Lecture 14: Phases

Lecture 14: Phases Summary Atmospheric pressure is the force per unit area exerted by the mass of the atmosphere onto everything it envelops, and other gasses, liquids, and solids can exert pressure in a similar fashion. In a closed system, an equilibrium develops as molecules convert from one phase to another (like liquid to gas), and vice versa (gas back to liquid). The pressure that one phase exerts on another depends strongly on what intermolecular forces are present in the system. Strong IMFs lead to low vapor pressures, while weak IMFs lead to high vapor pressures. The vapor pressure of a material is different than the weight of a gas; rather, it’s related to how likely a liquid or solid is to lose molecules to the gas phase. If the vapor pressure is higher than atmospheric pressure, the weight of the atmosphere isn’t enough to trap the gas that is released, and the material begins to boil. So far, boiling has been entirely described with respect to pressure, but temperature makes a difference too! The vapor pressure also depends strongly on temperature: as temperature rises, the vapor pressure increases exponentially. So as a material is heated up, its vapor pressure increases until it exceeds atmospheric pressure and it starts to boil. For example, if we start with water at 25 C, its vapor pressure is about 0.02 atm. By the time it reaches 100°C, the vapor pressure has increased 50-fold to reach 1 atm, at which point it begins to boil. We learned previously that a higher temperature yields higher kinetic energy and more molecular movement. However, when a material is “at” a certain temperature, not every molecule moves around the same. The distribution of kinetic energies associated with a given temperature can be very broad, with long tails. So temperature is used to describe the average kinetic energy, but some molecules will have more and some will have less. The Clausius-Clapeyron equation gives the exponential relationship between vapor pressure and temperature: ln(P ) = −ΔHvap /RT + C Diagram is in the public domain. Source: Wikimedia Commons. where ΔHvap is the enthalpy of vaporization, or the energy per mole required to convert a liquid molecule into a gas molecule. There is a latent heat or enthalpy involved in every kind of phase change: ΔHvap for vaporization, ΔHf us for fusion, and ΔHsub for sublimation. The enthalpy of sublimation is always larger than the enthalpy of fusion, because the solid-state atoms/molecules are more strongly bonded than liquid atoms/molecules. Hess’ law tells us that any path from one state to another is a valid path, because the total energy required to change states will be the sum of energy differences along the path. 27 Phase diagrams are helpful to know what the equilibrium phase of a material is at a given temperature and pressure. Phase boundaries are called coexistence curves: at these points, two phases exist simultaneously. If a phase boundary is crossed, a phase change will occur. Phase diagrams are like “maps” of a material. Why this matters Heat is an essential form of energy transfer for human beings, not only for maintaining body temperature but also for a range of primary and advanced activities, from cooking and sterilizing, to operating engines and generating electricity. Control of thermal energy to benefit humanity dates back to pre-historic times and heat remains the single most valuable energy currency of our existence. As illustrated in this figure, nearly 90% of all energy consumed globally is either generated by or consumed as thermal energy at some point during the supply/demand cycle. It is therefore surprising, even striking, that to date we have no viable means for storing thermal energy. Unlike mechanical energy, where material can be simply pumped up a potential energy hill and held there until needed as in the case of pumped hydro, or electrical energy where electrons can be pushed up an electrochemical hill and held there as in a battery, for the case of phonons – the carriers of thermal energy – there is no such stability. Instead, thermal energy rolls back down the energy hill and cannot be stopped. Heat always dissipates. It leaks and we cannot contain it no matter how hard we work to insulate a thermal reservoir. The slow leaking of thermal energy out of a material that’s hotter than its surrounding is called “sensible heat.” Eventually, enough energy will be transferred to the environment to make it the same temperature as the surroundings. In fact, if you take a thermodynamics class you’ll learn that the very definition of temperature is, “that which is equal when heat ceases to flow between systems in thermal contact.” So one way to store thermal energy is to heat something up, then that something will leak its heat out at some rate into some environment until its temperature is