Thermodynamics 1 Lecture Note 2

Size: px

Start display at page:

Download "Thermodynamics 1 Lecture Note 2"

Deirdre George
5 years ago
Views:

1 Thermodynamics 1 Lecture Note 2 March 20, 2015 Kwang Kim Yonsei University kbkim@yonsei.ac.kr Y O N Se I

2 Physical Chemistry Chemistry is the study of Matter and Changes it undergoes. Change in Matters accompanied by Changes in Energy AB + CD AC + BD Matter and Energy are what chemistry is all about. Means to change an energy of a system? Work and heat

3 Closed System Energy Work & Heat The State of the system defined by giving single-value number to T, P, V. and n Another state property : U (internal energy)

4 Work

5 Work For a constant force F which moves an object in a straight line from x 1 to x 2, the work done by the force can be visualized as the area enclosed under the force line below For the more general case of a variable force F(x) which is a function of x, the work is still the area under the force curve, and the work expression becomes an integral.

6 Conservation of Energy : The first law of thermodynamics Energy can be defined as the capacity of a system for doing work. - It may exist in a variety of forms and may be transformed from one type of energy to another. However, these energy transformations are constrained by the Conservation of Energy principle. Heat and work as methods of energy transfer which can bring about a change in the internal energy of a system - Another approach is to say that the total energy of an isolated system remains constant. - The first law of thermodynamics : U = q + w U : Change in internal energy of the system q : Heat flow into the system from the surroundings w : Work done on the system by the surroundings

7 Heat and Work Example To describe the energy that a high temperature object has, - it is not a correct use of the word heat to say that the object "possesses heat", it is better to say that it possesses internal energy as a result of its molecular motion. -The word heat is better reserved to describe the process of transfer of energy from a high temperature object to a lower temperature one. Don't refer to the "heat in a body", or say "this object has twice as much heat as that body".

8 Internal Energy Total energy of a macroscopic body E: E = potential energy of a macroscopic body + kinetic energy of a macroscopic body + kinetic energy of atoms in a macroscopic body (internal energy) Assumption : No force field on a macroscopic body (No potential energy) Stationary macroscopic body (No kinetic energy) E = internal energy

The internal energy of an ideal gas is therefore the sum of the kinetic energies of the particles in the gas.

9 Internal Energy Internal energy, E, is the sum of the kinetic and potential energies of the particles that form the system. Since the particles in an ideal gas do not interact, ideal gas has no potential energy. The internal energy of an ideal gas is therefore the sum of the kinetic energies of the particles in the gas. The kinetic molecular theory assumes that the temperature of a gas is directly proportional to the average kinetic energy of its particles. U sys = 3/2 RT The internal energy of an ideal gas is therefore directly proportional to the temperature of the gas.

10 Conservation of Energy : The first law of thermodynamics Energy can neither be created nor destroyed. - The total energy of an isolated system remains constant. U univ = U sys + U surr = 0 - U sys = q + w Energy can be defined as the capacity of a system for doing work. Heat and work as methods of energy transfer which can bring about a change in the internal energy of a system U : Change in internal energy of the system q : Heat flow into the system from the surroundings w : Work done on the system by the surroundings q : Heat flow w : lifting or lowering of a weight

11 Heat and Work Example First Law of Thermodynamics U = q + w : identifies both heat and work as methods of energy transfer which can bring about a change in the internal energy of a system. After that, neither the words work and heat have any usefulness in describing the final state of the system - we can speak only of the internal energy of the system.

12 Work Energy : capability of a system to do work Work and energy uses the same unit. Mechanical work related to volume change of a system The first law of thermodynamics : (system 의관점에서판단 ) U = q + w U : Change in internal energy of the system q : +ve heat : Heat flow into the system from the surroundings w : +ve work : Work done on the system by the surroundings System loses energy through the work on the surroundings by the system System gains energy by the work done on the system by the surroundings

13 PV work (Volume expansion and contraction) w : +ve work : Work done on the system by the surroundings Pa x m 3 = N/m 2 x m 3 = N x m = J

14 Change of the state of a system Final state Initial state Process We are not much interested in systems that just sit there and don't do anything. We are interested in changes. We usually have a system in an initial state, constrained somehow to keep anything from happening. We then remove the constraint and the system changes, ending up in a final state. An example would be a system containing two separate solutions, one of sodium chloride, the other of silver nitrate. That's the initial state. We now let the two solutions mix. A precipitate of silver chloride forms and settles to the bottom. When things come to rest we are in the final state. In going from its initial state to its final state the system undergoes a process. By definition the initial state of the system is an equilibrium state. Otherwise, it would not have a state. The final state is also an equilibrium state for the same reason. As the system moves from its initial to final state it passes through a large number of intermediate situations. Usually none of these are equilibrium states.

