Last Lecture Quiz 5,6,7 Re-evaluation Request Due at the time of Final 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. All the Quiz information (answers, rubrics, grades for Q1 ~ Q6 ) are posted on the website. Quiz 7,8 grades will be available by the end of this week. Final grade and Quiz grade (average of 7 highest individual Quiz grade) will be posted on the course website after March 24.

Final location 194 Chemistry A through P 179 Chemistry Q through Z Separated by family name:

Final checklist Calculator We will not have spare calculators, make sure you bring yours Pens and pencils Photo ID Without it you can’t sit the final, and you will fail the course. The pages will be separated -- write your name on every single page when you first get your final Formulas will be provided with the final

Final format 6 ~ 8 questions (most likely…) Quantitative and qualitative questions Questions are on any material throughout the quarter. To do science, one must practise! But make sure your practice is useful available resources : Quiz problems from this quarter, Quiz problems from lecture section A/B will be provided during DLM18 (also available from their website, follow the link from

Final Review sessions *Most useful when you go AFTER having solved/attempted Quiz/FNT questions by yourself. You are welcome to go to review session for either Physics 7A-AB or 7A-CD. Above schedule available on the course website.

Final Review Session location Mon Everson 266 Sat/Sun Roessler 55 Mon AM Roessler 66 (on the other side of the building from our lecture) This is Final Review Session location, NOT Final location.

Physical systems have an equilibrium state (the one with the most microstates, and therefore the highest entropy) If we wait “long enough” the system will most likely evolve to that equilibrium state. (by the laws of chance) For large (i.e. moles of atoms) systems, the system is (essentially) always evolving toward equilibrium. Therefore the total entropy never decreases: Let’s start with a recap… What was entropy again? Second law of Thermodynamics

Physical systems have an equilibrium state (the one with the most microstates, and therefore the highest entropy) If we wait “long enough” the system will most likely evolve to that equilibrium state. (by the laws of chance) For large (i.e. moles of atoms) systems, the system is (essentially) always evolving toward equilibrium. Therefore the total entropy never decreases: Let’s start with a recap… What was entropy again? Second law of Thermodynamics

Thermal equilibrium T final Energy leaves hot objects in the form of heat Energy enters cold objects in the form of heat Low tempHigh temp From everyday experience, we know that this process is irreversible and spontaneous….

Thermal equilibrium T final What about entropy change of this process?

AB The two blocks A and B are both made of copper, and have equal masses: m a = m b = 100 grams. The blocks exchange heat with each other, but a negligible amount with the environment. a) What is the final state of the system? b) What is the change in entropy of block A? c) What is the change in entropy of block B? d) What is the total change in entropy? (Heat of melting)

AB The two blocks A and B are both made of copper, and have equal masses: m a = m b = 100 grams. The blocks exchange heat with each other, but a negligible amount with the environment. a)What is the final state of the system? What is the final equilibrium temperature of the system? (Heat of melting)

AB Okay, now we have found the equilibrium state. How do we calculate the change in entropy? a)What is the final state of the system? b) What is the change in entropy of block A? c) What is the change in entropy of block B? d) What is the total change in entropy?

In this case T f = 150 K = T f,A = T f,B T i,A = 100 K, T i,B = 200 K What about the entropy change for this process? i,B m c In (T f,B /T i,B ) =

In this case T f = 150 K = T f,A = T f,B T i,A = 100 K, T i,B = 200 K What about the entropy change for this process? ∆S total > 0 Irreversible and spontaneous process

In this case T f = 150 K = T f,A = T f,B T i,A = 100 K, T i,B = 200 K What about the entropy change for this process? ∆S total > 0 Irreversible and spontaneous process ∆S total = 0 Reversible process

NOTEnvironment system Note: reversible means that

Gibbs Free Energy is a state function: - H depends only on state of system - T depends only on state of system - S depends only on state of system => G depends only on state of system Why is this useful?…. G = H - TS

Gibbs Free Energy G = H - TS  dG = dH - TdS + SdT At Const T, dG = dH - TdS or ∆G = ∆ H - T ∆S So then, Gibbs free energy reflects the change in the enthalpy of the system as well as the change in the entropy of the system Still …Why is this useful?

Gibbs Free Energy G = H - TS  dG = dH - TdS + SdT At Const T, dG = dH - TdS or ∆G = ∆ H - T ∆S Remember ∆H = Q for Const P process. (tells you whether a reaction is endothermic or exothermic) So then, ∆G = ∆ H - T ∆S -∆H/T can tell you about the change in the entropy of the environment: ∆S env This term is about the change in the entropy of the system: ∆S sys

Gibbs Free Energy ∆G = ∆ H - T ∆S -∆H/T can tell you about the change in the entropy of the environment: ∆S env This term is about the change in the entropy of the system: ∆S sys Sign of ∆G can tell you whether a process is spontaneous or not. Can help you predict what will and what won’t happen.

spontaneous changes occur with an increase in entropy. Laws of Thermodynamics Remember conservation of energy? (if there’s no change in ∆E mechanical ), ∆ U First law of Thermodynamics Ever heard of entropy? Rudolf Clausius ( ) Total entropy never decreases. the system always evolves toward equilibrium. Second law of Thermodynamics ∆S total  or  0

Energy changes form and transfers from place to place but the total amount doesn’t change. conservation of energy

Conserve energy? Why, energy is always conserved! Found in the PHYSICS department!

