Thermodynamics

1. Thermodynamics

2. Thermodynamics • Thermodynamics is the science of energy conversion involving heat and other forms of energy, most notably mechanical work. It studies and interrelates the macroscopic variables (temperature, volume and pressure). • A thermodynamic system (a physical system) is a precisely defined macroscopic region of the universe that is studied.

3. Branches of Thermodynamics • Classical thermodynamics is the description of the states of thermodynamical systems at near-equilibrium, using macroscopic, empirical properties directly measurable in the laboratory. It is used to model exchanges of energy, work and heat based on the laws of thermodynamics. • Statistical mechanics (or statistical thermodynamics) gives thermodynamics a molecular interpretation. This field relates the microscopic properties of individual atoms and molecules to the macroscopic or bulk properties of materials that can be observed in everyday life, thereby explaining thermodynamics as a natural result of statistics and mechanics (classical and quantum) at the microscopic level. • Chemical thermodynamics is the study of the interrelation of energy with chemical reactions. • Biological thermodynamics is the study of energy transformation in the biological systems.

4. Equilibrium and non-equilibrium thermodynamics • The word equilibrium implies a state of balance. In an equilibrium state there are no unbalanced potentials, or driving forces, within the system. • Equilibrium thermodynamics is the systematic study of transformations of matter and energy in systems as they approach equilibrium. • Most systems found in nature are not in thermodynamic equilibrium because they are not in stationary states, and are continuously and discontinuously subject to flux of matter and energy to and from other systems. Non-equilibrium thermodynamics deals with such systems.

5. Thermodynamic system. Thermodynamic parameters A thermodynamic system (a physical system) is a precisely defined macroscopic region of the universe that is studied. A thermodynamic system is characterized and defined by a set of thermodynamic parameters • An intensive property (parameter) is a physical property of a system that does not depend on the system size or the amount of material in the system • extensive property (parameter) is one that is additive for independent, noninteracting subsystems. It is directly proportional to the amount of material in the system.

6. All space in the universe outside the thermodynamic system is known as the surroundings (the environment, or a reservoir). A system is separated from its surroundings by a boundary which may be notional or real, but which by convention delimits a finite volume. Systems are distinguished depending on the kinds of interaction they undergo and the types of energy they exchange with the surrounding environment. Thermodynamic system

7. Thermodynamic systems • Isolated systems are completely isolated from their environment. They do not exchange heat, work or matter with their environment. An example of an isolated system is a completely insulated rigid container, such as a completely insulated gas cylinder.

8. Thermodynamic systems • Closed systems are able to exchange energy (heat and work) but not matter with their environment. A greenhouse is an example of a closed system exchanging heat but not work with its environment. Whether a system exchanges heat, work or both is usually thought of as a property of its boundary.

9. Thermodynamic systems • Open systems may exchange any form of energy as well as matter with their environment. A boundary allowing matter exchange is called permeable. The ocean would be an example of an open system.

10. Internal energy • Internal energy is defined as the energy associated with the random, disordered motion of molecules. • It is separated in scale from the macroscopic ordered energy associated with moving objects; it refers to the invisible microscopic energy on the atomic and molecular scale. • The internal energy is the total energy contained in a thermodynamic system. It is the energy necessary to create the system, but excludes the energy associated with a move as a whole, or due to external force fields. Internal energy has two major components, kinetic energy and potential energy. • For an ideal monoatomic gas, this is just the translational kinetic energy of the linear motion of the "hard sphere" type atoms. However, for polyatomic gases there is rotational and vibrational kinetic energy as well.

11. System Work • When work is done by a thermodynamic system, it is ususlly a gas that is doing the work. The work done by a gas at constant pressure is: • For non-constant pressure, the work can be visualized as the area under the pressure-volume curve which represents the process taking place. The more general expression for work done is:

12. Heat Transfer Heat is energy transferred from one body or thermodynamic system to another due to thermal contact when the systems are at different temperatures. Heat Conduction Conduction is heat transfer by means of molecular agitation within a material without any motion of the material as a whole. For heat transfer between two plane surfaces, such as heat loss through the wall of a house, the rate of conduction heat transfer is: Heat Conduction

13. Heat Transfer Heat Convection • Convection is heat transfer by mass motion of a fluid such as air or water when the heated fluid is caused to move away from the source of heat, carrying energy with it.

