Week 8 Ch 12 Thermodynamics

1. Week 8 Ch 12 Thermodynamics • Enthalpy: H=U + PV, H=U + (PV) accounts for expansion work -PV @ P=const in thermodynamics processes, e.g., reactions, phase transitions, etc. Both U and H are State Functions and are path independent • Heat of Reaction: U=q @ V=const and H=q @ P= const for both chemical and physical reactions. • Heat Capacity: C=q/T size dependent(extensive) Material property specific heat capacity cs=C/m size independent(Intensive), mostly used for non-pure substances, like allo phases). cP and cV are the molar heat capacities for P and V constant, respectively. It represents the ability of a substance to store energy in its rotations, vibrations, translation and electronic degrees of freedom, e.g., kT/2 for 1D trans and kT for per vibrations(<KE>=kT/2 and <PE>=kT/2) • Standard State: The Thermodynamically stable state for pure liquids and solid, for gases ideal gas behavior, for solutions 1molar concentration of the dissolved species at P= 1atm and some specified T in each case Midterm Friday: Ch 9, 10, 11.1-11.3, 11.5, 18, 12.1-12.6 One side of 1 page notes(must be hand written), closed book Review Session Today @ 2-3 pm, in FRANZ 1178

2. Equations of states for fixed amount of a pure substances, e.g., 1.0 mols of H2O P=F(V,T) State Functions are only defined in Equilibrium States, does not depend on path ! Equations of State P=nRT/V or PH2O=nRT/(V-nbH2O) - aH2O(n/V)2

3. Applies to Chemical as well as Physical Changes Equilibrium State B Equilibrium State A Fast V= VB – VA=V2 – V1 P= PB – PA=P2 – P1 P, V and T are Thermodynamic State Variables and defines the Thermodynamic States (A and B) They do not depend on the path of the process

4. Equations of states for fixed amount of a pure substances, e.g., 1.0 mols of H2O Equations of State Surface P=nRT/V or PH2O=nRT/(V-nbH2O) - aH2O(n/V)2 P=F(V,T) State Functions are only defined in Equilibrium States, does not depend on path !

5. The difference in State Properties are independent of path e.g., like P(V,T) and Altitude! Non-state properties like Heat(q), work(w) the or the distance travelled depend on the path Fig. 12-3, p. 491

6. Heat flows from hot to cold? At V=const U=q Hot q(T1) Cold (T2) T1  T2 for T2 < T1 For the hot system q < 0 And for the cold system q > 0 The process is driven by the overall Increase in entropy!

7. Equivalence of work and heat (Joule’s Experiment) Since q=0 and DU=w=-mgDh=mghBut T changes byDT!So the energy transferred as work would Correspond to a heat transfer q=CDT w=mgh 0 Dh work= w=-mgDh qin= 0 -h Fig. 12-7, p. 495

8. w = - (force) x (distance moved) Pext Pext Gas A A Gas h1 h2 w = -F(h2-h1)= PextA (h2-h1)=Pext(V2 - V1) w = - PextV V =hA and P=F/A w < 0: system (gas in cylinder) does work: reduces U; V >0 w > 0: work done on the system: increases U; V <0

9. First Law of Thermodynamics U= q + w Thermodynamic process at constant Volume V=const V=0 so, work=0 w=0 U= q + w qV = U q>0 A Flame: CH4 + 2O2 CO2 + 2H2O(l) combustion gives off energy that is transferred as heat(q) to the gas in the piston which can do work against the Pext but since V is held, no pressure volume

10. Reaction AB U=UA – UB can occur via 2 different paths, e.g., catalytic and non-catalytic, U is the same via either path since it is a state function Path(1) AB U=UA – UB Path(2) AB (1) AB (2) a catalyst U=UA – UB U is State function Path Independent A U=q B At V=const U=UA – UB = q since U= qV q < 0 exothermic, q > 0 endothermic, q = 0 thermo-neutral

11. What is the heat of reaction when V is not constant: When the system can do work against and external pressure ! Use the Enthalpy H=U + PV Since H = U + (PV) if P=const and not V H = U + PV but w = -PV Therefore H = U - w but U = q + w by the 1st Law @ P=const. qP= H Note that the Enthalpy is a state function and is therefore Independent of path; It only depends on other state functions H=U + PV !

12. What about when V=const what is q for a the reaction U= q + w = q - PextV q>0 A Flame: CH4 + 2O2 CO2 + 2H2O(l) combustion gives off energy that is transferred as heat(q) to the gas in the piston which does work (-PextV) against the Pext

13. For Chemical Reactions AB H=HA – HB= Hprod – Hreac Path(a) AB H=HA – HB Path(b) AB (1) AB (2) a catalyst U=HA – HB H is a State function Path Independent A H=q P=const B P=const H=HA – HB = q Vq < 0 exothermic, q > 0 endothermic, q = 0 thermo-neutral

14. H2O P-T Phase Diagram and phase transitions at P=const Melting Point: heat of fusion H2O(s)H2O(l) Hfus= q= 6 kJmol-1 Boiling point; heat of vaporization H2O(s)H2O(l) Hvap= 40 kJmol-1

15. For Phase Transitions at P=const: A(s)A(l) Hfus= q Heat of Fusion A(l)A(g) Hvap= q Heat of Vaporization A(s)A(g) Hvub= q Heat of Sublimation NaCl(s)Na+(l )+ Cl-(l ) Molten liquid TM = 801 °C Na+(l )+ Cl-(l )  Na(g) + Cl(g) TB= 1413 °C

16. Thermodynamic Processes inno reactions/phase Transitions Ideal Gas U= ncVT H=U + (PV) H =ncVT + nRT H=n(cV +R) T For P=const H=q=ncP T cP=(cV + R) for all ideal gases cV= (3/2)R atomic gases cV >(3/2)R for Polyatomic gases qin Pext isotherm qout UAC = qin + wAC qin= n cP(TB – TA) > 0 and wAC = - PextV UCB = qout + wCB qout= n cV(TC – TB) < 0 and wCB = - PV=0 UAB = UCA + UCB = n cP(TB – TA) - PextV + n cV(TC – TB)

17. Heat required to Change n mole of ice to steam at 1 atm H2O P-T Phase Diagram q= qics + nHfus + qwat + nHfus + qste qice=ncp(s)T, qwat=ncp(l)T and qst=ncp(g)T T1 T2