Is There A Temperature Change During A Phase Change?

Section Learning Objectives

Past the end of this section, you will exist able to exercise the following:

• Explicate 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

Instructor Back up

Instructor Support

The learning objectives in this section will assist your students chief the following standards:

• (6) Science concepts. The student knows that changes occur inside a physical system and applies the laws of conservation of energy and momentum. The student is expected to:
  • (E) describe how the macroscopic properties of a thermodynamic system such every bit temperature, specific rut, and pressure are related to the molecular level of matter, including kinetic or potential energy of atoms;
  • (F) contrast and give examples of dissimilar processes of thermal energy transfer, including conduction, convection, and radiation.

Section Key Terms

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

Teacher Support

Teacher Back up

Introduce this section by asking students to give examples of solids, liquids, and gases.

Stage Changes

Then far, we take learned that calculation thermal energy past heat increases the temperature of a substance. But surprisingly, there are situations where calculation free energy does not alter the temperature of a substance at all! Instead, the boosted thermal energy acts to loosen bonds between molecules or atoms and causes a phase change. Because this energy enters or leaves a arrangement 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 run across are solid, liquid and gas (see Figure xi.8). Solid has the to the lowest degree energetic state; atoms in solids are in close contact, with forces betwixt them that allow the particles to vibrate merely not change position with neighboring particles. (These forces can be idea of equally springs that can exist stretched or compressed, merely not easily broken.)

Liquid has a more energetic state, in which particles can slide smoothly past ane 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 cleaved gratuitous of their bonds. Particles in gases are separated past distances that are big compared with the size of the particles.

The most energetic state of all is plasma. Although you may non take heard much about plasma, it is actually the nigh mutual state of matter in the universe—stars are made up of plasma, every bit is lightning. The plasma country is reached by heating a gas to the point where particles are pulled autonomously, separating the electrons from the residual of the particle. This produces an ionized gas that is a combination of the negatively charged complimentary electrons and positively charged ions, known as plasma.

Figure 11.8 (a) Particles in a solid always have the aforementioned neighbors, held close past forces represented hither 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 property its atoms or molecules together. (b) Particles in a liquid are likewise in close contact but tin slide over one some other. Forces betwixt them strongly resist attempts to push them closer together and besides hold them in close contact. Water is an instance of a liquid. Water can menstruum, but it also remains in an open container considering of the forces between its molecules. (c) Particles in a gas are separated past distances that are considerably larger than the size of the particles themselves, and they motion about freely. A gas must exist held in a closed container to prevent information technology from moving out into its surroundings. (d) The atmosphere is ionized in the extreme heat of a lightning strike.

During a phase change, thing changes from 1 phase to another, either through the addition of free energy by estrus and the transition to a more energetic country, or from the removal of free energy by oestrus and the transition to a less energetic country.

Stage 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 land are as follows:

• Condensation—Gas to liquid
• Freezing—Liquid to solid

Energy is required to melt a solid because the bonds betwixt the particles in the solid must be cleaved. Since the energy involved in a stage 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 alter is completed. The temperature of a cup of soda and ice that is initially at 0 $\text{°C}$ stays at 0 $\text{°C}$ until all of the water ice has melted. In the reverse of these processes—freezing and condensation—free energy is released from the latent estrus (see Figure 11.ix).

Teacher Support

Instructor Support

[BL] [OL] Ask students if the same amount of energy is absorbed or released in melting or freezing a particular quantity of a substance.

[AL] Ask student how water is able to evaporate even when it is at room temperature and non at 100 $\text{°C}$ .

Figure 11.9 (a) Energy is required to partially overcome the attractive forces betwixt particles in a solid to form a liquid. That same free energy must be removed for freezing to accept place. (b) Particles are separated by large distances when irresolute 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 equally a substance undergoes sublimation.

The oestrus, Q, required to modify the stage of a sample of mass one thousand is

$Q=m{\mathrm{50}}_f$ (for melting/freezing),

$Q=\mathrm{one\; thousand}{L}_v$ (for vaporization/condensation),

where ${\mathrm{Fifty}}_f$ is the latent heat of fusion, and $L_v$ is the latent rut of vaporization. The latent oestrus of fusion is the corporeality of heat needed to crusade a phase change between solid and liquid. The latent oestrus of vaporization is the amount of heat needed to cause a phase alter between liquid and gas. $L_f$ and $L_{\mathrm{five}}$ are coefficients that vary from substance to substance, depending on the strength of intermolecular forces, and both accept standard units of J/kg. See Table eleven.3 for values of ${\mathrm{Fifty}}_f$ and $L_v$ of different substances.