the same as that of the environment. The storage and release of sensible heat is used all the time, from a heating pack that you microwave and put on your sore neck to focusing sunlight on a concrete slab as in a solar thermal power plant, to the old idea of heating an entire mountain for long-term energy generation as it slowly cools down. (that last one hasn’t been tried yet in case you’re wondering. . . but it’s a neat concept!). But whether a heat pack or a mountain, the problem with sensible heat is that you get what you get with almost no control. Apart from how much insulation you package your material with, there aren’t many good ways to slow and no ways at all to stop the flow of heat. Because in this mode of thermal storage, we heat something up to some temperature and it starts 28 Heat conversion diagram © source unknown. All rights reserved. This content is excluded from our Creative Commons license. For information, see https://ocw.mit.edu/fairuse. cooling right away, there’s also no control over the temperature you get out of the stored energy: it’s constantly changing as it cools. Ah, but there is in fact a way to “hold on” to thermal energy, and then release it back as heat when needed, much like electricity in batteries. And it gives you complete and total control over the release temperature. In fact, a simple bucket of wax is a thermal storage system. It works by taking advantage of its phase change: when wax melts it changes from solid to liquid, and the energy required to make this phase change happen is large (that would be the enthalpy of fusion, ΔHf us , as discussed in the lecture). When the wax cools back down it becomes a solid again, and all that phase change energy is given back out upon solidification. Materials that are used like this, where the enthalpy of one of its phase changes is used as a way to store and release thermal energy, are called “phase change materials” (PCMs). It’s a bit of an odd name since all materials are phase change materials, but the PCM label has stuck as a way to refer to ones where we try to do something useful technologically or scientifically with the energy stored/released by the phase change. PCM’s are used in many applications, including the simple heating pack (which I’ll get to in a moment), but also in high temperature applications. Take the molten salts used in solar thermal power plants as an example. Sunlight is focused onto a salt or mixture of salts (like sodium and potassium nitrate for example), which melts the salt into a liquid during the day. When it cools down at night the now-solidifying salt maintains a precise temperature at its phase change for a long period of time (which is good for a power plant), until it freezes completely back into a solid. There are many other PCM materials and many other uses of PCM materials, and knowing the phase diagram so that one can dial in exactly the right temperature of sto red heat release is the first step to making it possible! And let me conclude this Why This Matters with one more striking fact. I started by explaining that 90% of all energy is generated/consumed as thermal energy. But a massive 60% of the heat generated to power our world is wasted! We could capture and recycle much of that energy. There’s a lot of interest and research in the development of new PCMs with higher storage densities (higher enthalpies of fusion), which means new chemistries. The ability to make a new PCM that possesses all of the key desirable metrics for a given application requires a deep understanding of the intermolecular interactions in the PCM which in turn lead to its phase diagram. There’s also exciting new work towards making PCMs “triggerable,” so that it would stay stuck in the liquid state until some external trigger is applied. Then, when triggered, it would solidify and release all of its phase change energy, ready to be “charged” again as a solid. This already happens in some cases, and it takes advantage of the phenomenon of supercooling that we discussed in the lecture. In a pack of sodium 29 Phase change material molecules © source unknown. All rights reserved. This content is excluded from our Creative Commons license. For information, see https://ocw.mit.edu/fairuse. acetate trihydrate (chemistry shown here), for example, it’s fairly easy to supercool, so when the material heats up past its melting point of 58C it becomes a liquid but it can be cooled back down to room temperature without solidifying right away. It stays metastable in a supercooled state, until some trigger is applied like a little external mechanical force (or an ice cube would do it too). That trigger reminds the material that it actually wants to be a solid at this temperature, in other words it provides a nucleation site for the solid phase, and then since it’s a good 30°C below the melting