Basic Concepts of Thermodynamics

1. Basic Concepts of Thermodynamics • Thermodynamics is the study of transformations of energy • System and surroundings • the system is the part of the world in which we have a special interest. A system has definite boundaries • the surroundings is everything outside the boundaries • Classification of systems: • An open system can exchange matter as well as energy with its surroundings • a closed system can exchange energy with its surroundings. No transfer of matter across the boundaries is possible • an isolated system can exchange neither energy nor matter with its surroundings Chapter 2

2. Work, Heat, and Energy • The energy of a system is a measure of its capacity to do work • The energy of a system is the sum of the kinetic and potential energies of all particles in the system • The energy of a closed system can be changed by: • work done on or by the system • heat transfer across its boundaries • Work is transfer of energy using organized motion (expansion work, electrical work, etc.) • Heat is transfer of energy using thermal motion (chaotic, random motion of molecules) Chapter 2

3. Heat Transfer • The boundary of a system is diathermic if heat can be transferred between system and surroundings • The boundary of a system is adiabatic if heat cannot be transferred. • Adiabatic processes (no heat transfer between system and surroundings) take place in adiabatic systems • A process that releases energy as heat is called exothermic • A process that absorbs energy as heat is called endothermic Chapter 2

4. Internal Energy • The internal energy, U, is the total energy of a system • We cannot give an absolute value of U but we can calculate U for a process • U = Uf - Ui • Uf = final value of U • Ui = initial value of U • U is a state function (the value of U depends only on the current state of the system) • U is an extensive property Chapter 2

5. The First Law • U = q + w for a closed system • q = heat supplied to or removed from the system (q <0 if heat removed from system) • w = work done on or by the system (w <0 if work done by the system) • q and w depend on the process by which the state is changed; they are not state functions • U = 0 for an isolated system • the internal energy of an isolated system is constant • dU = dq + dw ( the First Law written for infinitesimal changes) Chapter 2

6. Expansion Work • dw = - pexdv • dw is the expansion work (pressure-volume work) when a system undergoes a change • pex is the external pressure • dV is the change in volume • dw <0 (work is done by the system) when system expands (dV>0) • w = -  pexdV • integration from Vi to Vf when volume changes from Vi to Vf Chapter 2

7. Expansion Work, cont • Free Expansion - no opposing force • pex = 0 (expansion into a vacuum) • w = 0 • Expansion against Constant Pressure • pex is constant • w = - pexV (V is the volume change) • Isothermal Reversible Expansion of Perfect Gas • pex = p (reversible expansion) • p = nRT/V (ideal gas) • w = -  nRT dV/V • w = - nRT ln(Vf/Vi) Chapter 2

8. Reversible Process • A process is regarded as thermodynamically reversible if it can be caused to go in either direction by an infinitesimal change in an external variable such as pressure or temperature • Reversible changes occur when a system is in equilibrium with its surroundings • For a reversible expansion: p = pex + dp • dp  0 • p = pex • w = -  p dV Chapter 2

9. Indicator Diagram or PV-diagram • The expansion work, w, can be obtained from an indicator diagram (a plot of p versus V) • The amount of work done by the gas is given by area under curve • The maximum work available for a system operating between specified initial and final states is obtained when the change takes place reversibly ( pex = p) Chapter 2

10. U for Process at Constant Volume • dU = dq + dw • dw = dwexp + dwe • wexp is expansion work (pressure-volume work) • we is other work (electrical work etc.) • dwexp = 0 for a process taking place at constant volume • dU = dq (if no electrical work) • dU = dqv (subscript v indicates process at constant volume) • U = qv for process at constant volume Chapter 2

11. Calorimetric Determination of U • An adiabatic bomb calorimeter (a constant volume calorimeter) is used to determine U • The change in temperature, T, of the calorimeter upon reaction is proportional to U or qv • qv = C T • C is the heat capacity of the calorimeter • C can be determined by electrical calibration • Electrical work is given by: w = IVt or w = I2Rt • I = current • V = voltage over heater • R = resistance of heater • t = heating time Chapter 2

12. Heat Capacity at Constant Volume • CV = (U/T)V • CV is the heat capacity at constant volume • (U/T)V is a partial derivative which shows how U varies with T when the volume is kept constant • CV,m = CV/n • CV,m is the molar heat capacity at constant volume Chapter 2

13. Change in U with T • dU = CV dT at constant volume • from definition of CV • U = CVT at constant volume • assuming that CV is independent of T • U = qv at constant volume • qv = CV T • qv is heat needed to change temperature by T Chapter 2

