Lecture #8 Cassandra Paul Physics 7A Summer Session II 2008

Announcements No Lecture or DL on Monday! (Labor Day) There is DL on Tuesday and Wednesday. I will be out of town next Tuesday and Wednesday. – Substitute for my office hours. Lecture next Wednesday – Sub – Evaluations – Short Lecture – Quiz 5 Review Sessions posted over the Weekend Final Lecture Monday September 8th

Today Intro Model to Thermodynamics Ideal Gas Model Practice with both Enthalpy Microstates Entropy

Intro Model of Thermodynamics A tool we use to talk about the internal energy of a system.

What is Thermodynamics? In a nutshell, it is the study of the transfer of energy between systems and how the energy instills movement, i.e., how the system responds. Ex. If we heat something, it expands. Open box of gas

But wait… does it have to expand? Closed box of gas Open box of gas No, we can constrain the system.

Does it take more or less energy to change the temperature of the constant volume system? Closed box of gas Open box of gas A) More B) Less C) The Same D) Depends on Substance

Does it take more or less energy to change the temperature of the constant volume system? Closed box of gas Open box of gas Closed box: all heat goes into the gas’s internal energy Open box: Some heat goes into pushing air out of the way (work is leaving the system) C V measurement C P measurement

What is ‘work’ in the Thermodynamic Model? Final Initial E th  T  Work Volume is decreasing, positive work is being done on the system. ΔE th = W

What is ‘work’ in the Thermodynamic Model? Initial Final E th  T  Work Volume is increasing, negative work is being done by the system. ΔE th = W

U = Internal Energy When we add heat or work to a substance we are changing the internal energy, but what is internal energy anyway? It is the energy of the system associated with the particles in the system. ΔE th + ΔE bond = ΔU = Q + W E th + E bond = U

Then how is U different than E tot ? It does not include external energies of the system. For example…

If we throw a coconut off the roof… The Internal Energy of the coconut: Does not account for the height of the coconut Does not account for the velocity of the coconut Does account for the Temperature of the coconut Does account for the bond energy of the coconut Does account for the average KE of the particles in the coconut Does account for the average PE of the particles in the coconut

∆U : Internal energy Energy associated with the atoms/molecules inside the body Of material ∆E total must include all changes of energy associated with the system… ∆E total = ∆E thermal + ∆E bond + ∆E atomic + ∆E nuclear + ∆E mechanical Energy associated with the motion of a body as a whole (KE and PE of total System) ΔU is a part of ΔE tot Remember conservation of energy? …if there’s no change in ∆E mechanical, ∆ U First law of Thermodynamics

External Energies vs. U External KE of the SYSTEM PE of the SYSTEM Internal (U) Average KE of the Particles in the system Average PE of the Particles in the system E th of the System E bond of the System

State Functions A State Function is a macroscopic property of a physical system of matter that has a definite value that depends only on certain observable parameters of a system. A State Function does not depend on how the system evolved, but only on the value of the current parameters. (Initial and Final values)

Let’s bring back a bucket of water… What are some observable (measurable) properties of the water in this bucket? Temperature Volume Pressure Eth Eb KE PE All State Functions!!!!!! Entropy Enthalpy

But can I measure how much heat was added and work was done on this bucket since the beginning of time? Only If you were there since the beginning of time!

State Functions can have an Instantaneous Value, Processes can not!

Processes Processes are quantities that depend on HOW a system ends up at it’s final state. The have no ‘instantaneous values.’ They can only be measured over some period of time. They are not considered properties of the system. Can you think of any processes? (Hint: they cause change, but aren’t changes themselves.) Heat and Work!

ΔU = Q + W This is the “First Law of Thermodynamics” It is often EXTREMELY useful to use it like this: ΔE th + ΔE bond = ΔU = Q + W And to also use it in conjunction with the Ideal gas law, so let’s pause a moment and (officially) introduce the ideal gas model…

Ideal Gas Model A tool we use to describe gases in situations where we can ignore inter- particle interactions.

PV=nRT or PV=Nk B T n= number of moles N=number of atoms k B =1.381x10-23 J/K R=8.314 J/(K mole) There are other constructs of this model, but most we have introduced in other places, check the blue pages for more information.

