuration where all of the molecules bunch up is low
Multiplicity The multiplicity of a configuration is the
number of microstates it has and is represented by:
W = N! /(nL! nR!)
n! = n(n-1)(n-2)(n-3) … (1)
For large N (N>100) the probability of the equal distribution configurations is enormous
Entropy and Multiplicity The more random configurations are most
probable
We can express the entropy with Boltzmann’s entropy equation as:
S = k ln W
Sometimes it helps to use the Stirling approximation:
ln N! = N (ln N) - N
Irreversibility Irreversible processes move from a low
probability state to a high probability one
All real processes are irreversible, so entropy will always increases
The universe is stochastic
Arrows of Time
Three arrows of time: Thermodynamic
Psychological
Cosmological
Direction of increasing expansion of the universe
Entropy and Memory
Memory requires energy dissipation as heat
Psychological arrow of time is related to the thermodynamic
Synchronized Arrows Why do all the arrows go in the same direction?
Can life exist with a backwards arrow of time?
Does life only exist because we have a universe with a forward thermodynamic arrow? (anthropic principle)
Fate of the Universe
If the universe has enough mass, its expansion will reverse
Cosmological arrow will go backwards
Universe seems to be open
Heat Death
Entropy keeps increasing
Stars burn out
Can live off of compact objects, but eventually will convert them all to heat
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