AN607

26

Rev. 1.7

Clausius-Clapeyron Equation

The Clausius-Clapeyron equation modifies the Clapeyron equation with two simplifying approximations that make

this equation useful for ice to water vapor and liquid water to water vapor transitions. The first assumption is that

the change in volume from liquid water to gas (water vapor) or solid (ice) to gas (water vapor) is approximately

equal to the volume of the gas (water vapor).

The second approximation is the gas (water vapor) can be treated as an ideal gas.

Incorporating these assumptions in the Clapeyron equation yields the following.

Rearranging:

Integrating as an indefinite integral and assuming

h is constant:

Where:

h = enthalpy change for phase change which varies between

2.501 x 106 and 2.257 x 106 J/kg in the range of 0–100 °C

R’ = universal gas constant

R = specific gas constant for water which is 461.5 J/(K – kg)

Rearranging:

VV

gas

V

liquid

–

V

gas

VV

gas

V

solid

–

V

gas



=



=

V

gas

nR

T

P

-------------

=

p

T

--------





h

T

nR

T

p



-------------

------------------

h

RT

2

p



-----------

-----------

==

dp



p



--------





h

RT

2

-----------dT

=

p



d

p



--------



h

R

------- 1

T

2

------

p





ln

C

0

+

h

–

R

----------

1

T

---





C

1

+

=

=

p



C

2

e

h

–

R

----------

1

T

---





=