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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
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