Phase Change and Latent Heat, Thermal Energy, Heat, and Work | Physics

Learning objectives

Section Key Terms

condensation	freezing	latent heat	sublimation
latent heat of fusion	latent heat of vaporization	melting	vaporization
phase change	phase diagram	plasma

Phase Changes

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_03_Phases). 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.

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Original figure description: A rock, representing a solid is shown in part (a), along with its tightly bound particles. In part (b), liquid water is shown with its molecules attracted to one another, but not tightly bound. In part (c) oxygen is shown with molecules far apart and bouncing off one another in random directions.

(a) Particles in a solid always have the same neighbors, held close by forces represented here by springs. These particles are essentially in contact with one another. A rock is an example of a solid. This rock retains its shape because of the forces holding its atoms or molecules together. (b) Particles in a liquid are also in close contact but can slide over one another. Forces between them strongly resist attempts to push them closer together and also hold them in close contact. Water is an example of a liquid. Water can flow, but it also remains in an open container because of the forces between its molecules. (c) Particles in a gas are separated by distances that are considerably larger than the size of the particles themselves, and they move about freely. A gas must be held in a closed container to prevent it from moving out into its surroundings. (d) The atmosphere is ionized in the extreme heat of a lightning strike.

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
IonizationGas to plasma

Phase changes to a less energetic state are as follows:

Condensation—Gas to liquid
Freezing—Liquid to solid
Recombination—Plasma to gas
DepositionGas 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 $°C$ stays at 0 $°C$ 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_03_PhaseChng).

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Original figure description: Energy input (melting) converts solid to liquid. Energy output (freezing) converts liquid to solid. Energy input (boiling) converts liquid to gas. Energy output (condensation) converts gas to liquid. Energy input (sublimation) converts solid to gas.

(a) Energy is required to partially overcome the attractive forces between particles in a solid to form a liquid. That same energy must be removed for freezing to take place. (b) Particles are separated by large distances when changing from liquid to vapor, requiring significant energy to overcome molecular attraction. The same energy must be removed for condensation to take place. There is no temperature change until a phase change is completed. (c) Enough energy is added that the liquid state is skipped over completely as a substance undergoes sublimation.

The heat, Q, required to change the phase of a sample of mass m is

$Q = m L_{f}$ (for melting/freezing),

$Q = m L_{v}$ (for vaporization/condensation),

where $L_{f}$ is the latent heat of fusion, and $L_{v}$ 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. $L_{f}$ and $L_{v}$ 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_03 for values of $L_{f}$ and $L_{v}$ of different substances.

Latent Heats of Fusion and Vaporization, along with Melting and Boiling Points
Substance	Melting Point ( $°C$ )	Lf (kJ/kg)	Boiling Point ( $°C$ )	Lv (kJ/kg)
Helium	‒269.7	5.23	‒268.9	20.9
Hydrogen	‒259.3	58.6	‒252.9	452
Nitrogen	‒210.0	25.5	‒195.8	201
Oxygen	‒218.8	13.8	‒183.0	213
Ethanol	‒114	104	78.3	854
Ammonia	‒78	332	‒33.4	1370
Mercury	‒38.9	11.8	357	272
Water	0.00	334	100.0	2256
Sulfur	119	38.1	444.6	326
Lead	327	24.5	1750	871
Antimony	631	165	1440	561
Aluminum	660	380	2520	11400
Silver	961	88.3	2193	2336
Gold	1063	64.5	2660	1578
Copper	1083	134	2595	5069
Uranium	1133	84	3900	1900
Tungsten	3410	184	5900	4810

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_03_WaterPhases. The ice starts out at −20 $°C$ , 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 $°C$ 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 $°C$ , 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.

View original figure (external; image not reproduced in this text edition)

Original figure description: A graph of change in heat per mass on the x-axis and change in temperature on the y-axis is shown. It is level during phase changes, indicating no change in temperature, and rises steeply after phase changes are completed.

A graph of temperature versus added energy. The system is constructed so that no vapor forms while ice warms to become liquid water, and so when vaporization occurs, the vapor remains in the system. The long stretches of constant temperature values at 0

°C

and 100

°C

reflect the large latent heats of melting and vaporization, respectively.

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 $Q = m L_{v}$ . Latent heat is also released into the environment when a liquid freezes, and can be calculated from $Q = m L_{f}$ .

Making Ice Cream

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Original figure description: A woman holds a strawberry ice cream cone.

With the proper ingredients, some ice and a couple of plastic bags, you could make your own ice cream in five minutes. (ElinorD, Wikimedia Commons)

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_03_IceCream).

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.

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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 $°C$ (freezing point), and b) how much energy is required to vaporize 1.000 kg of water at 100 $°C$ (boiling point).

Solution to (a)

The energy to melt 1.000 kg of ice is

$Q = m L_{f} = (1 .000 kg) (334 kJ/kg) = 334 kJ.$

Solution to (b)

The energy to vaporize 1.000 kg of liquid water is

$Q = m L_{v} = (1 .000 kg) (2256 kJ/kg) = 2256 kJ.$

Discussion

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 $°C$ to 79.8 $°C$ . 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 $°C$ and with a mass of $m_{s o d a} = 0.25 kg$ . The ice is at 0 $°C$ 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.

Strategy

The ice cubes are at the melting temperature of 0 $°C$ . 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 $°C$ , 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.

