Quiz 2 Info. Average 5.06 St. Dev Frequency. 2/20/2014 Physics 132

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1 Quiz 2 Info Average 5.06 St. Dev Frequency /20/2014 Physics 132 1

2 1. (3 pts) The internal energy of an object at atmospheric pressure is observed to increase. At the same time its volume changes, but pressure is held constant. Which of the following is true? A. Heat must have been added to the system. B. If the volume increased the system did positive work on its surroundings. C. Since pressure is constant, enthalpy is conserved. D. If the volume increased heat must have been added to the system. E. If the enthalpy is constant, the volume must have decreased. 2/17/2014 Physics 132 2

3 2. (2 pts) In a certain process, 400 J of heat is added to a system and the system simultaneously does 100 J of work. The change in internal energy of the system is A. 500 J B. 400 J C. 300 J D. 0 J E. 100 J F. 300 J G. The change in internal energy depends on how the heat was added and the work was done 2/20/2014 Physics 132 3

4 3. (2 pts) Suppose we have two identical boxes of matter, A and B, that are in thermal contact but cannot exchange materials. They come to thermal equilibrium. System 1 consists of box A alone, while system 2 consists of both boxes A and B. What can you say about the entropy of the two systems? A. The entropy of system 2 is twice as high as that of system 1. B. The entropy of system 2 is a lot more than twice as high compared to system 1. C. The number of microstates of system 2 is twice as high as those of system 1. D. The number of microstates of system 2 is a lot more than twice as high as those of system 1. E. You can t tell anything about the comparative entropy of the two systems without more information. 2/20/2014 Physics 132 4

5 4. (3 pts) Two rooms of a cabin are kept at different temperatures, as shown. If 5 J of energy pass through the interior wall from room 2 to room 1, the exchange is too small to change the temperature of either room by a measurable amount. S 1 and S 2 are the entropies of the two rooms. If only this exchange occurs A. S1 and S2 decrease by equal amounts. B. S1 and S2 decrease by unequal amounts. C. S1 increases, but S2 decreases by more. D. S1 increases and S2 decreases by equal amounts. E. None of the above exchanges occur. 2/20/2014 Physics 132 5

6 Your Questions Are you saying that the energy of the whole universe stays constant, but that the entropy is constantly increasing as systems lose heat to their environment? Yes What other types of free energy is there besides Gibbs? And what does it mean? It s a matter of what you is being held constant in the process you are examining. Gibbs is often used when holding pressure and temperature constant (common for bio and chem). Helmholtz free energy is often used when the temperature and volume are held constant. How can lower energy levels equate to a higher entropy? Goes back to what higher entropy means a greater number of possibilities for states with that energy level. The most probable configuration of states winds up having the lowest overall energy. What is the probability the distribution addresses? The probability of what? Finding the system in that particular state Can you quickly work out the example provided towards the end of this section? I have tried to use the numbers given but I can not seem to get the answer.** Why would there only be one packet of energy in object A while there would be 2 packets of energy in object B when there are 3 packets in total?

7 Josiah Willard Gibbs: Tidbits from Wikipedia: "In 1863, Yale awarded Gibbs the first American doctorate in engineering." "... for a thesis entitled "On the Form of the Teeth of Wheels in Spur Gearing", in which he used geometrical techniques to investigate the optimum design for gears." "... was praised by Albert Einstein as "the greatest mind in American history"." Gibbs, who had independent means and had yet to publish anything, was assigned to teach graduate students exclusively and was hired without salary. Known for Statistical mechanics Statistical ensemble Gibbs entropy Phase space Gibbs free energy Phase rule Gibbs paradox Vector calculus Cross product Gibbs phenomenon Gibbs Helmholtz equation Gibbs Duhem equation Gibbs algorithm Gibbs measure Gibbs state Gibbs Thomson effect Gibbs isotherm Gibbs Donnan effect Gibbs Marangoni effect Gibbs lemma Gibbs' inequality

8 Gibbs Energy: Can a change happen? External Environment: P and T fixed. Entropy goes up Internal System: Entropy changes: S int, Volume changes: V Heat transferred to environment: -Q Q W= P V Change can happen if T( S int + S ext ) > 0 But, T S ext = -Q = - H

9 External Environment: P and T fixed. Loses heat Q Internal System: Entropy changes: S int, Volume changes: V Heat transferred from environment: Q Q W= P V Change can happen if T( S int + S ext ) 0 But, T S ext = -Q = - H T S int - H > 0 or G = (H-TS) < 0

10 Foothold ideas: Energy changes in a process Internal energy: thermal and chemical Enthalpy: internal plus amount needed to make space at constant p Gibbs free energy: enthalpy minus amount associated with raising entropy of the rest of the universe due to energy dumped A process will go spontaneously if ΔG < 0. 2/13/13 Physics

