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Entropy
Physics 202Professor Lee
CarknerLecture 17
“Entropy isn’t what it used to be.”
--Anonymous
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
He gas, isobarically Q = nCPT, CP = CV + R = (5/2) R Q = (3)(5/2)R(100) = 6333 J
H2 gas, isochorically Q = nCVT, CV = (5/2) R, f = 5 for diatomic Q = (3)(5/2)R(100) = 6333 J
H2 gas, isobarically Q = nCPT, CP = CV + R = (7/2) R Q = (3)(7/2)R(100) = 8725 J
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
Random Gas Motions
Gas Motions
Why don’t gasses diffuse more rapidly?
They do not travel in a straight line
Energy and information is quickly transmitted through the gas
Mean Free Path
The average distance between collisions:
= 1 /[√2 d2 (N/V)] Where:
V is the volume
Millions of collisions per second!
Maxwell’sDistribution
Speed Distribution Maxwell’s distribution is not symmetrical
This means there are several ways to characterize a “average” speed
Most probable speed, vp vp = (2RT/M)½
Average speed, vavg vavg = (8RT/M)½
root-mean-squared speed, vrms vrms = (3RT/M)½
rms speed reflects the way the molecules produce pressure and carry energy
Titan
Why does it have an atmosphere?
What type of gas might the atmosphere be made of?
Planetary Atmospheres Why do some planets have
atmospheres and others do not?
So equating escape velocity to thermal velocity should define conditions for atmosphere retention
Escape velocity needs to be about 10 times large than rms velocity in order to keep an atmosphere for a long time:
(2GMplanet/Rplanet) > (300kT/mmolecule)
The Arrow of Time
Why? The smashing plate is an example of an
irreversible process, one that only happens in one direction
Examples:
Entropy
They all progress towards more randomness
For an irreversible process, entropy always increases
Determining 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:
Isothermal Expansion
A cylinder of gas rests on a thermal reservoir with a piston on top Heat also flows into the system from the reservoir
The temperature is constant so
S=Q/T
Closed Systems Consider a closed system
The heat lost by the reservoir was gained by the gas so there is no net heat loss or gain
For a reversible process in a closed system the entropy is constant
Second Law of Thermodynamics
No real process is truly reversible (due to friction, turbulence etc.), so we can say:
S>0
Entropy always increases
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