The rest of the story… An inescapable truth defined by the 2nd law of Thermodynamics 2nd Law of Thermodynamics tells you the direction of the energy flow. Each time energy gets transferred, some of it gets less useful… until finally, it becomes simply useless…. All of energy we use, sooner or later, ends up being low-grade thermal energy… Brake!

Falling rock The rest of the story… An inescapable truth defined by the 2nd law of Thermodynamics 2nd Law of Thermodynamics tells you the direction of the energy flow. Each time energy gets transferred, some of it gets less useful… until finally, it becomes simply useless…. All of energy we use, sooner or later, ends up being low-grade thermal energy…

Falling rock The rest of the story… An inescapable truth defined by the 2nd law of Thermodynamics 2nd Law of Thermodynamics tells you the direction of the energy flow. Each time energy gets transferred, some of it gets less useful… until finally, it becomes simply useless…. All of energy we use, sooner or later, ends up being low-grade thermal energy…

Summary Focus on main points Practise the “techniques of physics” - identifying the principles (need to be able to communicate effectively to your grader if asked) - setting up the problem - doing your ALGEBRA CORRECTLY! - units, units, units!!!!!!!!!! Addendum to this lecture contains a summary of some of the principles.(not an exhaustive list) Conserve “useful” “concentrated” ”high-grade” energy! Good luck! (don’t leave yet!)

Addendum

Energy basics: Energy: Some conserved quantity (i.e. the total amount in the entire universe never changes) Can be transferred from one type of energy into another inside an obj. (e.g. E bond -> E thermal for the heat pack) or can be transferred to other objects by either heat or work. i.e. change in energy = (amount coming in) - (amount leaving) Heat is the disordered energy that flows spontaneously from a higher temperature object to a lower temperature object. Work is the ordered energy that pushes on things

Mechanical energy: Kinetic (“moving”) energy: - Always positive (or zero for an object at rest) - Any type of additional motion increases KE - This leads to “trapped” or “bound” regions that particles cannot escape from -- escaping would mean KE < 0 somewhere which cannot happen Potential energy: - Function of position - The magnitude of the force (i.e. “push”) on a particle is the slope of the PE vs position graph. - The direction of the force is always in the direction that lowers PE - The force pushes an object in a direction. If the object is travelling in the opposite direction to the push it slows down. In the same direction it speeds up. The object may travel in the opposite direction to the force! - Absolute value of PE arbitrary; only changes in PE matter! - Relationship between work and force: Work = F || x ∆x

Mechanical energy (cont): Potential energy: One additional piece of information: the place where the force is zero, this special place is called “equilibrium position” * Note this means that an equilibrium occurs when the PE vs distance graph is flat/max/min

Raise temperature Concept of heat capacity: - How much heat is needed to raise the temp 1 K? - Heat process dependent. Therefore different processes have different heat capacities (I.e., C p vs C v )

Raise temperature (cont) Equipartition: Learn to count modes Learn that vibrational modes are frozen out at low temperatures Equal energy per mode: 1/2 k b T Now can write E thermal in terms of number of modes Can get a theoretical expressions for specific heat -- determined by amount of “stuff” and number of modes! i.e. Can see how the microscopic rules of physics influence the macroscopic rules.

Phase changes Concept of E bond changes - Have experimental tables that tell us how much heat it takes to change phase. - We can relate this energy to the energy it takes to break all the microscopic bonds that occur via atom-atom interactions. - Estimate of this energy comes from only considering the atoms that are closest to one another (nearest neighbour interactions) - Number of nearest neighbour bonds in a system of N molecules is (over 2 occurs because every bond is by definition between two atoms, so the bond will be counted twice)

Lennard-Jones Potential: Special case of general potential V(r) [see mechanical work section]: Generic potential between neutral atoms. Gives force between atoms. Shows there is a range of energies for which atoms are bound. Related to the properties of the atoms roughly as follows:

Lennard-Jones: No need to memorise silly rules for “when system is bound and when it is not” -- these follow automatically from the fact KE cannot be negative. (Notice that “silly rules” won’t necessarily work for other potentials -- the KE >= 0 rule always works!) Note: definition of bound -- particle trapped in a certain (finite) region

Phase changes State functions: Anything a system can “have” (e.g. U, P, V, T,...) is a state function. We can go to a system and measure it when the system is in a particular state. Any combination of state functions (e.g. H = U + PV) is also a state function (we can measure U, P and V and then do trivial mathematics to calculate H). Non-state functions: Anything that labels a process rather than a system in a particular state. e.g. Q, Work

PENCILS AND PENS ? (for filling the bubbles) (for comments in the back) Teaching Evaluations