14. Enthalpy, H • H = U + pV (Definition of enthalpy) • H is a state function (U, p, and V are all state functions) • H is an extensive property • H = qp for a process taking place at constant pressure • assuming pressure-volume work is the only type of work involved in the process Chapter 2

15. Heat Capacity at Constant Pressure • Cp = (H/T)p • Cp is the heat capacity at constant pressure • Cp shows the variation of H with T at constant pressure • Cp,m = Cp/n • Cp,m is the molar heat capacity at constant pressure • dH = Cp dT at constant pressure • H = Cp T at constant pressure • assuming Cp is independent of T • H for chemical reactions can be determined using a calorimeter operating at constant pressure Chapter 2

16. Relation between H and U • H = U + pV • H = U + (pV) for a process (change) • (pV) is small for processes involving condensed phases (solids and liquids) only • (pV) is generally significant for processes involving gases • H  U for processed involving condensed phases only • (pV) = (nRT) for a gas (ideal gas) • H = U + (ngasRT) for processes involving gases Chapter 2

17. Change in Temperature of Gas • (ngasRT) = ngasR T • for a change in temperature of a given amount of gas • H = U + ngasR T • relation between the change in enthalpy and internal energy of a given amount of gas when the gas is heated or cooled Chapter 2

18. Relation between H and U for a ReactionInvolving Gases • aA(g) + bB(g)  cC(g) + dD(g) • reaction is assumed to take place at constant temperature • ngas = (c + d) - (a + b) • ngas is the change in number of moles of gas upon reaction • (ngasRT) = RT ngas • H = U + RT ngas • relation between the enthalpy change and the change in internal energy for a reaction taking place at constant temperature Chapter 2

19. Adiabatic Changes • q = 0 for adiabatic changes • no heat transfer • The following is true for adiabatic compression (reduction of volume of system in an adiabatic change: • work is done on the system • the internal energy of the system increases • the temperature of the system increases • ln (Tf/Ti)c = ln (Vi/Vf) for reversible and adiabatic compression of an ideal gas • c = CV/nR Chapter 2

20. Thermochemistry • Exothermic reactions release heat • H < 0 for an exothermic reaction taking place at constant pressure • The standard state of a substance at a specified temperature is its pure form at 1 bar pressure • The standard enthalpy change, H°, is the change in enthalpy for a process in which the initial and final substances are in their standard states Chapter 2

21. Enthalpies of Phase Transitions • Standard Enthalpy of Vaporization, vapHº • vaporization: A(l)  A(g) • vapHº is the enthalpy change when 1 mol of pure liquid A at 1 bar vaporizes to give 1 mol of pure gaseous A at 1 bar pressure • vaporization is an endothermic process • Standard Enthalpy of Fusion, fusHº • fusion or melting: A(s)  A(l) • Enthalpies (heats) of fusion are positive (endothermic processes) • Standard Enthalpy of Sublimation, subHº • sublimation: A(s)  A(g) • sublimation processes are endothermic Chapter 2

22. Thermochemical Laws • The enthalpy change for a forward process and its reverse must be equal in magnitude but opposite in sign • H(AB) = -H(BA) for the process A B • If the overall reaction is composed of several individual steps, then the enthalpy change of the overall reaction is given by the sum of the enthalpy changes of the individual steps (Hess’s Law) • H = H(step1) + H(step2) + …….. • subHº = fusHº + vapHº Chapter 2

23. Enthalpies of Chemical Change • The standard reaction enthalpy , rHº, is the change in enthalpy when products and reactants are in their standard states • The standard enthalpy (heat) of combustion, cHº, is the standard reaction enthalpy for the complete oxidation of an organic compound • the products are CO2 and H2O if compound contains C, H, and O • N2 is also formed if compound contains N • heats of combustion values are listed in Table 2.5 Chapter 2

24. Standard Enthalpies of Formation • The standard enthalpy of formation , fHº, of a substance is the s6tandard enthalpy for its formation from its elements in their standard states (most stable state at 1 bar pressure • fHº = 0 for an element in its standard state • The standard reaction enthalpy is given by the sum of the enthalpies of formation of the products minus the sum of the standard enthalpies of formation of the reactants • aA + bB  cC + dD • rHº = cfHº(C) + dfHº(D) - (afHº(A) + bfHº(B)) Chapter 2

25. Temperature Dependence of Reaction Enthalpies • dH = Cp dT at constant pressure • H(T2) – H(T1) =  Cp dT • Integration from T1 to T2 • H(T2) - H(T1) =  Cp dT (Kirchhoff’s Law) • Integration from T1 to T2 • H(T2) is the enthalpy change of reaction at temp. T2 • H(T1) is the enthalpy change of reaction at temp. T1 • Cp = Cp(products) - Cp(reactants) Chapter 2