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