Winter 2013 Chem 254: Introductory Thermodynamics Chapter 2: Internal Energy (U), Work (w), Heat (q), Enthalpy (H) ................................................ 13 Heat Capacities ......................................................................................................................... 16 Calculating ΔU, ΔH, w, q in Ideal Gas ........................................................................................ 18 Isothermal Compression ........................................................................................................... 21 Reversible Process (limiting process) ....................................................................................... 22 Isothermal Expansion ............................................................................................................... 22 Chapter 2: Internal Energy (U), Work (w), Heat (q), Enthalpy (H) Internal Energy (excludes motion and rotation of vessel) Look at isolated part of universe UUUsystem Environment Total = isolated First law of thermodynamics: - Total U for isolated system is constant - Energy can be exchanged between various components - Energy forms can be interconverted Eg. Chemical En Heat Work UUUtotal system environement 0 Chapter 2: Internal Energy, Work, Heat and Enthalpy 13 Winter 2013 Chem 254: Introductory Thermodynamics Work In classical mechanics, move object a distance d with force F in direction of displacement is work N m = J F mg dh w mgh (kg m s-2 m = N m = J) h w mgd cos cos d h w mgd mgh d General formula w F dL Line integral PV work (constant external pressure) F m applies constant force P A F w mgh Fh ()() Ah P V V A ext 12 w Pext() V final V initial Joules, or L Bar (1 L Bar = 100 J) Chapter 2: Internal Energy, Work, Heat and Enthalpy 14 Winter 2013 Chem 254: Introductory Thermodynamics More general formula for PV work, P does not need to be constant Vf w P dV V ext i Sign Convention : Work done on the system raises internal energy of system ( w 0) Work done by the system lowers the internal energy ( w 0) Other forms of work: - electrical work wQ Q is charge in coulombs difference in potential (in Volts or J/C) Run a current over Q I t I is current (in Amps or C/s) w I t Important: Work is associated with a process, with change. Work is transitory. You cannot say that a system contains that amount of energy or heat Heat: associated with a process going from State 1 State 2 Usystem q w q is heat; w is the work Heat is exchanged between system and environment q 0: system loses energy q 0 : system gains energy qqsystem environment note: TTsystem environment for heat to flow Isolated system Chapter 2: Internal Energy, Work, Heat and Enthalpy 15 Winter 2013 Chem 254: Introductory Thermodynamics TTouter inner (regulate) So there is no flow of heat UUsystem environment 0 Uinner 0 Beaker + Lab +… = environment (isolated) UI 0; UII 0 UUI II 0 Chemical Energy Butane + O2 CO 2 H 2 Note : UII 0even if temperature increases! Why? Chemical energy of butane is converted to heat. Heat Capacities The amount of energy (heat) required to raise the temperature of 1 gram of substance by 1 oC. Heat capacity of water is 4.18 J/g K = 1 calorie 1) Heat capacity is dependent on heat Eg. 10 oC 11 oC and 80 oC 81 oC, require slightly different energies 2) At least 2 types of heat capacity a) Keep volume constant CV b) Keep pressure constant CP 3) Heat capacity is proportional to amount of substance Molar heat capacities : CPm, ,CVm, n moles : CV nC V, m , CP nC P, m 4) General formula Chapter 2: Internal Energy, Work, Heat and Enthalpy 16 Winter 2013 Chem 254: Introductory Thermodynamics Tf q C dT VVT i If CV is constant over temperature range: T f Tf qV C V dT C V T C V T f T i T Ti i qVV C() T And qPP C() T Which is larger CP or CV ? Relation for and for ideal gas? VV21 ; TT21 U qP w q P P ext () V21 V PV nRT U qP nR() T21 T qPP C T ; U qVV C T CPV