Elementary Thermodynamics - Applications of Phase Changes
Propane storage tanks
A common example of a saturated liquid/vapor (two-phase) system is the internal environment of a propane storage tank, such as the kind commonly used to store propane fuel for portable stoves and gas cooking grills. If multiple propane storage tanks holding different volumes of liquid propane are set side by side, pressure gauges attached to each tank will all register the exact same pressure:
This is counter-intuitive, as most people tend to think the fullest tank should register the highest pressure (having the least space for the vapor to occupy). However, since the interior of each tank is a liquid/vapor system in equilibrium, the pressure is defined by the point on the liquid/vapor transition curve on the phase diagram for pure propane matching the tanks’ temperature. Thus, the pressure gauge on each tank actually functions as a thermometer, since pressure is a direct function of temperature for a saturated liquid/vapor system and therefore cannot change without a corresponding change in temperature. This is a thermodynamic system with just one degree of freedom.
Storage tanks containing liquid/vapor mixtures in equilibrium present unique safety hazards. If ever a rupture were to occur in such a vessel, the resulting decrease in pressure causes the liquid to spontaneously boil, halting any further decrease in pressure. Thus, a punctured propane tank does not lose pressure in the same manner than a punctured compressed air tank loses pressure. This gives the escaping vapor more “power” to worsen the rupture, as its pressure does not fall off over time the way it would in a simple compressed-gas application. As a result, relatively small punctures can and often do grow into catastrophic ruptures, where all liquid previously held inside the tank escapes and flashes into vapor, generating a vapor cloud of surprisingly large volume1.
Compounding the problem of catastrophic tank rupture is the fact that propane happens to be highly flammable. The thermodynamic properties of a boiling liquid combined with the chemical property of flammability in air makes propane tank explosions particularly violent. Fire fighters often refer to this as a BLEVE: a Boiling Liquid Expanding Vapor Explosion.
Class II Filled-bulb thermometers
This same pressure-temperature interdependence finds application in a type of temperature measurement instrument called a Class II filled-bulb, where a metal bulb, tube, and pressure-sensing element are all filled with a saturated liquid/vapor mixture:
Heat applied to the bulb literally “boils” the liquid inside until its pressure reaches the equilibrium point with temperature. As the bulb’s temperature increases, so does the pressure throughout the sealed system, indicating at the operator display where a bellows (or some other pressure-sensing element) moves a pointer across a calibrated scale.
The only difference between the two filled-bulb thermometers shown in the illustration is which end of the instrument is warmer. The Class IIA system on the left (where liquid fills the pressure-indicating element) is warmer at the bulb than at the indicating end. The Class IIB system on the right (where vapor fills the indicating bellows) has a cooler bulb than the indicating bellows. The long length and small internal diameter of the connecting tube prevents any substantial heat transfer from one end of the system to the other, allowing the sensing bulb to easily be at a different temperature than the indicating bellows. Both types of Class II thermometers work the same2, the indicated pressure being a strict function of the bulb’s temperature where the liquid and vapor coexist in equilibrium.
Nuclear reactor pressurizers
Nuclear reactors using pressurized water as the moderating and heat-transfer medium must maintain the water coolant in liquid form despite the immense heat output of the reactor core, to avoid the formation of steam bubbles which could lead to destructive “hot spots” inside the reactor. The following diagram shows a simplified3 pressurized water reactor (PWR) cooling system:
In order to maintain a liquid-only cooling environment for the reactor core, the water is held at a pressure too high for boiling to occur inside the reactor vessel. Referencing the phase diagram for water, the operating point of the reactor core is maintained above the liquid/vapor phase transition line by an externally supplied pressure.
This excess pressure comes from a device in the primary coolant loop called a pressurizer. Inside the pressurizer is an array of immersion-style electric heater elements. The pressurizer is essentially an electric boiler, purposely boiling the water inside at a temperature greater4 than that reached by the reactor core itself.
By maintaining the water temperature inside the pressurizer greater than at the reactor core, the water flowing through the reactor core literally cannot boil. The water/vapor equilibrium inside the pressurizer is a system with one degree of freedom (pressure and temperature linked), while the water-only environment inside the reactor core has two degrees of freedom (temperature may vary to any amount below the pressurizer’s temperature without water pressure changing at all). Thus, the pressurizer functions like the temperature-sensing bulb of a gigantic Class IIA filled-bulb thermometer, with a liquid/vapor equilibrium inside the pressurizer vessel and liquid only inside the reactor vessel and all other portions of the primary coolant loop. Reactor pressure is then controlled by the temperature inside the pressurizer, which is in turn controlled by the amount of power applied to the heating element array5.
Boilers in general (the nuclear reactor system previously described being just one example of a large “power” boiler) are outstanding examples of phase change applied to practical use. The purpose of a boiler is to convert water into steam, sometimes for heating purposes, sometimes as a means of producing mechanical power (through a steam engine), sometimes for chemical processes requiring pressurized steam as a reactant, sometimes for utility purposes (maintenance-related cleaning, process vessel purging, sanitary disinfection, fire suppression, etc.) or all of the above. Steam is a tremendously useful substance in many industries, so you will find boilers in use at almost every industrial facility.