11 How does ΔG affect the rate of a given reaction? A. Reaction rate is directly proportional to ΔG B. ΔG has no effect on reaction rate C. Reaction rate is inversely proportional to ΔG A 33% 33% B 33% C That s why we need catalysts/inhibitors for certain reactions! 1/23/13 Physics

12 External Environment: V and T fixed. Loses heat Q Internal System: Entropy changes: S int, Volume changes: V Heat transferred from environment: Q Q W= P V=0 Change can happen if T( S int + S ext ) 0 But, T S ext = -Q = - U T S int - U What if 0 Volume or F is = fixed? (U-TS) < 0 Whiteboard, TA & LA

13 Foothold ideas: Energy distribution Due to the randomness of thermal collisions, even in (local) thermal equilibrium a range of energy is found in each degree of freedom. The probability of finding an energy E is proportional to the Boltzmann factor At 300 K, k B T ~ 1/40 ev N A k B T = RT ~ 2.4 kj/mol Physics

14 In the Boltzmann 17% 17% 17% 17% 17% 17% factor,, the "T" means: 1. Higher-energy states are only possible above a certain temperature 2. Higher-energy states are only possible below a certain temperature 3. Higher-energy states become more probable as the temperature increases 4. Higher-energy states become more probable as the temperature decreases 5. More than one of these 6. None of these 2/20/2014 Physics

15 The molecules in liquid water are connected by hydrogen bonds whose energy is about 23 kj/mol. (This is what is responsible for the heat of vaporization of water.) What is the probability that the thermal motion of the water molecules at STP will result in breaking one of those hydrogen bonds? To get probability of about.8 probability, need 1 ev/molecule ~ 100 kj/mole.

16 A gas of molecules at room temperature interacts with the potential shown below. Each molecule can be in the state E 1 or E 2. If the gas is at STP and E 1 E 2 = 25 mev, then at equilibrium, the number of molecules found in the state E 1 divided by the number of molecules found in the state E 2 will be A. About 1 B. About 1/3 C. About 3 D. Much, much larger than 1 E. Much, much smaller than 1 F. Cannot be determined from the information given 2/20/2014 Physics A 17% 17% 17% 17% 17% 17% B C D E F

17 The energy of a C-C single bond is about 350 kj/mol. What is the probability that thermal motion will result in breaking this bond? What if it were a double C=C bond? (Energy about 615 kj/mol)

18 If we assume that the atmosphere is in thermal equilibrium and at a uniform temperature (not really a great assumption!), then we expect the density of a given molecule in the atmosphere (say oxygen) to fall off with height by the Boltzmann factor: (this defines h 0 ). Find h 0, given that at STP, k B T 1/40 ev or RT 2.4 kj/mole and 1 ev/molecule ~ 100 kj/mole.

19 Foothold ideas: Using Boltzmann & Gibbs Energy Gibbs free energy combines the effects of energy (here, that's the original Boltzmann factor) and of entropy (the number of possible arrangements) For systems at constant pressure and temperature, the Gibbs free energy is what really tells us which states are more probable, and therefore what a system is actually going to do. That's why Gibbs free energy gets so much attention in chemistry and biology. 1/23/13 Physics

20 Week 4 Outline Review electric Forces Review electric Potential

21 Electric charges are key to life! Phosphate group is charged and has electric field Simulation based on F=ma (Newton s laws) What are the forces? Pastor Biophys J 2006

22 Model: Charge A hidden property of matter Matter is made up of two kinds of electric charges (positive and negative) that have equal magnitude and that cancel when they are together and hide matter s electrical nature. Like charges repel, unlike charges attract. The net charge (postive minus negative charges) is a constant Matter with an equal balance is called neutral. 22

23 Foothold idea: Coulomb s Law r k qq = C rˆ q Q 2 q Q rqq F 23

24 Making Sense of Coulomb s Law Changing the test charge Changing the source charge Changing the distance Specifying the direction Use Subscripts! r F k qq = C rˆ Q q 2 Q q 10/12/12 Physics R

25 What does ˆr mean? 1. Vector length 1, dimension length 2. Scalar length 1, dimension length 3. Vector length 1, dimensionless 4. Scalar length 1, dimensionless 5. Don t know 20% 20% 20% 20% 20% 2/20/2014 Physics Vector length 1, dimension... Vector length 1, dimensionless Scalar length 1, dimension l... Scalar length 1, dimensionless Don t know

26 MOVEMENT OF CHARGES 2/20/2014 Physics

27 Can Charges Move? Insulators Charges are bound and cannot move around freely. Excess charge tends to just sit there. Conductors Charges can move around throughout the object. Excess charge redistributes itself or flows off Solid: Electrons move Fluid: Charged atoms move Unbalanced charges attract neutral matter (polarization) 27