$Q_{i c e} = - Q_{s o d a}$

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 $Q = m c Δ T$ . For the ice, the temperature change is $T_{f} - 0 °C$ . The total heat transferred to the ice is therefore

$Q_{i c e} = m_{i c e} L_{f} + m_{i c e} c_{w} (T_{f} - 0 °C) .$

Since the soda doesn’t change phase, but only temperature, the heat given off by the soda is

$Q_{s o d a} = m_{s o d a} c_{w} (T_{f} - 20 °C) .$

Since $Q_{i c e} = - Q_{s o d a}$ ,

$m_{i c e} L_{f} + m_{i c e} c_{w} (T_{f} - 0 °C) = - m_{s o d a} c_{w} (T_{f} - 20 °C) .$

Bringing all terms involving $T_{f}$ to the left-hand-side of the equation, and all other terms to the right-hand-side, we can solve for $T_{f}$ .

$T_{f} = \frac{m_{s o d a} c_{w} (20 °C) - m_{i c e} L_{f}}{(m_{s o d a} + m_{i c e}) c_{w}}$

Substituting the known quantities

$T_{f} = \frac{(0.25 kg) (4186 J/kg \cdot °C) (20 °C) - (0.018 kg) (334,000 J/kg)}{(0 .25 kg + 0 .018 kg) (4186 K/kg \cdot °C)} = 13 °C$

Discussion

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.

Practice Problems

How much energy is needed to melt 2.00 kg of ice at 0 °C ?

334 kJ
336 kJ
167 kJ
668 kJ

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Check Your Understanding

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In which phases of matter are molecules capable of changing their positions?

gas, liquid, solid
liquid, plasma, solid
liquid, gas, plasma
plasma, gas, solid

Section Summary

Most substances have four distinct phases: solid, liquid, gas, and plasma.
Gas is the most energetic state and solid is the least.
During a phase change, a substance undergoes transition to a higher energy state when heat is added, or to a lower energy state when heat is removed.
Heat is added to a substance during melting and vaporization.
Latent heat is released by a substance during condensation and freezing.
Phase changes occur at fixed temperatures called boiling and freezing (or melting) points for a given substance.

Key Equations

heat transfer for melting/freezing phase change	$Q = m L_{f}$
heat transfer for vaporization/condensation phase change	$Q = m L_{v}$

Concept Items

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In which two phases of matter do atoms and molecules have the most distance between them?

gas and solid
gas and liquid
gas and plasma
liquid and plasma

Critical Thinking

Assume 1.0 kg of ice at 0 °C starts to melt. It absorbs 300 kJ of energy by heat. What is the temperature of the water afterwards?

10 °C
20 °C
5 °C
0 °C

Problems

How much energy would it take to heat 1.00 kg of ice at 0 °C to water at 15.0 °C?

271 kJ
334 kJ
62.8 kJ
397 kJ

Ice cubes are used to chill a soda with a mass m_soda = 0.300 kg at 15.0 °C. The ice is at 0 °C, and the total mass of the ice cubes is 0.020 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 ice has melted.

19.02 °C
90.3 °C
0.11 °C
9.03 °C

Test Prep Multiple Choice

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Which substance has the largest latent heat of fusion?

gold
water
mercury
tungsten

In which phase changes does matter undergo a transition to a more energetic state?

freezing and vaporization
melting and sublimation
melting and vaporization
melting and freezing

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Test Prep Short Answer

Upon what does the required amount of heat removed to freeze a sample of a substance depend?

The mass of the substance and its latent heat of vaporization
The mass of the substance and its latent heat of fusion
The mass of the substance and its latent heat of sublimation
The mass of the substance only

What do latent heats, L_f and L_v, depend on?

L_f and L_v depend on the forces between the particles in the substance.
L_f and L_v depend on the mass of the substance.
L_f and L_v depend on the volume of the substance.
L_f and L_v depend on the temperature of the substance.

How much energy is required to melt 7.00 kg a block of aluminum that is at its melting point? (Latent heat of fusion of aluminum is 380 kJ/kg.)

54.3 kJ
2.66 kJ
0.0184 kJ
2.66×10³ kJ

A 3.00 kg sample of a substance is at its boiling point. If 5,360 kJ of energy are enough to boil away the entire substance, what is its latent heat of vaporization?

2,685 kJ/kg
3,580 kJ/kg
895 kJ/kg
1,790 kJ/kg

Performance Task

You have been tasked with designing a baking pan that will bake batter the fastest. There are four materials available for you to test.

Four pans of similar design, consisting of aluminum, iron (steel), copper, and glass
Oven or similar heating source
Device for measuring high temperatures
Balance for measuring mass

Instructions

Procedure

Design a safe experiment to test the specific heat of each material (i.e., no extreme temperatures should be used)
Write down the materials needed for your experiment and the procedure you will follow. Make sure that you include every detail, so that the experiment can be repeated by others.
Carry out the experiment and record any data collected.
Review your results and make a recommendation as to which metal should be used for the pan.
1. What physical quantities do you need to measure to determine the specific heats for the different materials?
2. How does the glass differ from the metals in terms of thermal properties?
3. What are your sources of error?

Test Prep Extended Response

True or falseYou have an ice cube floating in a glass of water with a thin thread resting across the cube. If you cover the ice cube and thread with a layer of salt, they will stick together, so that you are able to lift the ice-cube when you pick up the thread.

True
False

Suppose the energy required to freeze 0.250 kg of water were added to the same mass of water at an initial temperature of 1.0 °C. What would be the final temperature of the water?

-69.8 °C
79.8 °C
-78.8 °C
80.8 °C

Glossary

condensation: phase change from gas to liquid
freezing: phase change from liquid to solid
latent heat: heat related to the phase change of a substance rather than a change of temperature
latent heat of fusion: amount of heat needed to cause a phase change between solid and liquid
latent heat of vaporization: amount of heat needed to cause a phase change between liquid and gas
melting: phase change from solid to liquid
phase change: transition between solid, liquid, or gas states of a substance
plasma: ionized gas that is a combination of the negatively charged free electrons and positively charged ions
sublimation: phase change from solid to gas
vaporization: phase change from liquid to gas

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