Transcript entropy - Helios

Entropy
Physics 202
Professor Lee Carkner
Lecture 15
PAL #14 Internal Energy
 3 moles of gas, temperature raised from 300 to 400 K
 He gas, isochorically
 Q = nCVDT, CV = (f/2)R = (3/2) R
 Q = (3)(3/2)R(100) = 3740 J

 He gas, isobarically
 Q = nCPDT, CP = CV + R = (5/2) R
 Q = (3)(5/2)R(100) = 6333 J

 H2 gas, isochorically
 Q = nCVDT, CV = (5/2) R, f = 5 for diatomic
 Q = (3)(5/2)R(100) = 6333 J

 H2 gas, isobarically
 Q = nCPDT, 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=pDV = (19475)(0.78-0.45) = 6427 J
 Q=nCp DT = (4)(7/2)(8.31)(457-263.7) =22489 J

 adiabatic process starts at the same point, ends where
V= 0.78 m3.
 piVig = pfVfg

 pf = piVig /Vfg = (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:
DS = Sf –Si = ∫ (dQ/T)
Isothermal Entropy

DS = (1/T) ∫ dQ
DS = 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 = mcDT, if m is very large, DT 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:
DS>0

Entropy always increases
Entropy Problems Using Q/T
Need to find heat

Sign of DS 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
DS = 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 I
1 microstate
Probability = (1/16)
Configuration II
4 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)
B)
C)
D)
E)
-34
0
100
458
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)
B)
C)
D)
E)
1J:1J
1 J : 12.5 J
12.5 J : 12.5 J
12.5 J : 20.8 J
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)
B)
C)
D)
E)
1J:1J
1 J : 12.5 J
12.5 J : 12.5 J
12.5 J : 20.8 J
8.3 J : 16.6 J