15 Change of the state of a system Initial state Process Final state This is important because the intensive variables of a system are not really defined when the system is not at equilibrium. The pressure and temperature, for example, may vary from point to point inside the system. The density may change from place to place as well. Indeed, it is fair to say that intensive variables don't even have values in a non-equilibrium system! Extensive variables are different. We can imagine that no matter how disturbed a system is, it still has a total energy, a total volume, and a total mass. Of course these values may change from moment to moment, but at any moment, at least in principle, they do have values. The sequence of situations the system goes through in passing from the initial state to the final state is called the path taken by the system. Because the intensive variables often have no values during a process, it is usually not possible to exactly specify the path a process takes in terms of them.

16 Change of the state of a system U = q + w Initial state Process Final state U initial state U final state U = U final state - U initial state w = w final state - w initial state q = q final state - q initial state

17 State function and path function w cannot be expressed as w f w i q cannot be expressed as q f q i U = U f U i For an infinitesimal change for a system, du = δq + δw Amount of walking : path dependent Altitude : path independent

19 Free expansion

20 Volume expansion work - - -

21 Volume expansion work M M T, P, V T, P1, V1 m T, P, V m T, P2, V2

22 Volume expansion work - {- }

23 Volume expansion work P P P V V V P P V V

24 Volume compression work m m M M

25 Volume compression work -

26 Reversible volume expansion work

27 Reversible volume expansion work Maximum expansion work - P : internal pressure

28 Reversible volume compression work P : internal pressure - - -

29 Work P gas : internal pressure

For example, let us assume that our system is an amount of a gas trapped inside a cylinder, pushing on a piston forming one end of the cylinder.

30 Quasi-static process Sometimes a process takes place relatively slowly. Slowly enough so that all the intensive variables can have actually definite values through the entire path taken by the process. Such a process is called a quasi-static process. For example, let us assume that our system is an amount of a gas trapped inside a cylinder, pushing on a piston forming one end of the cylinder. If the piston moves out rapidly, the gas expands rapidly and the pressure will vary from point to point inside the gas. But if the piston moves very very slowly, possibly due to friction or some artificial restriction limiting its speed, the pressure may well have a common value throughout the system at every instant in time. p-v diagram showing an initial and a final state p-v showing a path between two states

31 Reversible process

32 Irreversible process

33 Reversible work and irreversible processes An irreversible process: is a real or actual process occurs in a finite number of steps requires a finite amount of time is one in which the system and surroundings are not in equilibrium A reversible process: requires an infinite number of steps occurs in an infinite amount of time can be reversed on an infinitesimal scale by reversing the direction of the variables driving the change is one in which the system and surroundings are in equilibrium at each point in the process is an ideal or limiting process that can never actually occur

34 Reversible work and irreversible work

35 Reversible work and irreversible work

38 Y = f(x) In "ordinary" calculus, one deals with functions of a single independent variable such as y = f(x) Now we could ask "if I change x by a little bit, how much does y change? The answer to that question is the derivative, usually denoted by the ordinary derivative. For Z = f(x, y), z will certainly change if x and y are changed. How do we calculate that change? Partial derivative of z with respect to x holding y constant, What happens to z, when both x and y are changed by small amounts at the same time? The total derivative answers the question.