14. Heat Transfer Heat Radiation • Radiation is heat transfer by the emission of electromagnetic waves which carry energy away from the emitting object. For ordinary temperatures (less than red hot"), the radiation is in the infrared region of the electromagnetic spectrum. The relationship governing radiation from hot objects is called the Stefan-Boltzmann law: where P is net radiated power, heat Q transferred in unit time t, σ – Stefan’s constant, σ=5.6703x10-8 Watt/m2 k4 S – radiating area, Tr – absolute temperature of radiator, Ts– absolute temperature of surroundings, e - emissivity (=1 for ideal radiator – black body)

15. Heat Transfer Heat Transfer by Vaporization • If part of a liquid evaporates, it cools the liquid remaining behind because it must extract the necessary heat of vaporization from that liquid in order to make the phase change to the gaseous state. It is therefore an important means of heat transfer in certain circumstances, such as the cooling of the human body when it is subjected to ambient temperatures above the normal body temperature. where m is mass of liquid L - heat of vaporization at liquid boiling point

16. First law of thermodynamics • The first law of thermodynamics is the application of the conservation of energy principle to heat and thermodynamic processes: Heat added to the thermodynamic system goes to change the internal energy and to do the work by the system.

17. First law of thermodynamics The internal energy of a system can be changed by heating the system or by doing work on it. • If the system is isolated, its internal energy cannot change.

18. Hot reservoir Energy intake Qin Working body A=Qin-Qout Qout Energy exhaust Cold reservoir Heat Engine • Aheat engine is a system that performs the conversion of heat to mechanical work. A heat "source" generates thermal energy that brings the working substance to the high temperature state. The working substance generates work in the "working body" of the engine while transferring heat to the cold reservoir until it reaches a low temperature state. During this process some of the thermal energy is converted into work by exploiting the properties of the working substance. The working substance can be any system with a non-zero heat capacity, but it usually is a gas or liquid.

19. Heat Engine • Qinis the heat flow from the hot reservoir to the engine • Qout is the heat flow from the engine to the cold reservoir. • The work done by the heat engine is the difference between Qin and Qout. • Heat engine efficiency:

20. Entropy as a Measure of the Multiplicity of a System The probability of finding a system in a given state depends upon the multiplicity of that state. That is to say, it is proportional to the number of ways you can produce that state. Here a "state" is defined by some measurable property which would allow you to distinguish it from other states. Entropy: where k is Boltzmann's constant,Wis the number of microstatesThe k is included as part of the historical definition of entropy and gives the units J/K in the SI system of units. The logarithm is used to make the defined entropy of reasonable size. The multiplicity for ordinary collections of matter are on the order of Avogadro's number, so using the logarithm of the multiplicity is convenient.

21. Entropy in Terms of Heat and Temperature • A the change in entropy can be described as the heat added per unit temperature ΔS = Q/T where S is the change in entropy, Q is the heat flow into or out of a system, and T is the absolute temperature in degrees Kelvin (K). • This is often a sufficient definition of entropy if you don't need to know about the microscopic details. It can be integrated to calculate the change in entropy during a part of an engine cycle. • The concept of entropy (S) gives us a more quantitative way to describe the tendency for energy to flow in a particular direction.

22. Entropy

23. Thermodynamic Potentials • Four quantities called "thermodynamic potentials" are useful in the chemical thermodynamics of reactions and non-cyclic processes. They are internal energy, the enthalpy, the Helmholtz free energy and the Gibbs free energy. The four thermodynamic potentials are related by offsets of the "energy from the environment" term TS and the "expansion work" term PV. A mnemonic diagram help you keep track of the relationships between the four thermodynamic potentials.

