1. Chapter 21 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

2. Chapter 22 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)

3. Chapter 23 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

4. Chapter 24 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 = U f - U i –U f = final value of U –U i = 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

5. Chapter 25 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)

6. Chapter 26 Expansion Work dw = - p ex dv –dw is the expansion work (pressure-volume work) when a system undergoes a change –p ex is the external pressure –dV is the change in volume –dw 0) w = -  p ex dV –integration from V i to V f when volume changes from V i to V f

7. Chapter 27 Expansion Work, cont Free Expansion - no opposing force –p ex = 0 (expansion into a vacuum) –w = 0 Expansion against Constant Pressure –p ex is constant –w = - p ex  V (  V is the volume change) Isothermal Reversible Expansion of Perfect Gas –p ex = p (reversible expansion) –p = nRT/V (ideal gas) –w = -  nRT dV/V –w = - nRT ln(V f /V i )

8. Chapter 28 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 = p ex + dp –dp  0 –p = p ex –w = -  p dV

9. Chapter 29 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 ( p ex = p)

10. Chapter 210  U for Process at Constant Volume dU = dq + dw –dw = dw exp + dw e –w exp is expansion work (pressure-volume work) –w e is other work (electrical work etc.) dw exp = 0 for a process taking place at constant volume dU = dq (if no electrical work) dU = dq v (subscript v indicates process at constant volume)  U = q v for process at constant volume

11. Chapter 211 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 q v q v = 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 = I 2 Rt –I = current –V = voltage over heater –R = resistance of heater –t = heating time

12. Chapter 212 Heat Capacity at Constant Volume C V = (  U/  T) V –C V 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 C V,m = C V /n –C V,m is the molar heat capacity at constant volume

13. Chapter 213 Change in U with T dU = C V dT at constant volume –from definition of C V  U = C V  T at constant volume – assuming that C V is independent of T  U = q v at constant volume q v = C V  T –q v is heat needed to change temperature by  T

14. Chapter 214 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 = q p for a process taking place at constant pressure –assuming pressure-volume work is the only type of work involved in the process

15. Chapter 215 Heat Capacity at Constant Pressure C p = (  H/  T) p –C p is the heat capacity at constant pressure –C p shows the variation of H with T at constant pressure C p,m = C p /n –C p,m is the molar heat capacity at constant pressure dH = C p dT at constant pressure  H = C p  T at constant pressure –assuming C p is independent of T –  H for chemical reactions can be determined using a calorimeter operating at constant pressure

16. Chapter 216 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 +  (n gas RT) for processes involving gases

17. Chapter 217 Change in Temperature of Gas  (n gas RT) = n gas R  T – for a change in temperature of a given amount of gas  H =  U + n gas R  T –relation between the change in enthalpy and internal energy of a given amount of gas when the gas is heated or cooled

18. Chapter 218 Relation between  H and  U for a Reaction Involving Gases aA(g) + bB(g)  cC(g) + dD(g) –reaction is assumed to take place at constant temperature –  n gas = (c + d) - (a + b) –  n gas is the change in number of moles of gas upon reaction  (n gas RT) = RT  n gas  H =  U + RT  n gas –relation between the enthalpy change and the change in internal energy for a reaction taking place at constant temperature

19. Chapter 219 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 (T f /T i ) c = ln (V i /V f ) for reversible and adiabatic compression of an ideal gas –c = C V /nR

20. Chapter 220 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

21. Chapter 221 Enthalpies of Phase Transitions Standard Enthalpy of Vaporization,  vap Hº –vaporization: A(l)  A(g) –  vap Hº 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,  fus Hº –fusion or melting: A(s)  A(l) –Enthalpies (heats) of fusion are positive (endothermic processes) Standard Enthalpy of Sublimation,  sub Hº –sublimation: A(s)  A(g) –sublimation processes are endothermic

22. Chapter 222 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) + …….. –  sub Hº =  fus Hº +  vap Hº

23. Chapter 223 Enthalpies of Chemical Change The standard reaction enthalpy,  r Hº, is the change in enthalpy when products and reactants are in their standard states The standard enthalpy (heat) of combustion,  c Hº, is the standard reaction enthalpy for the complete oxidation of an organic compound –the products are CO 2 and H 2 O if compound contains C, H, and O –N 2 is also formed if compound contains N –heats of combustion values are listed in Table 2.5

24. Chapter 224 Standard Enthalpies of Formation The standard enthalpy of formation,  f Hº, of a substance is the s6tandard enthalpy for its formation from its elements in their standard states (most stable state at 1 bar pressure –  f Hº = 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 –  r Hº = c  f Hº(C) + d  f Hº(D) - (a  f Hº(A) + b  f Hº(B))

25. Chapter 225 Temperature Dependence of Reaction Enthalpies dH = C p dT at constant pressure H(T 2 ) – H(T 1 ) =  C p dT –Integration from T 1 to T 2  H(T 2 ) -  H(T 1 ) =   C p dT (Kirchhoff’s Law) –Integration from T 1 to T 2 –  H(T 2 ) is the enthalpy change of reaction at temp. T 2 –  H(T 1 ) is the enthalpy change of reaction at temp. T 1 –  C p = C p (products) - C p (reactants)