# Change of State

## Explore the energy required to convert a substance between gas, liquid, and solid

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Change of State

TEKS

6E:  Describe how the macroscopic properties of a thermodynamic system such as temperature, specific heat, and pressure are related to the molecular level of matter, including kinetic or potential energy of atoms.

6G:  Analyze and explain everyday examples that illustrate the laws of thermodynamics, including the law of conservation of energy and the law of entropy.

### Objective

• Students will understand how the heat of fusion and heat of vaporization energy is used to create a phase change and how a phase change can be used to do work.

### Equations

\begin{align*}Q = mc \Delta t\end{align*}

\begin{align*}Q = mH_f\end{align*}

\begin{align*}Q = mH_v\end{align*}

License: CC BY-NC 3.0

Steam traction engine depended on water changing from a liquid to gaseous state [Figure1]

Before the internal combustion engine was invented, steam engines were the power source for ships, locomotives, tractors, lumber saws, and most industrial machines. Coal or wood was burned to boil water into steam, which ran the engine. As the water is boiled it creates steam under pressure. The steam is allowed to expand to do positive work on the pistons. The work done on the piston to turn the wheels is at the expense of the steams internal energy. The steam loses its internal energy by being able to expand under lower pressure of the outside atmosphere. The largest problem with steam engines was their size!  A large oven had to support fire which was used to heat the water to a boil.  The work done by a steam engine does not come free.

### Change of State

Most substances may exist in any of the three common states of matter. In the gaseous state, the molecular motion has completely overcome any attraction between the particles and the particles are totally separate from each other. There are large spaces between the particles and they move large distances between collisions. In the liquid state, the molecular motion and the molecular attractions are more balanced. While the particles stay more or less in contact with each other, they are still free to move and can slide past one another easily. In the solid state, the attractive forces dominate. The particles are pulled together into a tightly packed pattern which does not allow the particles to pass each other. The molecular motion in this form is essentially reduced to vibration in place. Increasing the temperature of a substance means increasing the molecular motion (kinetic energy) of the molecules in the substance. The phase in which a substance exists is the result of a competition between attractive forces and molecular motion.

Credit: Christopher Auyeung
Source: CK-12 Foundation
License: CC BY-NC 3.0

For most substances, when the temperature of the solid is raised high enough, the substance changes to a liquid, and when the temperature of the liquid is raised high enough, the substance changes to a gas. We typically visualize a solid as tiny particles in constant motion held together by attractive forces. As we add heat to the solid, the motion, or the kinetic energy, of the particles increases. At some temperature, the motion of the particles becomes great enough to overcome the attractive forces. The thermal energy that was added to the solid up to this point was absorbed by the solid as kinetic energy, increasing the speed of the molecules. The lowest temperature at which the particles are able to exist in the liquid form is called the freezing point as it turns from a liquid to a solid.  The temperature at which a solid begins to turn into a liquid is called the melting point

In order for the molecules to actually separate from each other, more energy must be added. This energy, called latent heat of fusion or heat of melting, is absorbed by the particles as potential energy as the solid changes to a liquid. Recognize that, once the temperature of a solid has been raised to the melting point, it is still necessary for the solid to absorb additional thermal energy in the form of potential energy as the molecules separate.

The boiling point of a liquid is the temperature at which the particles have sufficient molecular motion to exist in the form of a gas and will rapidly break away from the liquid state. This process can happen slowly in a process called evaporation.  The temperature that gasses condense into liquids is called the condensation point. Once again, however, in order for the particles to separate to the gaseous form, they must absorb a sufficient amount of potential energy. The amount of potential energy necessary for a phase change to gaseous form is called the latent heat of vaporization. Consider the heating curve shown below.

Credit: Christopher Auyeung
Source: CK-12 Foundation
License: CC BY-NC 3.0

Heating curve of water [Figure3]

The heating curve shown is for water but other substances have similarly shaped heating curves. Suppose you begin with solid water (ice) at -30°C and add heat at a constant rate. The heat you add in the beginning will be absorbed as kinetic energy and the temperature of the solid will increase. When you reach a temperature of 0°C (the melting point for water), the heat you add is no longer absorbed as kinetic energy. Instead, the added heat is absorbed as potential energy and the particles separate from each other. During the flat part of the curve labeled “melting”, heat is being added constantly but the temperature does not increase. At the left edge of this flat line, the water is solid; by the time enough heat has been added to get to the right edge, the water is liquid, but maintains the same temperature. Once all the water is in the liquid form, the added heat will once again be absorbed as kinetic energy and the temperature will increase again. During the time labeled “water being heated as a liquid”, all the added heat is absorbed as kinetic energy.

