EAS 6140 Thermodynamics of Atmospheres and Oceans

Worksheet 8 – Phase Diagrams

1. Liquid water has the highest specific heat of all liquids except for NH3 (True, False)True

2. The molecular viscosity of water is less than most liquids at comparable temperatures (True, False)

True3. Water has the highest value of latent heat of evaporation of all substances (True, False)

True4. The surface tension of water is the highest of all liquids. (True, False)

True5. Water dissolves more substances and in greater quantity than all liquids. (True, False)

True6. Fill in the table:

Thermodynamic system Components Phases

Salt dissolved in water 2 1

Mixture of O2 and N2 (gas) 2 1

Oil and vinegar 2 2

Gin and tonic 2 1

Sand in water 2 2

Liquid water in ice 1 2

Consider a one component system, water.

7. Water vapor has __2____ thermodynamic degrees of freedom

8. Temperature and pressure can be varied independently for water vapor (True, False)True

9. Liquid in equilibrium with its vapor has ___1____ thermodynamic degrees of freedom

10. Temperature and pressure can be varied independently for liquid in equilibrium with its vapor (True, False)

False11. Liquid, ice, and vapor in equilibrium has _____ thermodynamic degrees of freedom

Zero

7. On the diagram below is the phase diagram for water in the p-T plane. Label the following on the diagram:a) triple point b) critical point c) fusion curve

Mark on the diagram points which are examples of each of the followingA. A parcel of unsaturated vaporB. A parcel containing liquid and solid in equilibriumC. A parcel of saturated vapor and liquid in metastable equilibrium at temperaturre below 0oC.

8. At temperatures below the triple point, the saturation vapor pressure over liquid water is (greater than, less than, equal to) the saturation vapor pressure over ice.

Greater than9.. Water existing below the freezing point is called __super cooled_______

10. The change of phase from gas to solid is called ___deposition________

Pcrit

Solid

Liquid

Vapor

Fusion Curve

Ptr

AB

C

273.16K

6.11hPa

11. Refer to Fig. 4.4. During a phase change from liquid to vapor, state whether the following variables increase, decrease, or remain the sameTemperature __same________________

Pressure __same________________

Specific Volume __increase_____________

12. During a phase change from liquid to vapor, state whether the following variables increase, decrease, or remain the same

Entropy __increase_____________

Enthalpy __increase_____________

Gibbs energy __same________________

Phase equilibria

1. Chemical potential is defined as __ Gibbs Free Energy_____ per mole

2. The difference in enthalpy between the liquid and solid phases is called ___latent heat of fusion____

3. Matching:

____C____________ latent heat of fusion a. 677 cal g-1

____B____________ latent heat of vaporization b. 597.3 cal g-1

____A____________ latent heat of sublimation c. 77.7 cal g-1

4. When water freezes (liquid- solid phase transition), does the entropy increase or decrease? decrease

5. When water boils (liquid- vapor phase transition), does the entropy increase or decrease? increase

6. How many thermodynamic degrees of freedom are associated with equilibrium between vapor and liquid phases? 1

Derive an equation for the slopes of the equilibrium line between liquid and vapor in the phase diagram in #3. Follow the steps below.

12. Write the first and second law combined, Gibbs energy form, intensive, for a reversible process.

13. Write #12 for the vapor phase (indicated by subscript 1 on the variables) and for the liquid phase (indicated by subscript 2 on the variables) (4.12)

14. In the context of #12, what are the conditions for equilibrium between phases (say liquid and vapor?)

When dg is the same for each phase

15. Using the results from #13 and #14, write a single equation that reflects the equilibrium between the liquid and vapor phases. If you have done this correctly, you should have obtained equation (4.13)

If then

16. The slope of the equilibrium line between liquid and vapor is dp/dT. Using the results from #15, write an expression for the slope of this line. (4.14)

17. The enthalpy change during the transition between the vapor and liquid phases is called latent heat of vaporization, where h = hl - hv =Llv. Use the first and second law combined, enthalpy form, to evaluate the change in entropy during this phase transition. (4.11)

18. Combine the results from #16 and #17 to write equation for dp/dT, that does not include entropy (4.17)

19. At the triple point (T=273.16K, p=6.11 hPa, is the specific volume of water vapor (greater than, less than) the specific volume of liquid water. (Note this difference in specific volume values is several orders of magnitude).

Greater than

20. Rewrite the expression in #18, neglecting the smaller specific volume (4.18)

21. Substitute the ideal gas law for vv into the expression in #20. This is the Clausius-Clapeyron equation, and gives an expression for the variation of the saturation vapor pressure with temperature. (4.19)

22. Integrate the expression in #21 assuming that Llv(T) is constant over the range T1, T2. e = water vapor pressure

23. Examine Table 4.2. Is the assumption Llv(T) is constant a good one? Under which conditions would this not be a good assumption?

Generally speaking it is a reasonable assumption as long as the change in T is small. It does however become problematic with large changes in T, near the triple point, and in places where we switch signs.