point it all ends up solidifying and giving off all its phase change (enthalpy of fusion) energy. There’s a lot of interest and work towards developing new ways to keep PCMs supercooled, which in turn could make thermal energy storage look much more like electrical energy storage: triggerable and distributable energy on demand. That, in turn, would revolutionize the energy consumption landscape! Why this employs How can a phase diagram get you a job? It’s easier than you might have thought! Many companies make and use materials (like, almost all), and in the use of materials many companies have needs. These could mean the development of completely new materials or it could mean the slight tweaking of existing materials properties. But either way, the starting place for any materials design is the phase diagram of the material. And one place where that starts is in knowing how to calculate phase diagrams. There are companies you could work at that directly make and sell sophisticated software to compute phase diagrams (check out thermo-calc or factsage for example), and then there are the thousands of companies that post jobs where knowledge of how to use such software is required. Want to design new rocket engines? Lockheed has openings where deep knowledge of thermodynamics is required. Or how about the “thermodynamics engineer” posting at United Launch Alliance (which makes rocket engines too). Or if you want to make buildings more energy efficient you could join PassiveLogic, which is working on, “developing the next generation control technology for the future of smart cities,” and is currently seeking a, “thermodynamics and simulation intern.” Or you could join one of MIT Course 3’s spin-outs, Boston Metal, which is working on greener metal production and has a current opening that requests applicants have a, “strong understanding of thermodynamics/phase equilibrium.” Of course, this list goes into the thousands because ultimately any form of engineering uses materials, and the form of materials used is based on its phase diagram. 30 Extra practice 1. Rank the following molecules in ascending vapor pressure order: i) Hexane ii) Methanol iii) Isooctane 2. Three ice cubes are used to chill a soda at 20C. The soda has a mass of 0.25kg. The ice is at 0C and each ice cube has mass 6.0g. Find the temperature when all ice has melted. 3. Imagine a substance with the following points on the phase diagram: a triple point at .5 atm and -5°C; a normal melting point at 20°C; a normal boiling point at 150°C; and a critical point at 5 atm and 1000°C. The solid liquid line is ”normal” (meaning positive sloping). a) Roughly sketch the phase diagram, using units of atmosphere and Kelvin. b) Describe what one would see at pressures and temperatures above 5 atm and 1000°C. c) Describe what will happen to the substance when it begins in a vaccum at -15°C and is slowly pressurized. Diagram of methanol is in the public domain. Source: Wikimedia Commons. Diagram of hexane © source unknown. Diagram of isoctane © Merck KGaA. All rights reserved. This content is excluded from our Creative Commons license. For information, see https://ocw.mit.edu/fairuse. 31 Solutions 1. Methanol has the least vapor pressure because its OH group allows it to hydrogen bond to other methanol molecules. Next is hexane because, though it does not have hydrogen bonding capabilities, it is more linear than isooctane so can experience greater London dispersion forces. Isooctane has the highest vapor pressure because it has no hydrogen bonding capability and is less stackable than hexane so it has less London dispersion forces present. 2. The ice cubes are at the melting temperature of 0C. Heat transfers from the soda to the ice. Melting of the ice occurs in two steps: first the phase change occurs and solid ice transforms into liquid water at the melting temperature, then the temperature of this water rises. Melting yields water at 0C, so more heat is transferred from the soda to the water until the water plus soda system reaches thermal equilibrium. Qice = −Qsoda The heat transferred to the ice is: Qice = mice × Lf + mice × cW × (Tf − 20C) Bringing all terms involcing Tf on the left-hand-side and all other terms on the right hand side, solve for the unknown quantity Tf : Tf = msoda × cW × 20C − mice × Lf (msoda + mice ) × cW The resulting value is 13C. 3. a) 1-solid, 2-liquid, 3-gas, 4-supercritical fluid, point O-triple point, C-critical point -78.5 °C (The phase of dry ice changes from solid to gas at -78.5 °C) b) One would see a super-critical fluid, when approaching the point, one would see the meniscus between the liquid and gas disappear. c) The substance would begin as a gas and as the pressure increases, it would compress and eventually solidify without liquefying as the temperature is below the triple point temperature. 32