Enthalpy H(T,p)

#4




Enthalpy H(T,p) H ≡U + pV
Chemical reactions and biological processes usually take place under
constant pressure and with reversible pV work. Enthalpy turns out to
be an especially useful function of state under those conditions.

reversible gas (p, T1, V1)
= gas (p, T2, V2)
const .p


U1 U2

∆ =U q+ =w q p − ∆pV


∆ + U p∆ = V q p define as H
∆ +U ∆(pV ) =q p ⇒ ∆(U +pV ) =qp

H U ≡+pV ⇒ ∆H =qp for a reversible constant p process


⎛ ∂H ⎞ ∂H
Choose HT ( , p ) ⇒ dH = ⎜ ⎟ dT +⎜⎛ ⎟⎞
dp
⎝∂T ⎠p ⎝ ∂p ⎠T

What are ⎛⎜ ∂H ⎞⎟ and ⎛⎜ ∂H ⎞⎟ ?
⎝∂T ⎠p ⎝ ∂p ⎠T



• ⎛⎜ ∂H ⎞⎟ ⇒ for a reversible process at constant p (dp = 0)
⎝∂T ⎠p

, 5.60 Spring 2008 Lecture page 1
dH = đqp and dH = ⎛⎜ ∂H ⎞⎟ dT
⎝∂T ⎠p


⇒ đqp = ⎛⎜ ∂H ⎞⎟ dT but đqp =C p dT also
⎝∂T ⎠p

⎛∂H ⎞
∴ ⎜ ⎟ =Cp
⎝∂T ⎠p #4


⎛∂H ⎞
• ⎜ ⎟ ⇒ Joule-Thomson expansion
⎝ ∂p ⎠T




porous partition (throttle)



gas (p, T1) = gas (p, T2)



w =pV 1 1 − p2 2V ⇒ ∆U =q +w = pV 11 − p2 2V = −∆(pV )
∴ ∆ U+∆ ( p V ) = 0 ⇒ ∆ (U +pV )=0
∴ ∆H = 0


Joule-Thomson is a constant Enthalpy process.

⎛∂H ⎞ ⎛∂H ⎞
dH =C pdT +⎜ ⎟ dp ⇒ C p dT = −⎜ ⎟ dpH
⎝ ∂p ⎠T ⎝ ∂p ⎠T
⎛∂H ⎞ ⎛∂T ⎞ ⎛∆T ⎞ ⎜ ⎟ = −Cp ⎜ ⎟ ← can
⇒ measure this ⎜ ⎟
⎝ ∂p ⎠T ⎝ ∂p ⎠H ⎝ ∆p ⎠H
⎛∆T ⎞ ⎛∂T ⎞