# Phase Change – Phase Transition

## Examples

Evaporation of water at atmospheric pressure
Calculate heat required to evaporate 1 kg of water at the atmospheric pressure (p = 1.0133 bar) and at the temperature of 100°C.

Solution:

Since these parameters corresponds to the saturated liquid state, only latent heat of vaporization of 1 kg of water is required. From steam tables, the latent heat of vaporization is L = 2257 kJ/kg. Therefore the heat required is equal to:

ΔH = 2257 kJ

Note that the initial specific enthalpy h1 = 419 kJ/kg, whereas the final specific enthalpy will be h2 = 2676 kJ/kg. The specific enthalpy of low-pressure dry steam is very similar to the specific enthalpy of high-pressure dry steam, despite the fact they have different temperatures.

Evaporation of water at high pressure
Calculate heat required to evaporate 1 kg of feedwater at the pressure of 6 MPa (p = 60 bar) and at the temperature of 275.6°C (saturation temperature).

Solution:

Since these parameters corresponds to the saturated liquid state, only latent heat of vaporization of 1 kg of water is required. From steam tables, the latent heat of vaporization is L = 1571 kJ/kg. Therefore the heat required is equal to:

ΔH = 1571 kJ

Note that the initial specific enthalpy h1 = 1214 kJ/kg, whereas the final specific enthalpy will be h2 = 2785 kJ/kg. The specific enthalpy of low-pressure dry steam is very similar to the specific enthalpy of high-pressure dry steam, despite the fact they have different temperatures.

Evaporation of water at high pressure - Energy balance in a steam generator

Calculate the amount of primary coolant, which is required to evaporate 1 kg of feedwater in a typical steam generator. Assume that there are no energy losses, this is only idealized example.

Balance of the primary circuit

The hot primary coolant (water 330°C; 626°F; 16MPa) is pumped into the steam generator through primary inlet. The primary coolant leaves (water 295°C; 563°F; 16MPa) the steam generator through primary outlet.

hI, inlet = 1516 kJ/kg

=> ΔhI = -206 kJ/kg

hI, outlet = 1310 kJ/kg

Balance of the feedwater

The feedwater (water 230°C; 446°F; 6,5MPa) is pumped into the steam generator through the feedwater inlet. The feedwater (secondary circuit) is heated from ~230°C 446°F to the boiling point of that fluid (280°C; 536°F; 6,5MPa). Feedwater is then evaporated and the pressurized steam (saturated steam 280°C; 536°F; 6,5 MPa) leaves the steam generator through steam outlet and continues to the steam turbine.

hII, inlet = 991 kJ/kg

=> ΔhII = 1789 kJ/kg

hII, outlet = 2780 kJ/kg

Balance of the steam generator

Since the difference in specific enthalpies is less for primary coolant than for feedwater, it is obvious that the amount of primary coolant will be higher than 1kg. To produce of 1 kg of saturated steam from feedwater, about 1789/206 x 1 kg =  8.68 kg of primary coolant is required.

## Sublimation

In general, sublimation is a phase change of a substance directly from the solid to the gas phase without passing through the intermediate liquid phase. Sublimation is an endothermic phase change that occurs at temperatures and pressures below a substance’s triple point in its phase diagram.

Consider the ice at -10°C  and at the pressure of 500 Pa. In this case, heat transfer to the ice first results in an increase in temperature to -8°C. At this point, however, the ice passes directly from the solid phase to the vapor phase in the process known as sublimation. The corresponding heat is called the heat of sublimation, Ls. Further heat transfer would result in superheating the vapor.

Since sublimation is an endothermic phase change, it requires additional energy. This additional energy required can be calculated by adding the enthalpy of fusion and the enthalpy of vaporization and is known as the enthalpy of sublimation (also called heat of sublimation).

For some substances, sublimation is much easier than evaporation from the melt. It depends on their triple point. When the pressure of its triple point is too high,  it is difficult to obtain them as liquids.

The reverse process of sublimation is desublimation, in which a substance passes directly from a gas to a solid phase.

## Desublimation

In general, desublimation (or deposition)  is a phase transition of a substance directly from the gas phase to the solid phase without passing through the intermediate liquid phase. Desublimation is an exothermic phase change that occurs at temperatures and pressures below a substance’s triple point in its phase diagram.

Consider the water vapor at -5°C  and at the pressure of 500 Pa. In this case, when heat is taken from the water vapor, the vapor results in an decrease in temperature to -8°C. At this point, however, the vapor passes directly from the gas phase to the solid phase in the process known as desublimation. The corresponding heat is called the heat of sublimation, Ls.

Since desublimation is an exothermic phase change, it releases energy. This energy released can be calculated by adding the enthalpy of fusion and the enthalpy of vaporization and is known as the enthalpy of sublimation (also called heat of sublimation).

For some substances, desublimation is much easier than passing through liquid phase. It depends on their triple point. When the pressure of its triple point is too high,  it is difficult to obtain them as liquids.

The reverse process of desublimation is sublimation, in which a substance passes directly from a solid to a gas phase.

One example of desublimation is when frost forms on a leaf in winter. For desublimation to occur, thermal energy must be removed from a gas. Therefore, when the leaf becomes cold enough, water vapor in the air surrounding the leaf can lose enough thermal energy to change directly into a solid.

References:
Reactor Physics and Thermal Hydraulics:
1. J. R. Lamarsh, Introduction to Nuclear Reactor Theory, 2nd ed., Addison-Wesley, Reading, MA (1983).
2. J. R. Lamarsh, A. J. Baratta, Introduction to Nuclear Engineering, 3d ed., Prentice-Hall, 2001, ISBN: 0-201-82498-1.
3. W. M. Stacey, Nuclear Reactor Physics, John Wiley & Sons, 2001, ISBN: 0- 471-39127-1.
4. Glasstone, Sesonske. Nuclear Reactor Engineering: Reactor Systems Engineering, Springer; 4th edition, 1994, ISBN: 978-0412985317
5. Todreas Neil E., Kazimi Mujid S. Nuclear Systems Volume I: Thermal Hydraulic Fundamentals, Second Edition. CRC Press; 2 edition, 2012, ISBN: 978-0415802871
6. Zohuri B., McDaniel P. Thermodynamics in Nuclear Power Plant Systems. Springer; 2015, ISBN: 978-3-319-13419-2
7. Moran Michal J., Shapiro Howard N. Fundamentals of Engineering Thermodynamics, Fifth Edition, John Wiley & Sons, 2006, ISBN: 978-0-470-03037-0
8. Kleinstreuer C. Modern Fluid Dynamics. Springer, 2010, ISBN 978-1-4020-8670-0.
9. U.S. Department of Energy, THERMODYNAMICS, HEAT TRANSFER, AND FLUID FLOW. DOE Fundamentals Handbook, Volume 1, 2 and 3. June 1992.

Thermodynamics