8/25/2016. Key concepts from last time

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1 Key concepts from last time 44 Units of the international system: Fundamental: m (distance), kg (mass), s (time), mol (amount of substance), K (temperature) Derived: N (force), Pa (pressure), J (energy), etc Pressure: Force/area The state of a sample of substance can be specified by giving the values of its volume, pressure, temperature and the amount of substance: p, V, T, n BUT They are not independent: you change one, you change at least another one. The equation that relates these variables is called the Equation of state Van der Waals: b: corrects for the finite volume of the molecules a: corrects for attractive forces Energy: kinetic (due to motion), potential (due to position) Work and heat: two ways to exchange energy (they are not energy themselves) Work: force times a distance =. But F may change as we change x =. =. Describing the state of a system: m, V, n, T, P Units! Equations of state: The ideal gas, the van der Waals gas. Types of Energy: kinetic, potential. Units. Work: mechanical work against a constant or variable force. Thermodynamics : definitions Energy exchanges: work and heat. pv work Heat: Heat capacity. Internal energy: molecular interpretation Internal energy: First principle Heat capacity Enthalpy: Definition, Reversible processes. 45 1

2 Thermodynamics: Some Definitions 46 System: The specific part of the universe on which one chooses to focus Surroundings: Everything else in the universe Boundary: What separates the system from the surroundings. Real or imaginary! Three idealized systems: defined depending on whether they are capable exchanging matter and/or energy with the surroundings Thermodynamics: Some Definitions 47 System: what s inside the flask/thermos (we always need to define the system to make sense of what we say afterwards) The most difficult to consider 2

3 Thermodynamics: Some Definitions 48 This sounds weird be patient Describing the state of a system: m, V, n, T, P Units! Equations of state: The ideal gas, the van der Waals gas. Types of Energy: kinetic, potential. Units. Work: mechanical work against a constant or variable force. Thermodynamics : definitions Energy exchanges: work and heat. pv work Heat: Heat capacity. Internal energy: molecular interpretation Internal energy: First principle Heat capacity Enthalpy: Definition, Reversible processes. 49 3

4 Energy Exchanges: Heat and Work 50 In thermodynamics we are interested in changes in energy more than in absolute values of energy (which are often difficult to define) How can we change the energy of a system? Work (w) Work is the energy transfer associated with a force acting through a distance. Heat (q) Heat is energy transferred from/to the system to/from the surroundings solely because of a temperature difference. Initial Final Assume the container is adiabatic (no heat exchanged with the surroundings). If you reduce the volume of the gas, the temperature will increase. 20 C 150 C >20 C <150 C The hot body loses energy and the cold body gains energy and warms up Energy Exchanges: Heat and Work 51 Heat and work cannot be stored: they are transient quantities that only apply to a system that undergoes a change in its state. There is no change in heat, because there is no initial and final heats. Instead, we ll talk about the heat (and/or work) involved in changing the system from an initial to a final state. Note: We could talk about a change in temperature (volume, pressure, etc). Initial Final V initial T initial P initial 20 C q >20 C V final T final P final q initial 150 C <150 C qfinal Hum..Some variables are used to describe the system in a particular state while others are used to describe the change in state. (more to come!) 4

5 Energy Exchanges: Heat and Work 52 Heat can be converted into work and work can be converted into heat But heads up! We can completely convert work into heat, but complete conversion of heat into work is impossible (second law of thermodynamics, coming later!). Excerpt from: Heat vs Work 53 Heat can be converted into work and work can be converted into heat. But heads up! We can completely convert work into heat, but complete conversion of heat into work is impossible (second law of thermodynamics, coming later!). What is the main difference between work and heat? From The molecules of Life by Kuriyan et al. 5

6 Work: More details 54 Work is defined as the product of a force times a distance. Be careful: signs matter, and can be confusing. Physical chemists and biochemists usually follow the same convention: Work is positive if the surroundings are doing work on the system Work is negative if the system is doing work on the surroundings Two results of a google search first law of thermodynamics. Who is right? Describing the state of a system: m, V, n, T, P Units! Equations of state: The ideal gas, the van der Waals gas. Types of Energy: kinetic, potential. Units. Work: mechanical work against a constant or variable force. Thermodynamics : definitions Energy exchanges: work and heat. pv work Heat: Heat capacity. Internal energy: molecular interpretation Internal energy: First principle Heat capacity Enthalpy: Definition, Reversible processes. 55 6

7 Mechanical work in Biochemistry 56 uh-oh maybe they do Mechanical work? Isn t that physics? Right, proteins don t push on objects!?? Molecular motors are biological machines that are responsible for most forms of movement we encounter in the cellular world. They convert chemical energy (that we get from breaking up food) into mechanical work, that is, into force and movement. Mechanical work in Biochemistry 57 From The molecules of Life by Kuriyan et al. 7

8 Mechanical work in Biochemistry 58 From The molecules of Life by Kuriyan et al. Prof. Carlos Bustamante (UC Berkeley) 59 He answers my question: Do I need to teach mechanical work? 3 min 8

