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Always True (blue) Conditional
Δ Adiabatic: q = 0 ; ΔE = w ;
361 Lec 7 Fri, 7sep12
ΔE = q + w Adiabatic: q = 0 ; ΔE = w ;Constant V:ΔE = Cv (T2‐T1) if Cv constant
ΔE C dTvTT= ∫ 1
2
For ideal gas the above is always true (even if volume changes)
H = E + PV For P=Pext = constant and PV work only:Δ T∫
2
ΔH = ΔE + P2V2 ‐ P1V1ΔH = q =
ΔH = CP (T2‐T1) if CP constantFor ideal gas the above is always true (even if pressure
ΔH C dTpTT= ∫ 1
2
For ideal gas the above is always true (even if pressure changes)
for Pext constant: wpv = ‐Pext (V2 – V1) ;if isothermal reversible and ideal gas:
dwpv = −P dVext if isothermal reversible and ideal gas:
Solids and Liquids (volume changes are very small)d Δ Δ
wpv = −∫ P dVextVV
12 wpv = − = −∫ PdV nRT
VVV
V ln 211
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Cp ≅ Cv and ΔH ≅ ΔE
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High pressure applied to a solid ppwill often turn it into another crystal form that is more dense e g
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more dense, e.g., graphite into diamond.
Reversible Isothermal PV work (ideal gas)P P nRT/V ( f )P = Pext = nRT/V (balanced forces)
VVV
∫∫∫ −=−=−=2
1
2
1
2
1
V
V
V
V
V
VdV
VnRTPdVdVPw ext
1
2lnVVnRT
VdVnRTw −=−= ∫
2
1
V
V
An integral is just a
Sum
Sum of fractional changes
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ONLY if P = Pext = and ideal gas (but is common case)
What are ΔE ,q ? ΔE =0 (isothermal), therefore q = ‐w3
“chemical energy”
From a table of ΔH fora few dozen reactionswe can know the ΔHf h d ffor thousands of reactions that may have never been measured.
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Table A.5Appendix
715 Diff f ΔHpage 715 Difference of ΔHfovalues is ΔHvapo
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Definition
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Hesse’s Law using gasesous ATOMS:Concept of Bond Enthalpies (Energies)
Definition
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where Δn is the changeof moles of gases only.
(b) “Energy equivalent” = ΔH0 of the reaction in (a)
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