When a temperature of 100°C (the boiling point of water) is reached, the added heat is once again absorbed as potential energy and the molecules separate from liquid form into gaseous form. When all the substance has been converted into gas, the temperature will again begin to rise.

Here is a simulation where you can interactively change the state of matter of molecules.

Here is a follow-up activity to complete while using this simulation.

 Substance Heat of Fusion, \begin{align*}\underline{H_f \ (J/kg)}\end{align*} Heat of Vaporization, \begin{align*}\underline{H_v \ (J/kg)}\end{align*} Copper \begin{align*}2.05 \times 10^5\end{align*} \begin{align*}5.07 \times 10^6\end{align*} Gold \begin{align*}6.30 \times 10^4\end{align*} \begin{align*}1.64 \times 10^6\end{align*} Iron \begin{align*}2.66 \times 10^5\end{align*} \begin{align*}6.29 \times 10^6\end{align*} Methanol \begin{align*}1.09 \times 10^5\end{align*} \begin{align*}8.78 \times 10^5\end{align*} Water \begin{align*}3.34 \times 10^5\end{align*} \begin{align*}2.26 \times 10^6\end{align*}

When the temperature of a substance is changing, we can use the specific heat to determine the amount of heat that is being gained or lost. When a substance is changing phase, we can use the heat of fusion or heat of vaporization to determine the amount of heat being gained or lost. When a substance freezes from liquid to solid, the amount of heat given off is exactly the same as the amount of heat absorbed when the substance melts from solid to liquid. The equations for heat gained or lost are given here:

The heat gained or lost during a temperature change: \begin{align*}Q = mc \Delta t\end{align*}.

The heat gained or lost during a phase change of solid to liquid: \begin{align*}Q = mH_f\end{align*}.

The heat gained or lost during a phase change of liquid to gas: \begin{align*}Q = mH_v\end{align*}.

#### Change in Volume Can Do Work:

The First Law of Thermodynamics describes how heat added or taken away from a system can change the internal energy of the system and if it is a gas substance then the increase in heat added will also change the ability of the system to do work due to the volume change of a gas due to changing temperatures.   According to the ideal gas law, gasses will have a direct change in pressure or volume based on any changes in the gases temperature.   As long as the number of gas molecules do not change in the gas sample, the pressure will increase if volume is kept constant and temperature is increased.   On the other hand if pressure is held constant, the volume of a gas will increase as temperature increases.

License: CC BY-NC 3.0

[Figure4]

The change in volume during a phase change from a solid to a liquid is not very large so its uses for work are very limited.  However when a liquid goes through a phase change in to the vapor or gas state, the gas state takes up considerable more volume than the liquid state.  This change in volume can be used to do work like in the steam engine.  Once the water in the steam engine begins to boil, any additional heat added to the steam by the oven will increase the internal energy of the steam by increasing the average kinetic energy of the molecules of steam.   This in turn increase the pressure in the steam being contained in the plumbing of the steam engine.  This stored steam now has stored potential energy that can be used to do some work.

The diagram below shows the equations used to quantify the values of heat, internal energy and work for the system.  Simply put, since pressure is force per unit area and that force is moved the distance of a piston stroke, the steam does work on the piston as it expands to push the piston.  The energy for the work comes from the loss of internal energy of the steam by letting it expand to decrease its internal energy.  Therefore the initial phase change from liquid to vapor was required to super heat the steam and get some work out of all the energy put into the system from the oven fire.

License: CC BY-NC 3.0

[Figure5]

Example Problem: 5000. Joules of heat is added to ice at 273 K. All the heat goes into changing solid ice into liquid water. How much ice is melted?

Solution: \begin{align*}m=\frac{Q}{H_f}=\frac{5000 \ J}{3.34 \times 10^5 \ J/kg}=0.0150 \ kg\end{align*}

Example Problem: Beginning with 1.00 kg of ice at -20.0°C, heat is added until the substance becomes water vapor at 130.0°C. How much heat was added? The specific heat of ice is \begin{align*}2108 \ J/kg^\circ C\end{align*}, the specific heat of liquid water is \begin{align*}4187 \ J/kg^\circ C\end{align*}, and the specific heat of water vapor is \begin{align*}1996 \ J/kg^\circ C\end{align*}.