Substance	Melting Point ( $\mathrm{°C}$ )	Lf (kJ/kg)	Boiling Signal ( $\mathrm{°C}$ )	Lv (kJ/kg)
Helium	‒269.7	5.23	‒268.nine	20.nine
Hydrogen	‒259.3	58.6	‒252.9	452
Nitrogen	‒210.0	25.v	‒195.eight	201
Oxygen	‒218.8	13.8	‒183.0	213
Ethanol	‒114	104	78.3	854
Ammonia	‒78	332	‒33.4	1370
Mercury	‒38.ix	11.eight	357	272
Water	0.00	334	100.0	2256
Sulfur	119	38.1	444.vi	326
Atomic number 82	327	24.v	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

Table 11.three Latent Heats of Fusion and Vaporization, along with Melting and Humid Points

Permit's consider the example of adding oestrus to ice to examine its transitions through all three phases—solid to liquid to gas. A stage diagram indicating the temperature changes of water as energy is added is shown in Figure 11.10. The ice starts out at −xx $\text{°C}$ , and its temperature rises linearly, arresting heat at a constant rate until it reaches 0 $\text{°}\text{.}$ Once at this temperature, the ice gradually melts, absorbing 334 kJ/kg. The temperature remains abiding at 0 $\text{°C}$ during this phase change. Once all the ice has melted, the temperature of the liquid water rises, arresting heat at a new abiding rate. At 100 $\text{°C}$ , the water begins to boil and the temperature again remains constant while the h2o absorbs 2256 kJ/kg during this phase modify. When all the liquid has go steam, the temperature rises once again at a constant rate.

Figure 11.ten 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 $\text{°C}$ and 100 $\text{°C}$ 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 procedure, where estrus in transferred away from a substance to its environs. 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 common 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 $Q=\mathrm{one\; thousand}{\mathrm{Fifty}}_5$ . Latent heat is also released into the environment when a liquid freezes, and can exist calculated from $Q=m{\mathrm{Fifty}}_f$ .

Fun In Physics

Making Ice Cream

Figure xi.11 With the proper ingredients, some ice and a couple of plastic bags, you could brand your ain ice foam in v minutes. (ElinorD, Wikimedia Commons)

Ice cream is certainly like shooting fish in a barrel enough to buy at the supermarket, but for the hardcore ice foam enthusiast, that may not be satisfying plenty. Going through the process of making your own water ice cream lets you invent your own flavors and marvel at the physics firsthand (Figure 11.11).

The first step to making homemade ice foam is to mix heavy foam, whole milk, sugar, and your flavor of choice; information technology could exist as unproblematic as cocoa pulverisation or vanilla extract, or as fancy as pomegranates or pistachios.

The next step is to pour the mixture into a container that is deep plenty that you volition be able to churn the mixture without information technology spilling over, and that is also freezer-safety. After placing it in the freezer, the ice cream has to exist stirred vigorously every 45 minutes for four to v hours. This slows the freezing process and prevents the water ice foam from turning into a solid block of water ice. Most people adopt a soft creamy texture instead of one behemothic popsicle.

As it freezes, the foam undergoes a stage modify from liquid to solid. By now, we're experienced enough to know that this means that the cream must experience a loss of rut. Where does that heat go? Due to the temperature divergence betwixt the freezer and the ice foam 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 fashion to make ice foam is to chill it by placing the mixture in a plastic bag, surrounded by another plastic bag half full of ice. (You can as well add together a teaspoon of salt to the outer handbag to lower the temperature of the ice/table salt mixture.) Shaking the bag for 5 minutes churns the ice cream while cooling information technology 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-fabricated ice foam using ice and plastic numberless.

Why does the water ice bag method work so much faster than the freezer method for making ice cream?

1. Ice has a smaller specific heat than the surrounding air in a freezer. Hence, it absorbs more than energy from the water ice-cream mixture.

2. Ice has a smaller specific heat than the surrounding air in a freezer. Hence, information technology absorbs less free energy from the ice-foam mixture.

3. Ice has a greater specific rut than the surrounding air in a freezer. Hence, it absorbs more energy from the ice-cream mixture.

4. Water ice has a greater specific heat than the surrounding air in a freezer. Hence, information technology absorbs less energy from the water ice-cream mixture.

Solving Thermal Energy Problems with Phase Changes

Worked Example

Calculating Rut Required for a Stage Change

Calculate a) how much energy is needed to cook one.000 kg of ice at 0 $\text{°C}$ (freezing point), and b) how much energy is required to vaporize 1.000 kg of h2o at 100 $\text{°C}$ (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, nosotros can solve for part (a).

Strategy FOR (B)

To solve role (b), we utilize the equation for heat required for vaporization, along with the latent heat of vaporization of water from the previous table.

Discussion

The corporeality of energy need to melt a kilogram of ice (334 kJ) is the same amount of free energy needed to raise the temperature of one.000 kg of liquid h2o from 0 $\text{°C}$ to 79.8 $\text{°C}$ . This example shows that the free energy for a stage change is enormous compared to free energy associated with temperature changes. It also demonstrates that the amount of energy needed for vaporization is even greater.