9 Work: pv work Mechanical work F =. 60 Expansion work (pv work, for pressure and volume) pv work is the work associated with a change in the volume of the system Consider a system such as a gas or liquid enclosed in a container with a movable piston. The system can expand and do work on the surroundings if the external pressure (p ex ) is less than the pressure of the system (p). The opposite will be true if p ex > p (the system will compress: the final volume will be smaller than the initial volume) boundary system Why do we talk about pressure and volume instead of force and displacement? Work: pv work 61 Expansion work (pv work, for pressure and volume) I want to be able to calculate the work from the change in volume and the pressure. Pressure is (by definition) force per unit area. The volume of a cylinder is area times height (x).. (Multiply and divide by A) Then,. Note, if the displacement is positive, you reduce the volume, so the final volume is smaller than the initial volume, and V is negative boundary system 9

10 Work: pv work 62 =. boundary system Work: pv work 63 Let s assume you compress the volume from an initial value V i to a final volume V f. You keep the external pressure constant at a value P ex all times.... is a constant, and I can take constants out of the integral. boundary system 10

11 Work: pv work 64 The total work is the area under the curve (except for the sign) P ex (Pa) Vi If P ex is constant Vf w= w = V (m 3 ) Work: pv work 65 The total work is the area under the curve (except for the sign) P ex (Pa) w V (m 3 ) 11

12 Work: pv work 66 Example Initial state: P ext = 1 bar, V = 22.4 L You apply a constant external pressure of 10 bar to reduce the volume to 2.24L. What is the work done on the gas? 1 bar Sudden change of P 10 bar 10 bar 22.4L 22.4L 2.24L What do you expect? w > 0? w < 0? Work: pv work 68 Initial state: P ext = 1 bar, V = 22.4 L You apply a constant external pressure of 10 bar to reduce the volume to 2.24L. What is the work done on the gas? P ex (Pa) bar w= w = - w = 10 " #$ ( ) 20.2 kj > 0 (as expected) V (m 3 ) 12

13 Work: pv work 69 Now we go backwards 10 bar Sudden change of P 1 bar 1 bar 22.4L 2.24L 2.24L What do you expect? w > 0? w < 0? Work: pv work 70 Initial state: P ext = 10 bar, V = 2.44 L You apply a constant external pressure of 1 bar to increase the volume to 22.4L (you go backwards) What is the work done on the gas? P ex (Pa) w= bar w = - w = 10 * #$ ( ) kj < 0 (as expected) V (m 3 ) 13

14 Work: pv work 71 Note that you did more work to compress the gas than the system did on you when it expanded Overall: compressing and then expanding back to the original state required 20.2 kj 2.02 kj = 18.2 kj of work done on the system (that is a lot of wasted energy) Work: pv work 72 Overall: you do 18.2 kj of work on the system P ex (Pa) bar bar V (m 3 ) 14

15 Mastering Chemistry Tutorial : Understanding pv Diagrams and Calculating Work Done 78 w= +. Available for practice and as a screencast. Mastering Chemistry Tutorial : Understanding pv Diagrams and Calculating Work Done 79 Jeez OK, let s try it Where are the numbers? This is symbolic math, just think of V 0 and P 0 as numbers w +. 15

16 Mastering Chemistry Tutorial : Understanding pv Diagrams and Calculating Work Done 84 Can t we use =? Then we need to use the original equation w= +. But this is valid only when P is constant, and now it is changing all the time But what is p(v)? Mastering Chemistry Tutorial : Understanding pv Diagrams and Calculating Work Done 85 w +. The straight line connecting the final and initial states 16

17 Mastering Chemistry Tutorial : Understanding pv Diagrams and Calculating Work Done 86 w= +. Initial The straight line connecting the final and initial states The equation for a straight line is y = m + bx In this case: p = m + bv final We need to find m and b Solve with tablet Mastering Chemistry Tutorial : Understanding pv Diagrams and Calculating Work Done 93 We are getting good at this. Let s try part E Nah, let s ask the audience Initial final 17

18 Mastering Chemistry Tutorial : Understanding pv Diagrams and Calculating Work Done 95 Part F looks weird Because the initial state is the same as the final state! Why? Then V = 0 and w = 0 Are you sure? No Initial = final Mastering Chemistry Tutorial : Understanding pv Diagrams and Calculating Work Done 96 Good because I m getting tired Let s add all the works of the 4 different parts We have all the numbers from previous parts Initial = final We need to add w =

19 Mastering Chemistry Tutorial : Understanding pv Diagrams and Calculating Work Done 97 So w 0 after all What if we do the one in the figure? Will it be the same? I guess it makes sense you need to do work to do all this stuff, even if you end up in the same place you started I ll try when I get home, but it looks like it not only depends on the initial and final states, but also on the particular path you follow Initial = final Stop and test your self: Are you on track? 98 Finish HW2 19