A simplified diagram of a basic water tube boiler appears here:
Water enters the boiler through a heat exchanger in the stack called an economizer. This allows cold water to be pre-heated by the relatively cool exhaust gases before they exit the stack. After pre-heating in the economizer, the water enters the boiler itself, where water circulates by natural convection (“thermosiphon”) through a set of tubes exposed to high-temperature fire. Steam collects in the “steam drum,” where it is drawn off through a pipe at the top. Since this steam is in direct contact with the boiling water, it will be at the same temperature as the water, and the steam/water environment inside the steam drum represents a two-phase system with only one degree of freedom.
With just a single degree of freedom, steam temperature and pressure are direct functions of each other – coordinates at a single point along the liquid/vapor phase transition line of water’s phase diagram. One cannot change one variable without changing the other.
Consulting a steam table6, you will find that the temperature required to boil water at a pressure of 120 PSIG is approximately 350 degrees Fahrenheit. Thus, a steam boiler operating at that pressure will have its temperature fixed at 350 degrees. The only way to increase pressure in that boiler is to increase its temperature, and visa-versa.
When steam is at the same temperature as the boiling water it came from, it is referred to as saturated steam. Steam in this form is very useful for heating and cleaning, but not as much for operating mechanical engines or for process chemistry. If saturated steam loses any temperature at all (by losing its latent heat), it immediately condenses back into water. Liquid water can cause major mechanical problems inside steam engines (although “wet” steam works wonderfully well as a cleaning agent!), and so steam must be made completely “dry” for some process applications.
The way this is done is by a process known as superheating. If steam exiting the steam drum of a boiler is fed through another heat exchanger inside the firebox so it may receive more heat, its temperature will rise beyond the saturation point. This steam is now said to be superheated:
Superheated steam is absolutely dry, containing no liquid water at all. It is therefore safe to use as a fluid medium for engines (piston and turbine alike) and as a process reactant where liquid water is not tolerable. The difference in temperature between superheated steam and saturated steam at any given pressure is the amount of superheat. For example, if saturated steam at 350 degrees Fahrenheit and 120 PSI drawn from the top of the steam drum in a boiler is heated to a higher temperature of 380 degrees Fahrenheit (at the same pressure of 120 PSI), it is said to have 30 degrees (Fahrenheit) of superheat.
Fruit crop freeze protection
An interesting application of phase changes and latent heat occurs in agriculture. Fruit growers, needing to protect their budding crop from the damaging effects of a late frost, will spray water over the fruit trees to maintain the sensitive buds above freezing temperature. As cold air freezes the water, the water’s latent heat of fusion prevents the temperature at the ice/water interface from dropping below 32 degrees Fahrenheit. So long as liquid water continues to spray over the trees, the buds’ temperature cannot fall below freezing. Indeed, the buds cannot even freeze in this condition, because once they cool down to the freezing point, there will be no more temperature difference between the freezing water and the buds. With no difference of temperature, no heat will transfer out of the buds. With no heat loss, water inside the buds cannot change phase from liquid to solid (ice) even if held at the freezing point for long periods of time, thus preventing freeze damage7.
Only if the buds are exposed to cold air (below the freezing point), or the water turns completely to ice and no longer holds stable at the freezing point, can the buds themselves ever freeze solid.
1Steam boilers exhibit this same explosive tendency. The expansion ratio of water to steam is on the order of a thousand to one (1000:1), making steam boiler ruptures very violent even at relatively low operating pressures.
2Class IIA systems do suffer from elevation error where the indicator may read a higher or lower temperature than it should due to hydrostatic pressure exerted by the column of liquid inside the tube connecting the indicator to the sensing bulb. Class IIB systems do not suffer from this problem, as the gas inside the tube exerts no pressure over an elevation.
3Circulation pumps and a multitude of accessory devices are omitted from this diagram for the sake of simplicity.
4This is another example of an important thermodynamic concept: the distinction between heat and temperature. While the temperature of the pressurizer heating elements exceeds that of the reactor core, the total heat output of course does not. Typical comparative values for pressurizer power versus reactor core power are 1800 kW versus 3800 MW, respectively. The pressurizer heating elements don’t have to dissipate much power (compared to the reactor core) because the pressurizer is not being cooled by a forced convection of water like the reactor core is.
5In this application, the heaters are the final control element for the reactor pressure control system.
6Since the relationship between saturated steam pressure and temperature does not follow a simple mathematical formula, it is more practical to consult published tables of pressure/temperature data for steam. A great many engineering manuals contain steam tables, and in fact entire books exist devoted to nothing but steam tables.
7An experiment illustrative of this point is to maintain an ice-water mixture in an open container, then to insert a sealed balloon containing liquid water into this mixture. The water inside the balloon will eventually equalize in temperature with the surrounding ice-water mix, but it will not itself freeze. Once the balloon’s water reaches 0 degrees Celsius, it stops losing heat to the surrounding ice-water mix, and therefore cannot make the phase change to solid form.
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