By the end of this section, you will be able to do the following:
- Explain changes in heat during changes of state, and describe latent heats of fusion and vaporization
- Solve problems involving thermal energy changes when heating and cooling substances with phase changes
|latent heat of fusion
|latent heat of vaporization
So far, we have learned that adding thermal energy by heat increases the temperature of a substance. But surprisingly, there are situations where adding energy does not change the temperature of a substance at all! Instead, the additional thermal energy acts to loosen bonds between molecules or atoms and causes a phase change. Because this energy enters or leaves a system during a phase change without causing a temperature change in the system, it is known as latent heat (latent means hidden).
The three phases of matter that you frequently encounter are solid, liquid and gas (see Figure 11.9). Solid has the least energetic state; atoms in solids are in close contact, with forces between them that allow the particles to vibrate but not change position with neighboring particles. (These forces can be thought of as springs that can be stretched or compressed, but not easily broken.)
Liquid has a more energetic state, in which particles can slide smoothly past one another and change neighbors, although they are still held together by their mutual attraction.
Gas has a more energetic state than liquid, in which particles are broken free of their bonds. Particles in gases are separated by distances that are large compared with the size of the particles.
The most energetic state of all is plasma. Although you may not have heard much about plasma, it is actually the most common state of matter in the universe—stars are made up of plasma, as is lightning. The plasma state is reached by heating a gas to the point where particles are pulled apart, separating the electrons from the rest of the particle. This produces an ionized gas that is a combination of the negatively charged free electrons and positively charged ions, known as plasma.
During a phase change, matter changes from one phase to another, either through the addition of energy by heat and the transition to a more energetic state, or from the removal of energy by heat and the transition to a less energetic state.
Phase changes to a more energetic state include the following:
- Melting—Solid to liquid
- Vaporization—Liquid to gas (included boiling and evaporation)
- Sublimation—Solid to gas
Phase changes to a less energetic state are as follows:
- Condensation—Gas to liquid
- Freezing—Liquid to solid
Energy is required to melt a solid because the bonds between the particles in the solid must be broken. Since the energy involved in a phase changes is used to break bonds, there is no increase in the kinetic energies of the particles, and therefore no rise in temperature. Similarly, energy is needed to vaporize a liquid to overcome the attractive forces between particles in the liquid. There is no temperature change until a phase change is completed. The temperature of a cup of soda and ice that is initially at 0 stays at 0 until all of the ice has melted. In the reverse of these processes—freezing and condensation—energy is released from the latent heat (see Figure 11.10).
The heat, Q, required to change the phase of a sample of mass m is
where is the latent heat of fusion, and is the latent heat of vaporization. The latent heat of fusion is the amount of heat needed to cause a phase change between solid and liquid. The latent heat of vaporization is the amount of heat needed to cause a phase change between liquid and gas. and are coefficients that vary from substance to substance, depending on the strength of intermolecular forces, and both have standard units of J/kg. See Table 11.2 for values of and of different substances.
|Melting Point ( )
|Boiling Point ( )
Let’s consider the example of adding heat to ice to examine its transitions through all three phases—solid to liquid to gas. A phase diagram indicating the temperature changes of water as energy is added is shown in Figure 11.11. The ice starts out at −20, and its temperature rises linearly, absorbing heat at a constant rate until it reaches 0 Once at this temperature, the ice gradually melts, absorbing 334 kJ/kg. The temperature remains constant at 0 during this phase change. Once all the ice has melted, the temperature of the liquid water rises, absorbing heat at a new constant rate. At 100, the water begins to boil and the temperature again remains constant while the water absorbs 2256 kJ/kg during this phase change. When all the liquid has become steam, the temperature rises again at a constant rate.
We have seen that vaporization requires heat transfer to a substance from its surroundings. Condensation is the reverse process, where heat in transferred away from a substance to its surroundings. This release of latent heat increases the temperature of the surroundings. Energy must be removed from the condensing particles to make a vapor condense. This is why condensation occurs on cold surfaces: the heat transfers energy away from the warm vapor to the cold surface. The energy is exactly the same as that required to cause the phase change in the other direction, from liquid to vapor, and so it can be calculated from . Latent heat is also released into the environment when a liquid freezes, and can be calculated from .
Fun In Physics
Making Ice Cream
Ice cream is certainly easy enough to buy at the supermarket, but for the hardcore ice cream enthusiast, that may not be satisfying enough. Going through the process of making your own ice cream lets you invent your own flavors and marvel at the physics firsthand (Figure 11.12).
The first step to making homemade ice cream is to mix heavy cream, whole milk, sugar, and your flavor of choice; it could be as simple as cocoa powder or vanilla extract, or as fancy as pomegranates or pistachios.
