Week 8 Ch 12 Thermodynamics• Enthalpy: H=U + PV, H=U + (PV)

accounts for expansion work -PV @ 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= constfor 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 allophases). 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, forsolutions 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

Equations of states for fixed amount of a pure substances, e.g., 1.0 mols of H2O

P=F(V,T)StateFunctionsare onlydefined inEquilibriumStates, doesnot dependon path !

Equations of State P=nRT/V orPH2O=nRT/(V-nbH2O) - aH2O(n/V)2

Applies to Chemical as well as Physical Changes

V= VB – VA=V2 – V1

P= PB – PA=P2 – P1

Fast

P, V and T are Thermodynamic State Variablesand defines the Thermodynamic States (A and B)They do not depend on the path of the process

EquilibriumState A

EquilibriumState B

Equations of states for fixed amount of a pure substances, e.g., 1.0 mols of H2O

P=F(V,T)StateFunctionsare onlydefined inEquilibriumStates, doesnot dependon path !

Equations of State Surface P=nRT/V orPH2O=nRT/(V-nbH2O) - aH2O(n/V)2

Fig. 12-3, p. 491

The difference in State Properties are independent of pathe.g., like P(V,T) and Altitude! Non-state properties likeHeat(q), work(w) the or the distance travelled depend on the path

Hot q(T1) Cold (T2)

T1 T2 for T2 < T1

Heat flows from hot to cold?

For the hot system q < 0And for the cold system q > 0

The process is driven by the overallIncrease in entropy!

At V=const U=q

Fig. 12-7, p. 495

Equivalence of work and heat (Joule’s Experiment)

h work=w=-mgh

-h

0

qin= 0

Since q=0 and U=w=-mgh=mgh But T changes by T!So the energy transferred as work would Correspond to a heat transfer q=CT

w=mgh

w = - (force) x (distance moved)

Gas

Pext Pext

Gash1 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

AA

First Law of ThermodynamicsU= q + w

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 sinceV is held, no pressure volume

q>0

Thermodynamic process at constant Volume V=const

V=0 so, work=0

w=0

U= q + w

qV = U

Thermodynamic process at constant Volume V=const

V=0 so, work=0

w=0

U= q + w

qV = U

Reaction AB 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

At V=const U=UA – UB = q since U= qV

q < 0 exothermic, q > 0 endothermic, q = 0 thermo-neutral

Path(1) AB U=UA – UB

AB (1)

AB (2) a catalyst

U=UA – UB

U is State functionPath Independent

Path(2)

B

AU=q

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 + PV but w = -PV

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 thereforeIndependent of path; It only depends on other state functions

H=U + PV !

What about when V=const what is q for a the reactionU= q + w = q - Pext V

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

q>0

For Chemical Reactions AB H=HA – HB= Hprod – Hreac

Path(a) AB H=HA – HB

P=const H=HA – HB = q

Vq < 0 exothermic, q > 0 endothermic, q = 0 thermo-neutral

Path(b)

B

AH=q

P=const

AB (1)

AB (2) a catalyst

U=HA – HB

H is a State functionPath Independent

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 vaporizationH2O(s)H2O(l) Hvap= 40 kJmol-1

For Phase Transitions at P=const:

A(s)A(l) Hfus= q Heat of FusionA(l)A(g) Hvap= q Heat of VaporizationA(s)A(g) Hvub= q Heat of Sublimation

NaCl(s)Na+(l )+ Cl-(l ) Molten liquid TM = 801 °CNa+(l )+ Cl-(l ) Na(g) + Cl(g) TB= 1413 °C

Thermodynamic Processes inno reactions/phase Transitions

isotherm

qin

qout

UAC = qin + wAC qin= n cP(TB – TA) > 0 and wAC = - PextVUCB = qout + wCB qout= n cV(TC – TB) < 0 and wCB = - PV=0UAB = UCA + UCB = n cP(TB – TA) - PextV + n cV(TC – TB)

Pext

Ideal Gas U= ncVT

H=U + (PV)H =ncVT + nRTH=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

Heat required to Change n mole of ice to steam at 1 atm

H2O P-T Phase Diagram

T1 T2

q= qics + nHfus + qwat + nHfus + qste

qice=ncp(s)T, qwat=ncp(l) T

and qst=ncp(g) T