# A Brief History of Planetary Science Entropy Physics 202 Professor Lee Carkner Lecture 17 Entropy isnt 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 dont 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! Maxwells Distribution Speed Distribution Maxwells distribution is not symmetrical

This means there are several ways to characterize a average speed Most probable speed, vp vp = (2RT/M) Average speed, vavg

vavg = (8RT/M) root-mean-squared speed, vrms vrms = (3RT/M) 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