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( , )

+ .

+ .

'

T

U U U dV V

∂ = + ∂

' U

U U dT T

∂ = + ∂

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&

,

&

T V

U U dU dV dT

V T

∂ ∂ = + ∂ ∂

,

T T

U V

π ∂

= ∂

T V dU dV C dT π = +

V V

U C

T

∂ = ∂

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/,

,

, π 0

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π

0 0 , Δ 0

, π 0

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T V P P

U V

C T T π

∂ ∂ = +

∂ ∂

1

P

V V T

α ∂

= ∂

1T

T

V V p

κ ∂

= − ∂

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.

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α ,

., π 0

T V P

U V C T

απ ∂ = + ∂

V P

U C T

∂ = ∂

+ +

,

P V P P

C C T T − = − ∂ ∂

P V P P

U U C C nR nR

T T

∂ ∂ − = + − =

∂ ∂ 2

P V T

TV C C

K α − =

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,

At const. pressure, ∆H = q P

Let H = H(p,T)For a closed s stem of const. n

Joule-Thomson coefficientP PdH C dp C dT µ

= − +

H

T

p µ

∂=

∂

pT

H H dH dP dT p T

∂ ∂ = + ∂ ∂

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Joule-Thomson coefficientT p

µ ∂

= ∂ Joule-Thomson effect

cooling by isenthalpicexpansion