Worked Instance

Calculating Final Temperature from Phase Alter: Cooling Soda with Ice Cubes

Ice cubes are used to chill a soda at 20 $\text{°C}$ and with a mass of $k_{soda}=0.25\text{ kg}$ . The ice is at 0 $\text{°C}$ and the full mass of the water ice cubes is 0.018 kg. Presume that the soda is kept in a foam container so that heat loss can exist ignored, and that the soda has the same specific oestrus as water. Find the final temperature when all of the ice has melted.

Strategy

The ice cubes are at the melting temperature of 0 $\text{°C}$ . Heat is transferred from the soda to the ice for melting. Melting of water ice occurs in two steps: first, the phase change occurs and solid (ice) transforms into liquid water at the melting temperature; and then, the temperature of this water rises. Melting yields water at 0 $\text{°C}$ , so more than 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 rut transferred to the ice.

$$Q_{ice}=-Q_{soda}$$

11.20

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 modify is $Q=mc\Delta T$ . For the water ice, the temperature change is $T_f-0\text{°C}$ . The full heat transferred to the ice is therefore

$$Q_{ic\mathrm{eastward}}={\mathrm{thousand}}_{ice}{\mathrm{Fifty}}_f+m_{ice}{c}_{\mathrm{westward}}(T_f-0\text{°C}).$$

11.21

Since the soda doesn't alter phase, but simply temperature, the heat given off by the soda is

$$Q_{\mathrm{due\; south}oda}={\mathrm{one\; thousand}}_{soda}{c}_w(T_f-\mathrm{twenty}\text{°C}).$$

xi.22

Since $Q_{ice}=-Q_{soda}$ ,

$${\mathrm{1000}}_{ic\mathrm{east}}{\mathrm{50}}_f+{\mathrm{thou}}_{ice}{c}_{\mathrm{west}}(T_f-0\text{°C})=-m_{\mathrm{south}oda}{c}_{\mathrm{west}}(T_f-\mathrm{xx}\text{°C}).$$

eleven.23

Bringing all terms involving $T_f$ to the left-paw-side of the equation, and all other terms to the right-hand-side, nosotros can solve for $T_f$ .

$$T_f=\frac{m_{\mathrm{southward}oda}{c}_{\mathrm{westward}}(\mathrm{xx}\text{°C})-m_{ice}{L}_f}{(m_{\mathrm{southward}oda}+m_{ice})c_w}$$

11.24

Substituting the known quantities

$$T_f=\frac{\left(0.25\text{ kg}\right)\left(4186\text{ J/kg}\cdot \text{°C}\right)\left(20\text{°C}\right)-\left(0.018\text{ kg}\right)\left(\text{334,000 J/kg}\right)}{\left(\text{0}\text{.25 kg + 0}\text{.018 kg}\right)\left(4186\text{ One thousand/kg}\cdot \text{°C}\right)}=\mathrm{xiii}\text{°C}$$

eleven.25

Discussion

This example shows the enormous energies involved during a stage change. The mass of the water ice is near vii pct the mass of the soda, yet information technology causes a noticeable change in the soda's temperature.

Tips For Success

If the ice were non already at the freezing indicate, we would also have to factor in how much energy would go into raising its temperature upwardly to 0 $\text{°C}$ , before the phase change occurs. This would be a realistic scenario, because the temperature of water ice is often below 0 $\text{°C}$ .

Practice Issues

11 .

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

1. 334 kJ
2. 336 kJ
3. 167 kJ
4. 668 kJ

12 .

If 2500\,\text{kJ} of energy is just enough to melt three.0\,\text{kg} of a substance, what is the substance's latent oestrus of fusion?

1. 7500\,\text{kJ} \cdot \text{kg}

2. 7500\,\text{kJ/kg}

3. 830\,\text{kJ} \cdot \text{kg}

4. 830\,\text{kJ/kg}

Check Your Understanding

Teacher Support

Instructor Back up

Use these questions to assess student achievement of the section's learning objectives. If students are struggling with a specific objective, these questions will help identify which and direct students to the relevant content.

13 .

What is latent heat?

1. Information technology is the heat that must transfer energy to or from a arrangement in order to cause a mass change with a slight change in the temperature of the system.

2. It is the heat that must transfer free energy to or from a system in order to crusade a mass change without a temperature change in the system.

3. It is the heat that must transfer energy to or from a arrangement in order to cause a phase modify with a slight change in the temperature of the system.

4. It is the rut that must transfer energy to or from a system in order to crusade a phase change without a temperature alter in the system.

14 .

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

1. gas, liquid, solid
2. liquid, plasma, solid
3. liquid, gas, plasma
4. plasma, gas, solid

Source: https://openstax.org/books/physics/pages/11-3-phase-change-and-latent-heat

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