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

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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

5

6

Definition

7?

Hesse’s Law using gasesous ATOMS:Concept of Bond Enthalpies (Energies)

Definition

8

9

10

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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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