28 When two objects with the same sign of charge but different magnitudes are put together, they accelerate A. with the same acceleration. B. With different acceleration - Larger charge has higher acceleration. C. With different acceleration Smaller charge has higher acceleration. D. Not enough information with the same acceleration. 25% 25% 25% 25% With different acceleration -... With different acceleration Not enough information 2/20/2014 Physics

29 Two small objects each with a net charge of Q (positive) exert a force of magnitude F on each other. We replace one of the objects with another whose net charge is 4Q. The original magnitude of the force on the Q charge was F; what is the magnitude of the force on the Q now? A. 16F B. 4F C. F D. F/4 E. other 20% 20% 20% 20% 20% 2/20/2014 Physics F 4F F F/4 other

30 20% 20% 20% 20% 20% What is the magnitude of the force on the 4Q charge? 16F 4F F F/4 other A. 16F B. 4F C. F D. F/4 E. other 2/20/2014 Physics

31 ADDITION OF FORCES 2/20/2014 Physics

32 In the figure are shown four arrangements of charge. Each charge has the same magnitude, but some are + and some are -. All distances are to the same scale. In which arrangement would the magnitude of the force felt by a positive test charge placed at P be the largest? A. A B. B C. C D. D E. You can t tell 20% 20% 20% 20% 20% A B C D You can t tell 1/23/13 Physics

33 Compare the magnitude and direction of the net force exerted on Q A +q d A. Same magnitude B. Same direction +q + 20% 20% 20% 20% 20% C. Same magnitude and direction D. Same magnitude, opposite direction E. Neither same magnitude nor same direction 1/23/13 Physics B Same magnitude Same direction Same magnitude and direction Neither same magnitude no... Same magnitude, opposite d q d -q

34 A test charge (labeled q) is placed in a situation in which it feels the electrical force from three other charges (of opposite sign to it) labeled A, B, and C. (The charges are on a uniform grid as shown and the positions are to scale.) Which of the following combinations of forces has the greatest magnitude? FF AA 25% 25% 25% 25% + FF BB qq FF CC + + FF AA qq FF BB qq FF CC Not enough information to tell 1. FF AA qq 2. FF BB qq + FF CC qq 3. FF AA qq + FF BB qq + FF CC qq 4. Not enough information to tell 2/20/2014 Physics

35 ELECTRIC FIELDS 2/20/2014 Physics

36 E is defined everywhere in space not just in places where charges are present Foothold idea: Electric Forces and Fields When we focus our attention on the electric force on a particular object with charge q 0 (a test charge ) we see the force it feels depends on q 0. Define quantity that does not depend on charge of test object test charge -> Electric Field E

37 Foothold ideas: Fields A field is a concept we use to describe anything that exists at all points in space, even if no object is present. A field can have a different in magnitude at different points in space. (and if it s a vector field, direction). Examples: temperature, wind speed, wind direction A gravitational, electric, or magnetic field is a force field. Fields allow us to predicts the force that a test object would experience. The field does not depend on what test object is used. gg rr = FF acting on mm ( rr) mm EE rr = FF acting on qq ( rr) qq Field is the value at a position in space r assuming that the force is measured by placing the object at r. 10/17/12 Physics

38 See the system below. A B and C are positive charges, q is a negative charge. How many interactions do we need to add to compute the force exerted on a test charge? Test Charge 38

39 See the system below. A B and C are positive charges, q is a negative charge. How many terms do we need to add to compute the electric field? 39

40 The electric field at a particular point in space A. Depends only on the magnitude of the test charge used to measure it. B. Depends only on the sign of the test charge used to measure it. C. Depends on both the sign and magnitude of the test charge used to measure it. D. Does not depend on the test charge used to measure it. E. None of the above Depends only on the sign of... Depends only on the magni... 20% 20% 20% 20% 20% Depends on both the sign a.. Does not depend on the test... None of the above 1/23/13 Physics

41 POTENTIAL ENERGY 2/20/2014 Physics

42 Foothold ideas: Energies between charge clusters Atoms and molecules are made up of charges. The potential energy between two charges is The potential energy between many charges is 2/15/13 Physics

43 A positive charge might be placed at one of three spots in a region. It feels the same force (pointing to the left) in each of the spots. How does the electric potential energy, U elec, on the charge at positions 1, 2, and 3 compare? A. U is greatest at 1 B. U is greatest at 2 C. U is greatest at 3 D. U = 0 at all three spots E. U 0 but same at all three spots F. Not enough information 1/23/13 Physics

44 Does the potential energy of the system change when I add a test charge? Test Charge 2/20/2014 Physics