39 Exact differential : state function Inexact differential : path function

40 Exact differential : state function Inexact differential : path function

42 U, T. P. V : state function q, w : path function

43 Heat

44 Heat associated with constant volume : U The system is usually defined as the chemical reaction and the boundary is the container in which the reaction is run. In the course of the reaction, heat is either given off or absorbed by the system. Furthermore, the system either does work on it surroundings or has work done on it by its surroundings. Either of these interactions can affect the internal energy of the system. U = q + w

45 Heat associated with constant volume process : U What would happen if we created a set of conditions under which no work is done by the system on its surroundings, or vice versa, during a chemical reaction? Under these conditions, the heat given off or absorbed by the reaction would be equal to the change in the internal energy of the system. U = q (if and only if w = 0) The easiest way to achieve these conditions is to run the reaction at constant volume, where no work of expansion is possible. At constant volume, the heat given off or absorbed by the reaction is equal to the change in the internal energy that occurs during the reaction. U = q v (at constant volume)

46 Heat : path function The heat capacity is directly related to q. It is defined as the amount of heat needed to raise the temperature of something by one degree Kelvin. In symbol, with C as the heat capacity for small changes But there are many ways to heat something. For example one can heat an object at constant pressure. Or we can heat something at constant volume. Usually we heat something in useful ways. Constant pressure is a common experimental condition. However, gases are usually heated at constant volume. U = q + w = q P ext V For a constant volume process, V = 0, U = q C v = (əq/ət) v = (əu/ət) v

47 Heat : path function What's the difference between heat capacities at a constant volume process and a constant pressure process? The two quantities are not the same. Why? In the constant pressure case the system expands. That means that it does work against the surrounding atmosphere. At constant volume no such work is done. So more energy is needed to increase the temperature of a system in the constant pressure case; part to heat the system and part to expand it.

48 Heat associated with constant pressure process H = U + PV : enthalpy (H) definition, not a calculation equation H : state function Initial state H 1 = U 1 + P 1 V 1 Final state H 2 = U 2 + P 2 V 2 H 2 H 1 = U 2 U 1 + (P 2 V 2 P 1 V 1 ), H = U + (PV) For infinitesimal changes, dh = du + d(pv) = du + PdV + VdP du = dq PdV for a reversible process dh = dq - PdV + PdV + VdP dh = dq + VdP (reversible process assumed) At a constant pressure process, dh = dq For a reversible constant pressure process the enthalpy is identical to the heat involved in the process. All that is needed is that the initial state and the final state be at the same pressure. Then the enthalpy is fixed. And it is equal to q for the process. The heat involved in any process starting and ending at constant pressure is actually indenpent of any other details of the real path taken between those two states.

49 Heat associated with constant pressure process : H, H = U + PV For a constant pressure process, H = q C p = (əq/ət) p = (əh/ət) p

Difference between U and H U = q v, H = q p, The change in internal energy is not equal to the heat transferred when the system is free to change its volume.

50 Difference between U and H U = q v, H = q p, The change in internal energy is not equal to the heat transferred when the system is free to change its volume. Under this circumstances, some of the energy supplied as heat to the system is returned to the surroundings as expansion work, so du is less that δq. The energy supplied as heat at constant P is equal to H. H = U + PV Heat q applied to the system under constant p

51 Heat associated with constant volume : U Heat associated with constant pressure : H It will be convenient to express U and H as a function of state properties of a system since they are easily measured.

53 Total Derivative and Partial Derivatives How is one state variable affected when another state variable changes? Total derivatives of function of multiple variables F (x, y, z,.) the derivative of the function F taken w.r.t. one variable at a time with the other variables held constant the derivative of the function F taken w.r.t. x only with y, z and so on treated as constants : partial derivatives

56 U = U(T,V) du =

57 U = U(T,V) du =

59 ət

61 ət

63 ət

67 for a van der Walls gas

69 Adiabatic boundary Adiabatic expansion

70 Isothermal : meaning a constant temperature process Isobaric : meaning a constant pressure process Isochoric : meaning a constant volume process Isoenthalpic : meaning a constant enthalpy process The Joule-Thomson Experiment

71 Adiabatic boundary P1>P2 Adiabatic expansion Imagine a tube with a porous plate separating it into two parts. The porous plate will allow a gas to go through it, but only slowly. It acts as a throttle. On each side of the plate there is a piston that fits the tube tightly. Each piston can (in principle) be pushed up against the porous plate. Imagine that some gas is placed between the porous plate and the piston on the left side of the tube. On the other side the piston is pushed against the porous plate. Now during the experiment gas is pushed through the porous plate by pushing on the piston on the left side. At the same time the piston on the right side is pulled in such a way that the pressure on the right side is always P2. At the end of the experiment all of the gas has been pushed through the porous plate. The volume on side 1 is zero. The final volume on the right side (side 2) is V2, the pressure is p2 and the temperature T2. T2 is not equal to T1.

