topic 2 CHM 2229 basic thermodynamics work

This is related to thermodynamics taught at Makerere university Kampala Uganda

1. 1 Topic 2 will introduce you to the laws governing thermodynamic systems. It will also cover gas expansions at specified state variables, and the associated work and heat. Subtopics: Systems and boundaries. State and path functions. Laws of Thermodynamics and Limitations. Work and heat. Heat capacities. Enthalpy and internal energy. Gas expansions. Intended learning outcome Explain the laws governing Thermodynamics and the basic principles of Thermochemistry. TOPIC 2: LAWS OF THERMODYNAMICS

2. SYSTEMS AND BOUNDARIES 2 WEEK 4

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5. 5 A system at equilibrium is defined by the collection of all macroscopic properties that are described by State variables (p, n, T, V,…) Note its independent of the history/ path taken by the system and only depends on the final and initial states For a one-component System, all that is required is “ n ” and 2 variables; All other properties then follow; V =f( n,p,T ) or p = g( n,V,T ) The state of system changes/transforms through a given path Note : Path is a sequence of intermediate states STATE AND PATH FUNCTIONS

6. illustration 6 Definitions Equilibrium refers to a stage reached during a process change such that there is no more change in the amount of a substance undergoing a change and that being formed. A thermodynamic equilibrium state of a system is one in which the thermodynamic state functions have defined time-independent values that are independent of the method by which the system was brought to that state . Reading list : Discuss types of equilibrium

7. Process : Describes the Path Types of process Reversible (always in Equilibrium) Irreversible (defines direction of time) Adiabatic (no heat transfer between system and surroundings) Isobaric (constant pressure) Isothermal (constant temperature) etc. Reading List list of natural examples of each kind of system Types of boundaries (adiabatic & diathermic) 7 A reversible process is one in which the system throughout the process is never more than infinitesimally removed from a state of thermodynamic equilibrium and to which therefore, the equation of state is applicable . An irreversible thermodynamic process is a process for which it is impossible by any means, to restore every where, the exact initial states once the process has taken place .

8. Note: Work and heat are Path functions and NOT state functions (i.e. we cannot write w = f(p, V) and For a cyclic process, it is possible for ∫d w≠ 0) state function - any thermodynamic function such as T, P,V for which the change (  X) in the function depends only on the initial value (X 1 ) and the final value (X 2 ), and not on the way in which the change has been performed. Examples ∆T, ∆P and ∆V Or A property whose value depends only on the current state of the system and is independent of how that state has been prepared.  Path functions- properties that relate the preparation of the state. Examples work, energy, etc. 8

9. LAWS OF THERMODYNAMICS Thermodynamics refers to the study of the interchange between heat and work. Note : Both heat and work are forms of energy (Energy is the capacity to do work or transfer heat) Facts about Thermodynamics: → Describes macroscopic properties of equilibrium systems → Entirely Empirical → Built on 4 Laws and “simple” mathematics 9 9 WEEK 5

10. 10 Thermodynamics is built on 4 laws 10

11. ZERO’th LAW of Thermodynamics Note Heat flow stops at thermal equilibrium B acts as thermometer, and A, B and C are at the same temperature. 11

12. First Law ”can be stated as follows: “The Internal energy U is a thermodynamic state function that is subject to a conservation principle.” In other words, the first law tells that energy may be converted from one form to another but cannot be created or destroyed First Law of Thermodynamics 12

13. 13 Weakliness of first law of Thermodynamics Weakness of first law - U and  H are not good criteria of spontaneity i.e. doesn’t restrict direction of heat flow. For instance, the law doesn’t forbid flow of heat from cold to hot reservoir ( Question: define a heat reservoir ) -Also Since some endothermic process are spontaneous, there is need for a state function called entropy, S ( not  U and  H ) to satisfy this condition Entropy, S – is a thermodynamic function which can be used to measure the disorder (or “randomness”) of a system

14. 14 Statements of the Second law of Thermodynamics “ In an isolated system the direction of change is such that the entropy increases to a maximum; at equilibrium the entropy is constant ” Reading list Explain with examples, what is meant by a spontaneous process.