T C T nR T CPV C nR or CCRP,, m V m Therefore CP is larger than CV . At constant P , the system also does PV work when raising T . (analysis for ideal gas) No work because V is constant U qV w qV UCT V Bomb calorimetry qsystem q surrounding C Calorimeter T V V V measure U reaction Chapter 2: Internal Energy, Work, Heat and Enthalpy 17 Winter 2013 Chem 254: Introductory Thermodynamics system surroundings qqPV system Calorimeter qP C V T measure system qHP reaction True definition of Enthalpy H U () PV PV PV2 2 PV 1 1 ; for PV1 1 PV 2 2 ; H U PV At constant Pressure H U PV2 2 PV 1 1 HUPV H qPP w P V q P()() V P V H qPP C T Completely general :UH, are function of state specify TVP,, UUTPVUTPV (,,)(,,)2 2 2 1 1 1 HHTPVHTPV (,,)(,,) 2 2 2 1 1 1 Change in UH, are the same for both paths Change in qw, are different for different paths Calculating ΔU, ΔH, w, q in Ideal Gas 1) Calculating UH, is easy if T is known T f Tf UUT()] U CdTCT CT T T V V Ti V f i i UCT V for any process HHT( ) ..... Chapter 2: Internal Energy, Work, Heat and Enthalpy 18 Winter 2013 Chem 254: Introductory Thermodynamics HCT P for any process (if CP is constant) We know CPV C nR Special cases: Isothermal Process T is constant T 0 ; UH 0 2) Work: w P dV PV work only ext - Constant V Vif V w 0 ; q qV U Vf - Constant Pext w P dV P() V V ; q q H extV ext f i P i Isothermal reversible process: (Reversible process: delicate, see later) 1 P nRT nRT is constant ext V Vf dV V w nRT nRTln V f V Vi i V Vf nRTln Vfi ln V nRT ln Vi Vf w nRT ln Vi 3) Heat Adiabatic process : q 0 by definition U q w; Uw Adiabatic Reversible Process nRT q 0 , Uw, P ext V Vf nRT U w dV V i V nRT nC dT dV Vm, V dT nR nC dV Vm, TV Chapter 2: Internal Energy, Work, Heat and Enthalpy 19 Winter 2013 Chem 254: Introductory Thermodynamics ffdT dV nC nR Vm, iiTV TVff nCvm, ln nR ln TVii Cvm, TVff ln ln RTVii For adiabatic reversible process: C TV C T P V C P vm, lnff ln OR Pm, lnf ln i OR lnf Pm, ln i RTVii RTPif VCPi V, m f 1) R C TVVf R f f Vm, ln ln ln TCVVi V, m i i R C TVffVm, TVii 2) C T nRT P Vm, lnff ln i R Ti P f nRT i T P ln f i TPif T P lnf ln i TPif C T P Vm, 1 lnf ln i RTPif CRVm, Tf Pi ln ln RTP if C T P Pm, lnf ln i RTPif Chapter 2: Internal Energy, Work, Heat and Enthalpy 20 Winter 2013 Chem 254: Introductory Thermodynamics Adiabatic Isobaric Process Constant external pressure AND q 0 Isothermal Compression Constant external pressure w Pf V f V i 0 qw 0 (because U 0 because isothermal) What is work in 2-step process? w2 P int V int Vi P f V f V int ww21 ; qq21 Chapter 2: Internal Energy, Work, Heat and Enthalpy 21 Winter 2013 Chem 254: Introductory Thermodynamics Conclusion: w and q depend on details of process, not only on initial and final state. Repeat for 3 step, 4…. w5 w 4 w 3 w 2 w 1 ; q5 q 4 q 3 q 2 q 1 The more steps, the less w and less heat Reversible Process (limiting process) PPext gas at each step nRT P ext V Isothermal Reversible Process VVffdV w P dV nRT VVext iiV V Vf f nRTln | nRT ln work, q is minimal Vi Vi Isothermal Expansion Chapter 2: Internal Energy, Work, Heat and Enthalpy 22 Winter 2013 Chem 254: Introductory Thermodynamics w1 Pf V f V i 0 ; qw11 0 ww21 ; qq21 w3 w 2 w 1 ; q3 q 2 q 1 More processes more work ( w ), more heat ( q ) w5 w 4 w 3 w 2 w 1 ; q5 q 4 q 3 q 2 q 1 Limiting Expansion Work compressionexp ansion wwlimit limit VVffdV Vf w P dV nRT nRT ln limit VVext ii VVi Chapter 2: Internal Energy, Work, Heat and Enthalpy 23 Winter 2013 Chem 254: Introductory Thermodynamics Grains of sand : I can run process either way The thermodynamic work is the same both ways for reversible process Irreversible Process (Big chunks of mass) Follows arrows in reverse: add mass, piston rises? ; removes mass, piston lowers? This is absurd, hence: Why do irreversible processes run in one way and not another? What is special about irreversible? Chapter 2: Internal Energy, Work, Heat and Enthalpy 24 .