72 Measure Temperature difference, T 2 - T 1, as a function of P 2 -P 1. Joule-Thomson Coefficient We need to relate μ JT to quantities that are experimentally measureable.

73 Adiabatic compression Adiabatic expansion

76 The experimental result is that μ JT is sometimes positive and sometimes negative. In fact it is found that there is a certain temperature called the inversion temperature such that if the initial temperature T1 is above the inversion temperature, the final temperature is higher than the initial temperature. If the initial temperature is below the inversion temperature, the final temperature is lower than the initial temperature. The inversion temperature is found, experimentally, to depend on the pressure.

78 If > 0, T < 0 (cooling) for P < 0. If < 0, T > 0 (heating) for P < 0.

79 We need to relate μ JT to quantities that are experimentally measureable.

81 : Joule Thompson Coefficient, 여기서 van der Waals gas 에대한의표현을구해야함. 이식에서 V 에대한표현을정리하면아래와같음 이식을 P 를고정시킨상태에서 T 에대해편미분후여기에 T 를곱하면이래식과같음

82 : van der Waals gas 의 Joule Thompson Coefficient 표현

83 As T goes to zero, > 0 at low temperature. It indicates the cooling effect in the Joule-Thompson experiment when T is below the inversion temperature. When T gets very large, < 0 at high temperature. It indicates the heating effect in the Joule-Thompson experiment when T is above the inversion temperature. Experimentally Inversion Temperature is a function of Pressure.

84 As T goes to zero, > 0 at low temperature. It indicates the cooling effect in the Joule-Thompson experiment when T is below the inversion temperature. At low temperatures the attractive forces predominate. At low temperatures the intermolecular attraction is the most important interaction. When the cold gas is expanded, the average distance between molecules is increased. This means that the molecules are pulled apart. Since they attract each other this takes energy. And since the process is adiabatic, the only source of energy is the internal energy of the gas itself. So, with the internal energy reduced, the gas cools.

85 When T gets very large, < 0 at high temperature. It indicates the heating effect in the Joule-Thompson experiment when T is above the inversion temperature. At high temperatures the repulsive forces predominate. On the other hand, at high enough temperatures the predominant interaction is repulsion. The gas wants to separate. It wants to expand. When it does expand energy is obtained as the molecules separate. This increases the internal energy of the gas. And the gas heats.

88 ( x y ) z ( y z ) x( z x ) y = 1

93 Change in state of a system of an ideal gas from (T i, V i ) to (T f, V f ) 1) Change in volume of the system at constant Ti from V i to V f, no change in U 2) Change in temperature at constant volume V f from T i to T f, U = Cv T

100

101

102

103 for adiabatic process

104

105

106

107 As a gas expands, the average distance between molecules grows. Because of intermolecular attractive forces (see Van der Waals force), expansion causes an increase in the potential energy of the gas. If no external work is extracted in the process and no heat is transferred, the total energy of the gas remains the same because of the conservation of energy. The increase in potential energy thus implies a decrease in kinetic energy and therefore decrease in temperature. A second mechanism has the opposite effect. During gas molecule collisions, kinetic energy is temporarily converted into potential energy. As the average intermolecular distance increases, there is a drop in the number of collisions per time unit, which causes a decrease in average potential energy. Again, total energy is conserved, so this leads to an increase in kinetic energy (temperature). Below the Joule Thomson inversion temperature, the former effect (work done internally against intermolecular attractive forces) dominates, and free expansion causes a decrease in temperature. Above the inversion temperature, gas molecules move faster and so collide more often, and the latter effect (reduced collisions causing a decrease in the average potential energy) dominates: Joule Thomson expansion causes a temperature increase.

What is thermodynamics? and what can it do for us?

What is thermodynamics? and what can it do for us? The overall goal of thermodynamics is to describe what happens to a system (anything of interest) when we change the variables that characterized the