The next step is to pour the mixture into a container that is deep enough that you will be able to churn the mixture without it spilling over, and that is also freezer-safe. After placing it in the freezer, the ice cream has to be stirred vigorously every 45 minutes for four to five hours. This slows the freezing process and prevents the ice cream from turning into a solid block of ice. Most people prefer a soft creamy texture instead of one giant popsicle.
As it freezes, the cream undergoes a phase change from liquid to solid. By now, we’re experienced enough to know that this means that the cream must experience a loss of heat. Where does that heat go? Due to the temperature difference between the freezer and the ice cream mixture, heat transfers thermal energy from the ice cream to the air in the freezer. Once the temperature in the freezer rises enough, the freezer is cooled by pumping excess heat outside into the kitchen.
A faster way to make ice cream is to chill it by placing the mixture in a plastic bag, surrounded by another plastic bag half full of ice. (You can also add a teaspoon of salt to the outer bag to lower the temperature of the ice/salt mixture.) Shaking the bag for five minutes churns the ice cream while cooling it evenly. In this case, the heat transfers energy out of the ice cream mixture and into the ice during the phase change.
This video gives a demonstration of how to make home-made ice cream using ice and plastic bags.
- Ice has a smaller specific heat than the surrounding air in a freezer. Hence, it absorbs more energy from the ice-cream mixture.
- Ice has a smaller specific heat than the surrounding air in a freezer. Hence, it absorbs less energy from the ice-cream mixture.
- Ice has a greater specific heat than the surrounding air in a freezer. Hence, it absorbs more energy from the ice-cream mixture.
- Ice has a greater specific heat than the surrounding air in a freezer. Hence, it absorbs less energy from the ice-cream mixture.
Solving Thermal Energy Problems with Phase Changes
Solving Thermal Energy Problems with Phase Changes
Calculating Heat Required for a Phase Change
Calculate a) how much energy is needed to melt 1.000 kg of ice at 0 (freezing point), and b) how much energy is required to vaporize 1.000 kg of water at 100 (boiling point).
STRATEGY FOR (A)
Using the equation for the heat required for melting, and the value of the latent heat of fusion of water from the previous table, we can solve for part (a).
The energy to melt 1.000 kg of ice is
STRATEGY FOR (B)
To solve part (b), we use the equation for heat required for vaporization, along with the latent heat of vaporization of water from the previous table.
The energy to vaporize 1.000 kg of liquid water is
The amount of energy need to melt a kilogram of ice (334 kJ) is the same amount of energy needed to raise the temperature of 1.000 kg of liquid water from 0 to 79.8. This example shows that the energy for a phase change is enormous compared to energy associated with temperature changes. It also demonstrates that the amount of energy needed for vaporization is even greater.
Calculating Final Temperature from Phase Change: Cooling Soda with Ice Cubes
Ice cubes are used to chill a soda at 20 and with a mass of . The ice is at 0 and the total mass of the ice cubes is 0.018 kg. Assume that the soda is kept in a foam container so that heat loss can be ignored, and that the soda has the same specific heat as water. Find the final temperature when all of the ice has melted.
The ice cubes are at the melting temperature of 0. Heat is transferred from the soda to the ice for melting. Melting of 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 0, so more heat is transferred from the soda to this water until they are the same temperature. Since the amount of heat leaving the soda is the same as the amount of heat transferred to the ice.
The heat transferred to the ice goes partly toward the phase change (melting), and partly toward raising the temperature after melting. Recall from the last section that the relationship between heat and temperature change is . For the ice, the temperature change is . The total heat transferred to the ice is therefore
Since the soda doesn’t change phase, but only temperature, the heat given off by the soda is
Bringing all terms involving to the left-hand-side of the equation, and all other terms to the right-hand-side, we can solve for .
Substituting the known quantities
This example shows the enormous energies involved during a phase change. The mass of the ice is about 7 percent the mass of the soda, yet it causes a noticeable change in the soda’s temperature.
Tips For Success
If the ice were not already at the freezing point, we would also have to factor in how much energy would go into raising its temperature up to 0, before the phase change occurs. This would be a realistic scenario, because the temperature of ice is often below 0.
How much energy is needed to melt 2.00 kg of ice at 0 °C ?
- 334 kJ
- 336 kJ
- 167 kJ
- 668 kJ
Check Your Understanding
Check Your Understanding
- It is the heat that must transfer energy to or from a system in order to cause a mass change with a slight change in the temperature of the system.
- It is the heat that must transfer energy to or from a system in order to cause a mass change without a temperature change in the system.
- It is the heat that must transfer energy to or from a system in order to cause a phase change with a slight change in the temperature of the system.
- It is the heat that must transfer energy to or from a system in order to cause a phase change without a temperature change in the system.
In which phases of matter are molecules capable of changing their positions?
- gas, liquid, solid
- liquid, plasma, solid
- liquid, gas, plasma
- plasma, gas, solid