24. Enthalpy • Enthalpy is a thermodynamic potential. It is a state function since it is defined in terms of three other precisely definable state variables, and it is an extensive quantity. Enthalpy is a measure of the total energy of a thermodynamic system. It includes the internal energy U, which is the energy required to create a system, and the amount of energy required to make room for it by displacing its environment and establishing its volume V and pressure P. H = U + PV • It is somewhat parallel to the first law of thermodynamics for a constant pressure system Q = ΔU + PΔV, since in this case Q=ΔH

25. Thermodynamic free energy • The thermodynamic free energy is the amount of work that a thermodynamic system can perform. The concept is useful in the thermodynamics of chemical or thermal processes in engineering and science. The free energy is the internal energy of a system less the amount of energy that cannot be used to perform work. This unusable energy is given by the entropy of a system multiplied by the temperature of the system. Free energy is that portion of any first-law energy that is available to perform thermodynamic work; i.e., work mediated by thermal energy. Free energy is subject to irreversible loss in the course of such work. Since a first-law energy is always conserved, it is evident that free energy is an expendable, second-law kind of energy that can perform work within finite amounts of time. Several free energy functions may be formulated based on system criteria.

26. Free energy functions • The historically earlier Helmholtz free energy is defined as • Its change is equal to the amount of reversible work done on, or obtainable from, a system at constant T. It is "work content“. Since it makes no reference to any quantities involved in work (such as p and V), the Helmholtz function is completely general: its decrease is the maximum amount of work which can be done by a system, and it can increase at most by the amount of work done on a system.

27. Free energy functions • The Gibbs free energy The internal energy U might be thought of as the energy required to create a system in the absence of changes in temperature or volume. But as discussed in defining enthalpy, an additional amount of work PV must be done if the system is created from a very small volume in order to "create room" for the system. As discussed in defining the Helmholtz free energy, an environment at constant temperature T will contribute an amount TS to the system, reducing the overall investment necessary for creating the system. This net energy contribution for a system created in environment temperature T from a negligible initial volume is the Gibbs free energy.

28. Free energy functions • Historically, these energy terms have been used inconsistently. In physics, free energy most often refers to the Helmholtz free energy, while in chemistry, free energy most often refers to the Gibbs free energy. • For processes involving a system at constant pressure p and temperature T, the Gibbs free energy is the most useful because, in addition to subsuming any entropy change due merely to heat, it does the same for the pdV work needed to "make space for additional molecules" produced by various processes. (Hence its utility to solution-phase chemists, including biochemists.) The Helmholtz free energy has a special theoretical importance since it is proportional to the logarithm of the partition function for the canonical ensemble in statistical mechanics. (Hence its utility to physicists; and to gas-phase chemists and engineers, who do not want to ignore pdV work.)

29. The second law of thermodynamicsClausius statement • The second law of thermodynamics describes the flow of energy in nature in processes which are irreversible. • The second law of thermodynamics may be expressed in many specific ways. Second Law and Refrigerator • It is not possible for heat to flow from a colder body to a warmer body without any work having been done to accomplish this flow. Energy will not flow spontaneously from a low temperature object to a higher temperature object. • This precludes a perfect refrigerator. • The statements about refrigerators apply to air conditioners and heat pumps, which embody the same principles.

30. Kelvin-Planck statement Second Law and Heat Engine • It is impossible to extract an amount of heat from a hot reservoir and use it all to do work. Some amount of heat must be exhausted to a cold reservoir. • It meams thatthe efficiency of a heat engine cycle is never 100%. • This precludes a perfect heat engine.

31. Second Law and Entropy • The second law of thermodynamics is closely related to the concept of entropy, or the disorder created during a thermodynamic process. • In any cyclic process the entropy will either increase or remain the same. • Since entropy gives information about the evolution of an isolated system with time, it is said to give us the direction of "time's arrow“.

32. Other Second Law Formulations • In practical applications, this law means that: • Any heat engine or similar device based upon the principles of thermodynamics cannot, even in theory, be 100% efficient.

33. Equivalence of the statements Derive Kelvin Statement from Clausius Statement Suppose there is an engine violating the Kelvin statement: i.e.,one that drains heat and converts it completely into work in a cyclic fashion without any other result. Now pair it with a reversed Carnot engine as shown by the graph. The net and sole effect of this newly created engine consisting of the two engines mentioned is transferring heat from the cooler reservoir to the hotter one, which violates the Clausius statement. Thus a violation of the Kelvin statement implies a violation of the Clausius statement, i.e. the Clausius statement implies the Kelvin statement. We can prove in a similar manner that the Kelvin statement implies the Clausius statement, and hence the two are equivalent.