Entropy

Physics 202Professor Lee

CarknerLecture 15

PAL #14 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

PAL #14 Internal Energy 4 moles of N2 gas isobaric expansion from 0.45

m3 to 0.78 m3 and 457 K pressure = p =nRT/V = (4)(8.31)(457)/(0.78)

= 19475 Pa initial temp = T = pV/nR = (19475)(0.45)/(4)

(8.31) = 263.7 K W=pV = (19475)(0.78-0.45) = 6427 J Q=nCp T = (4)(7/2)(8.31)(457-263.7)

=22489 J adiabatic process starts at the same point,

ends where V= 0.78 m3. piVi

pfVf

pf = piVi

Vf(19475)(0.45)1.4/(0.78)1.4 =

9017 Pa

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: Perfume diffuses throughout a room 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

S = (1/T) ∫ dQS = Q/T

Like heating something up by 1 degree

Heat Reservoir

Something that is too big to change temperature

A heat reservoir can gain or lose heat

without changing temperature Since Q = mcT, if m is very large, T can

be very small

Second Law of Thermodynamics

(Entropy) Consider objects A and B that exchange heat Q with each other isothermally:

We always find that the positive term is always a larger than the negative term, so:

S>0 Entropy always increases

Entropy Problems Using Q/T Need to find heat

Sign of S is sign of Q (positive in and negative

out)

T constant for phase change or heat reservoir

For total entropy, must add all sources and

sinks of heat

General Entropy

From the first law and the ideal gas law, we get

S = nRln(Vf/Vi) + nCVln(Tf/Ti)

Note that we only need to know the initial and final conditions, not the path

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

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:

Direction in which entropy increases

Direction that you do not remember

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

Head towards the Big Crunch

Will the others reverse as well?

Expand forever

Heat Death

Everything in the universe trying to be same temperature

Universe gets more and more disordered Left with white dwarfs, neutron stars and

radiation Can live off of compact objects, but eventually will

convert them all to heat

Next Time

Read: 20.5-20.7

Suppose it is 0 F outside today. What would the temperature need to be outside tomorrow (in F) to be twice as hot?

A) -34B) 0C) 100D) 458E) 510

How much heat does it take to change the temperature of one mole of a monatomic ideal gas 1 degree K in a constant volume process? How much heat does it take to change the temperature of one mole of a monatomic ideal gas 1 degree K in a constant pressure process?

A) 1 J : 1 JB) 1 J : 12.5 JC) 12.5 J : 12.5 JD) 12.5 J : 20.8 JE) 8.3 J : 16.6 J

What is the change in internal energy for an ideal monatomic gas whose temperature increases 1 degree K in a constant volume process? What is the change in internal energy for an ideal monatomic gas whose temperature increases 1 degree K in a constant pressure process?

A) 1 J : 1 JB) 1 J : 12.5 JC) 12.5 J : 12.5 JD) 12.5 J : 20.8 JE) 8.3 J : 16.6 J