15. 15 Other statements of Second law

16. 16 Limitation of the Second Law Entropy is temperature dependent: dS = Since the entropy of for instance, an isolated system never decreases leaves a question of what the entropy will be at absolute zero (0K), i.e. absolute entropy

17. 17 Third Law of Thermodynamics The absolute entropy can be determined by involving the Third Law of Thermodynamics, which states that “ The entropy of a perfect crystal at absolute zero is exactly zero” The Third Law (unlike Second Law) limits the behaviour of systems as the temperature approaches absolute zero The basis of the Third law can be explained in molecular terms At absolute zero all matter will be in the configuration that has the lowest possible energy This occurs when all the molecules are in the state of lowest energy The number of arrangements (W) of the system that satisfies this condition is only one , thus   S = k ln1 = 0

18. 18 Corollary/ consequences/limitations of Third Law rationally

19. 19 Because C p → 0 as T → 0 K , the heat đq p needed to achieve a temperature rise dT, (đq p = C p dT) also goes to zero at 0 K. If you somehow manage to make it to 0 K, you will not be able to maintain that temperature because any stray heat from a warmer object nearby will raise the temperature above zero, unless you have perfect thermal insulation, which is impossible . Second consequence of Third Law

20. 20 WORK AND HEAT

21. Heat refers to the quantity flowing between the system and the surroundings that can be used to change the temperature of the system and/or the surroundings 21 Note

22. Equivalence of Work and Heat It is possible to raise the temperature by heating or by doing work. This was demonstrated by Joule in 1840’s 22

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24. Note : the total energy of a system is called its internal energy and it is denoted as U, which is a sum of the total kinetic energy and potential energy of the molecules composing the system Summary 24

25. Reading list Definition of temperature, heat capacity and specific heat capacity Temperature scales/ measurement Process of heat flow Exothermic and endothermic process, and examples 25 HEAT CAPACITIES, ENTHALPY AND INTERNAL ENERGY WEEK 6

26. Process at constant pressure Δ U = Q p + Δ w Δ U = Q p –P Δ V Q p = Δ U + P Δ V …………since U and V are state functions. Therefore, for change in state from point 1 to 2 Q p = ( U 2 -U 1 ) + P (V 2 -V 1 ) Q p = ( U 2 +PV 2 ) - (U 1 +PV 1 )……….. but U+PV = H (enthalpy) Q p = H 2 -H 1 = Δ H Summary: for work at constant volume…. q v = Δ U for work at constant pressure... q p = Δ H 26 Note : Chemical reactions and biological processes usually take place under constant pressure and with reversible PV work. Enthalpy turns out to be an especially useful function of state under those conditions Relationship between enthalpy, internal energy and heat

27. Relationship between C p and C v C   At constant pressure =   At constant volume =   But dH = dU + PdV and PdV = RdT (for n=1) Therefore, = + RdT which rearranges to:     Note: For solids and liquids C p and C v are usually similar in magnitude but for gases they are significantly different. Explain why? 27    

28. 28 GAS EXPANSIONS Isothermal gas expansions ( Δ T = 0) 28

29. (3) Reversible change p = p ext throughout Remember: PV= nRT , ……….. P = nRT /V , 29

30. Frequent constraints (derived from First law) …………………….......… remember dU = 0 ………………….. remember dV = 0 ……………… remember dU = dq v 30

31. 31 The  inversion temperature  in thermodynamics and cryogenics is the critical temperature below which a non-ideal gas (all gases in reality) that is expanding at constant enthalpy will experience a temperature decrease, and above which will experience a temperature increase Reading list : Application of Joule-Thomson effect For real gases however, the Joule–Thomson coefficient may be positive, negative or zero, depending upon the temperature and pressure of the gas.

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33. 33 NOTE: for ideal gases   For isothermal processes, T = constant….PV = constant