OK what I was saying… It is VERY useful to use the first law of thermodynamics with the sum of the internal energies and with ideal gas law: ΔU = Q + W ΔU =ΔE th + ΔE bond PV=nRT Let’s See How…

Here is a particular cycle that happens to one mole of a monatomic gas, no phase change happens during this process. x10 5 x10 -3 a b c Let’s write this on the board so we can keep track of it.

From a  b  c  a, what is ΔU? Let’s see: ΔU =ΔE th + ΔE bond ΔU =ΔE th ΔU = (# of modes per particle)(# of particles) ½ k B ΔT ΔU = 3(6.02x10 23 ) ½ k B (T f -T i ) OK… let’s find the T at a and a…. wait… The final STATE is the same so: T f =T i ! Therefore ΔU = 0 Note: if you don’t believe me, use PV=nRT

OK well what is the Q for the process a  b  c  a ? ΔE th + ΔE bond = ΔU = Q + W Does Q equal zero for this process? (Don’t calculate anything.) A.Yes, Q = 0 B.No, Q has a negative value C.No, Q has a positive value D.Can’t be determined.

What is the Q for the process a  b  c  a ? ΔE th + ΔE bond = ΔU = Q + W ΔU = Q + W = 0 Work is easier to find, let’s find that and then get our Q.

Work for a  b  c: W abc = ½ (1x10 -3 x 1x10 5 ) + (1x10 -3 x 1x10 5 ) Work for c  a: W ca = (1x10 -3 x 1x10 5 ) W abca = W abc + W ca = -150J + 100J = -50J x10 5 x10 -3 a b c Positive of Negative? Negative W: V is increasing W abc = -150J Positive of Negative? Positive W: V is decreasing. W ca = 100J

What is the Q for the process a  b  c  a ? ΔE th + ΔE bond = ΔU = Q + W ΔU = Q + W = 0 = Q + -50J Q = 50J

Harder Problem… What is the change in E th from b  c? Start with: ΔE th + ΔE bond = ΔU = Q + W ΔE th = Q + W We could find W… but how do we find Q? Need to use something else… PV=nRT!

Harder Problem… What is the change in E th from b  c? ΔE th = Q + W P b V b =nRT b (2x10 5 )(1.8x10 -3 ) = (1)(8.31)T b T b = 43.3°K P c V c =nRT c (1x10 5 )(2.3x10 -3 ) = (1)(8.31)T c T c = 27.7°K

What is the change in E th from b  c? ΔE th = Q + W T b = 43.3°K T c = 27.7°K What equation do we use for E th ? ΔE th = (# of modes per particle)(# of particles) ½ k B ΔT ΔE th = (3)(6.02x10 23 ) ½ (1.38x ) (27.7 – 43.3) ΔE th = J

So… use all three equations together! ΔU = Q + W ΔU =ΔE th + ΔE bond PV=nRT

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)

initial final P V initialfinal P V W = 0 Constant volumeConstant pressure Note: works for solids and liquids too! Enthalpy *Derivation in P.84 ΔE th + ΔE bond = ΔU = Q + W

Intro to Statistical Model of Thermodynamics A tool we use discuss probability of particles or a system being in a certain state.

States and Microstates A state in the Thermodynamic Model is a combination of instantaneously measurable parameters. – Ex: Solid phase, 30C, at 1Atmosphere of Pressure. You can think of it is any point on any state diagram P V

What the heck is a Microstate? A microstate is one of the different ‘ways’ a system can be in that state. P V State 1 Microstate1

What the heck is a Microstate? A microstate is one of the different ‘ways’ a system can be in that state. P V State 1 Microstate 2

What the heck is a Microstate? A microstate is one of the different ‘ways’ a system can be in that state. P V State 1 Microstate 3

Let’s try a real world example.. (Well sort 0f real world)

After graduating from Davis, you decide you love it here so much that you want to start a farm and live here forever..

You go to the state Fair to get your first animals. There are only two kinds for sale and you can only buy 1. You go back the next day, and pick another one. What are your possible combinations?

What are the States? And what are the microstates of the system? State = 1Cow and 1 Sheep State = 2 Cows State = 2 Sheep Microstate = CS Microstate = SC Microstate = SS Microstate = CC Three States, but 4 microstates, which State is most probable?

If you leave it up to chance… You are most likely to have a state of one cow and one sheep, because there are more microstates in that state!