Solution: 5 steps.

1. Calculate the heat required to raise the sample from -20.0°C to 0°C.
2. Calculate the heat required to melt the sample.
3. Calculate the heat required to raise the sample from 0°C to 100°C.
4. Calculate the heat required to vaporize the sample.
5. Calculate the heat required to raise the sample from 100°C to 130°C.

The solution is the sum of these steps.

\begin{align*}1. Q_{HS} = mc_{\text{ice}} \Delta t = (1.00 \ kg)(2108 \ J/kg.^\circ C)(20.0^\circ C) = 42160 \ J\end{align*}

\begin{align*}2. Q_{\text{Melt}} = mH_f = (1.00 \ kg)(334000 \ J/kg) = 334000 \ J\end{align*}

\begin{align*}3. Q_{HL} = mc_{\text{water}} \Delta t = (1.00 \ kg)(4187 \ J/kg.^\circ C)(100.0^\circ C) = 418700 \ J\end{align*}

\begin{align*}4. Q_{\text{Vap}} = mH_v = (1.00 \ kg)(2260000 \ J/kg) = 2260000 \ J\end{align*}

\begin{align*}5. Q_{\text{HV}} = mc_{\text{vapor}} \Delta t = (1.00 \ kg)(1996 \ J/kg.^\circ C)(30.0^\circ C) = 59880 \ J\end{align*}

\begin{align*}\text{Total Heat} = 3.11 \times 10^6 \ J\end{align*}

### Summary

• Most substances may exist in any of the three common states of matter, solid, liquid, or gas.

• The phase in which a substance exists is the result of a competition between attractive forces and molecular motion.

• The potential energy absorbed by a solid as it changes to a liquid is called the heat of fusion or the heat of melting.

• The amount of potential energy necessary for a phase change to gaseous form is called the heat of vaporization.

• The heat gained or lost during a temperature change is given by, \begin{align*}Q = mc \Delta t\end{align*}.

• The heat gained or lost during a phase change of solid to liquid is given by, \begin{align*}Q = mH_f\end{align*}.

• The heat gained or lost during a phase change of liquid to gas is given by, \begin{align*}Q = mH_v\end{align*}.

### Vocabulary

• boiling point: The temperature at which a liquid rapidly begin to change phase into a vapor or gas depending on the substance.

• first law of thermodynamics:   Describes how work and heat are related to a system's internal energy.   Using energy conservation, the change in internal energy of a system and a systems ability to do work are related to any heat added or taken away from the system.

• latent heat of fusion:   The heat input required for a phase change from solid to liquid or the heat released for a phase change from liquid to solid

• heat of vaporization:  The heat input required for a phase change from liquid to vapor or gas or the heat released

• ideal gas law:  Describes the relationships between pressure, volume, temperature and numbers of gas molecules in a system as one or more of these conditions change.   This law is ideal and is limited to discrete temperature and pressure changes near STP.

• kinetic energy:  The energy of motion of a particle.   In a gas substance the moving gas particles have kinetic energy.

• melting point:  The temperature at which the phase change from liquid to solid occurs for a particular substance.

• phase change:   A change in the state of a substance from solid to liquid, or from a liquid to a gas.   Phase change also goes in the reverse direction from gas to liquid and from liquid to solid.

• potential energy:   Energy stored in a system due to a change in its position or a change in the systems internal energy.

### Review

Questions

1. A 200. g sample of water at 60.0°C is heated to water vapor at 140.0°C. How much heat was absorbed?
2. A 175 g lump of molten lead at its melting point (327°C) is placed into 55.0 g of water at 20.0°C. The specific heat of lead is \begin{align*}130 \ J/kg \cdot ^\circ C\end{align*} and the \begin{align*}H_f\end{align*} of lead is 20,400 J/kg.
1. When the lead has become solid but is still at the melting point, what is the temperature of the water?
2. When the lead and the water have reached equilibrium, what is the temperature of the mixture?

After reviewing the questions above, here's a quiz on changing the states of matter.

### Practice Problems

Questions

The following video explains heat of fusion and vaporization. Use this video to answer the questions that follow.

1. For water, which takes more energy, melting or evaporating?
2. When are there two phases present at the same time in the pot?

### Hands on Lab Activity

the following link will send you to a pdf file involving the latent heats of fusion and vaporization of ice to water to steam and the calculations based on the data obtained in the lab.

### Notes/Highlights Having trouble? Report an issue.

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