Quiz 8 (LAST QUIZ!) 8:30-8:50am TODAY Have your calculator ready. Cell phone calculator NOT allowed. Closed book Quiz 4 Re-evaluation Request Due this Thursday, 3/6. Quiz 5 Re-evaluation Request Due next Thursday, 3/13. Turn in you original Quiz along with the Re- evaluation Request Form. Note: It is possible for your grade to be lowered after the re- evaluation. Next Week Last lecture March 11 Last lecture + Information on Final, Final review sessions, among other things…
Transcript
Quiz 8 (LAST QUIZ!) 8:30-8:50am TODAYHave your calculator ready.
Cell phone calculator NOT allowed.Closed book
Quiz 4 Re-evaluation Request Due this Thursday, 3/6.Quiz 5 Re-evaluation Request Due next Thursday, 3/13.
Turn in you original Quiz along with the Re-evaluation Request Form. Note: It is possible for your grade to be lowered after the re-evaluation.
Next Week Last lecture March 11Last lecture + Information on Final, Final review sessions, among other things…
PHYSICS 7A Final ExamMarch 18, Tuesday, 10:30am - 12:30pm
Location TBABring pen/pencils, calculator, a photo ID to sit in the final
No makeup Final
PHYSICS 7A Final Review SessionsEvery 7A instructors (lecturers + DL instructors) will
hold a 1.5hours each session on
March 15,16,17 (Sat through Mon)Location and schedule are available on the
course website (click on “Review Sessions”). You can go to any session.
Enthalpy
Is a state function:- U depends only on state of system- P depends only on state of system- V depends only on state of system
=> H depends only on state of system
(Hess’s law)
Who cares?!?!
initial
final
P
V
initial
final
P
V
W = 0
Constant volume Constant pressure
Note: nothing about gasses used - works for solids and liquids too!
Enthalpy
*Derivation in P.84
spontaneous changes occur
with an increase in entropy.
Laws of Thermodynamics
Remember conservation of energy?
(if there’s no change in ∆Emechanical), ∆ U
First law of Thermodynamics
Ever heard of entropy?
Rudolf Clausius(1822-1888)
Total entropy never decreases.
the system always evolves toward
equilibrium.
Second law of Thermodynamics
Thermal equilibriumThermal equilibrium
Tfinal
Energy leaves hot objects in the form of heat Energy enters cold objects in the form of heat
Low temp High temp
From everyday experience, we know that this process is irreversible and spontaneous…. but WHY???
Microstates
So far we have described systems using P, V, T, .....
Incomplete information about the system
A microstate is a particular configuration of atoms/molecules in the system.
For example,For a box of gas, you need to specify where all the atoms are i.e., position (x,y,z), and how fast they are moving i.e., velocity (vx, vy, vz).
Tell us which microstates are allowed.Examples The volume of a box constraints the possible positions of gas atoms.The energy of the box constraints the possible speeds of gas atoms.
Groups of microstates that share some average properties,i.e. A collection of states that “look” the same macroscopically.Examplesgasses: P ~ average density, V~volume filled, T~average KE
Microstates vs states
Flipping a coin 3 times:
Microstates: all possible combinations of coin flips
Constraints: some combinations not possible (e.g. HHTHHH)
MicrostatesStates
States: total number of heads
Hypothesis: every microstate is equally likely. Hypothesis: every microstate is equally likely. The state that is most likely is the one with the most is the one with the most
microstatesmicrostates
Prob.
10 atoms in a box
Microstates vs states
10 atoms in a box
Microstates vs states
10 atoms in a box
Microstates vs states
“Ordered microstate”
equally likely as a random microstate
Are we likely to find the system in “ordered state” or “random state”??
…umm almost all the microstates look “random”
Microstates vs states
1024 microstates, each microstate equal width
Define states by “total number of heads”
Different states contain different # of microstates
Therefore even though each microstate is equally likely, some states are more
likely than others.
10 fair coin flips
We can also consider our physical system to be two “sub-systems”: * Sub-system A: the first two coin flips * Sub-system B: the final eight coin flips
HHHHHTHTTHTHTTTT
Any of the 256 micro.Any of the 256 micro.
Any of the 256 micro.Any of the 256 micro.
Any of the 256 micro.Any of the 256 micro.
Any of the 256 micro.Any of the 256 micro.
10 fair coin flips
where kB is Boltzman’s constant
If our system is composed of two sub-systems A and B:
We can add the entropy of the subsystems to get the total entropy.
Entropy
where kB is Boltzmann’s constant
ln(Omega) is always increasing.
As # microstates available increase, so does the entropy.
Entropy
Why split our system into subsystems?
Splitting 10 coin flips into the first 2 flips and the remaining 8 is perverse
ice (0ice (000 C) C)
Water (0Water (000 C) C)
But calculating heat needed to raise temperature of this system to 100 C we would split into subsystems:
the ice and the water
How to calculate entropy?
We should divide our box up into “atom-sized” chuncks. But how
big should our velocity microstates be?
ice (0ice (000 C)C)
Water (0Water (000 C) C)
How can we get a definite answer for the number of
microstates in this system?
Relating entropy to microstates is useful for conceptually understanding what entropy is.
At this level, it is not useful for calculating the change in entropy
For slow, reversible processes:
initial
final
final P
VS
T
initial
W > 0 when Delta V < 0W < 0 when Delta V > 0
Q > 0 when Delta S > 0Q < 0 when Delta S < 0
How to calculate entropy? Answered
For slow, reversible processes:
To get to entropy we can “turn this expression around”
If temperature is constant, then we can easily integrate:
This last equation is not generally true; as heat enters or leaves a system the temperature often
changes.
(isothermal only!)
How to calculate entropy? Answered
Q
If the process is not slow or reversible, or it is very difficult you can use the fact entropy is a
state function
If you can find any process from the initial to final state, you can use this path to calculate ∆ S for the
process in question!
(As in calculation of enthalpy in DLM14)
How to calculate entropy? Answered 2
Summary
STOP
SLOW
Why do we care about entropy?
That is our next topic..... the quest for equilibrium
or, “how presidential elections differ from thermodynamics”
Lesson: some states are more likely than others.
But once the coins are flipped we know what they are going to be. Our system does not evolve in time.
Solids, liquids and gasses do not stay in the same microstate -- they change in time.
10 fair coin flips
e.g.First coin flip is T. So I have 49 H, 1T => state is 49Second coin flip is H. Still have 49 H => state is 49Third coin flip is T. Now state is 48 etc.......
What does our state look like as a function of “time”?
10 fair coin flips50
“Short” example(400 flips)
with 50 coins
“Long” example(1500 flips)
with 50 coins
“Short” example(400 flips)
with 100 coins
“Long” example(1600 flips)
with 100 coins
“Interactions” (i.e. coin flips) take a certain amount of time each.
After many interactions, the systems settle down “close” to the most likely value. This is what is meant by equilibrium.
The system may depart from equilibrium, but large departures are rare and typically don’t last very long.
Equilibrium
• Equilibrium is the most likely state
• Each microstate is equally likely, so the equilibrium state has the most microstates.
• Therefore the equilibrium state has the highest entropy.
• For large (i.e. moles of atoms) systems, the system is (essentially) always evolving toward equilibrium. Therefore the total entropy never decreases:
