Heating and Cooling Curves — Overview & Examples

Heating and Cooling Curves

• These curves show a visualization of how phase changes occur (via adding or removing heat)

Heating Curve:

Note: Melting is also referred to as fusion

• In the sections of this curve where the temperature in constant (not changing), the average kinetic energy of the particles are not changing

• Superheating: when the substance is heated above it's boiling point but boiling does not occur

Cooling Curve:

Note: Freezing is also referred to as crystallization

• In the sections of this curve where the temperature in constant (not changing), the average kinetic energy of the particles are not changing

• Supercooling: when the substance is cooled below its freezing point but freezing does not occur

I want you to imagine you're heating a pan of ice cubes on the stove. What are you seeing? At first, nothing happens. But soon, the ice begins to melt. Now you have liquid water. If you keep heating, you'll vaporize the water. There is nothing unusual. But, what if you repeated the experiment with a thermometer?

If you measure the temperature, you'll discover something strange. At first, the ice cubes' temperature steadily increases. But suddenly, it stops changing. What's happening?

Heating and Cooling Curves

The experimental set-up we imagined would generate a heating curve. Heating and cooling curves are graphs. They plot a substance's temperature (y-axis) against heat (x-axis). For heating curves, we start with a solid and add heat energy. For cooling curves, we start with the gas phase and remove heat energy.

Cooling and heating curves have five segments. Let's study each one by looking at heating ice to steam.

Heating Ice

Let's return to our pan of ice cubes. Just for fun, we'll say they start at $-50^{o}C$. The melting point of ice is $0^{o}C$. Our graph would show an upward diagonal line from -50 to 0. The slope of the line depends on how quickly we added heat. If our stove is on a high setting, the graph's slope is steep. If we have it on low, the graph's slope is gradual. But, in both cases, the total heat energy we added is the same.

To calculate the total heat we added, we use the formula, $Q=mC_{p}\Delta T$. In our equation, $Q$ is heat energy, $m$ is the ice's mass, $C_{p}$ is the specific heat capacity, $\Delta T$ is the temperature change.

Let's calculate our heat energy if we started with 100.0 grams of ice. We look up the specific heat capacity. For ice, it's $2.03\frac{J}{g ^{o}C}$.

$Q=mC_{p}\Delta T=(100.0g)(2.03\frac{J}{g ^{o}C})(50^{o}C)=10150.0J$

So, to heat 100.0 grams of ice to its melting point required 10,150.0 joules. Remember, Q can be positive or negative. A positive Q means the process was endothermic. So, we added heat to the system. But, a negative Q means it was exothermic. We removed heat from the system.

What's happening to the molecules? In solids, the molecules vibrate. As we add more heat, the vibrations become bigger.

Rearranging the Molecules

Once we hit the melting point, you'll notice something weird. The temperature stops increasing. For a while, your graph will show a flat line. We're still adding heat but, the temperature is unchanging. What is going on?

Temperature is the average kinetic energy of the molecules. We are still adding heat energy. But, the added heat is not increasing the kinetic energy. So, it must be increasing the chemical potential energy. Substances store potential energy via electrostatic interactions. We know that water hydrogen bonds. But, for water to change phases, we must weaken the hydrogen bonds. Ice is a molecular solid. So, in ice, the water molecules are in a lattice. In liquid water, the molecules can move past one another.

How much energy do we need to convert ice to liquid water? That's the enthalpy of fusion! The heat of fusion for water is $333.55\frac{J}{g}$. So, $Q=m\times H_{fus}$.

Let's calculate the heat energy we used to convert 100.0 grams of ice to 100.0g of liquid water.

$Q=m\times H_{fus}=100.0g\times333.55\frac{J}{g}=33355.0J$.

Heating Liquid Water

After we have weakened all the hydrogen bonds, our temperature starts to rise again. Our water molecules are no longer just vibrating. Now, they have translational motion too. The heat we add makes the molecules move faster. Once again, our graph will be in an upward diagonal direction.

To calculate the total heat, we can use $Q=mC_{p}\Delta T$ again. The specific heat capacity of water is $4.18\frac{J}{g ^{o}C}$. Water's boiling point is $100^{o}C$.

$Q=mC_{p}\Delta T=(100.0g)(4.18\frac{J}{g ^{o}C})(100^{o}C)= 41800.0J$

Rearranging the Molecules Again!

At $100^{0}C$, our graph will flat-line again. But, this time we expect it! We know that for liquid water to become gaseous, we need to overcome the hydrogen bonds. So, we need to use the enthalpy of vaporization ($H_{vap}$). For water, $H_{vap}$ is $2260.0\frac{J}{g}$.

$Q=m\times H_{vap}=(100.0g)\times(2260.0\frac{J}{g})=226,000.0J$

Heating Steam

At this point, we've converted 100.0g of ice to steam. If we wanted to continue to heat our water vapor, we could continue to use $Q=mC_{p}\Delta T$. Our heating curve once again has an upward diagonal direction.

What about Plasma?

We could continue the process until we got a plasma. However, we only get plasmas at very high temperatures. So, you won't have to deal with that. For the phase change from gas to plasma, we would use the enthalpy of ionization.

A quick note about cooling curves

Let's say we wanted to go from steam to ice. We would use a cooling curve. The cooling curve is a mirror image of the heating curve. So, it will start at a high temperature and have downward diagonals. The diagonals alternate with plateaus. The flat lines are the enthalpy of condensation and freezing. Remember, during cooling, we remove heat energy. So, all our Q values will be negative.

Supercooling and Superheating

Superheating happens when liquid water exceeds its boiling point. Boiling occurs when a liquid's vapor pressure exceeds atmospheric pressure. But, water has a significant surface tension. Sometimes, the molecules on the surface resist releasing the gas. Qualitatively, you would not see any boiling. But, a thermometer would read over $100^{o}C$.

Superheating only appears in very smooth containers. To bubble, the gases need a high surface area. For example, let's say you placed a mug of water in the microwave. Most ceramic mugs have thousands of microscopic scratches. When the water boils, the scratches help create bubbles. We would say the scratches are nucleation sites. What if you have a new mug without scratches? Bubbles wouldn't form and, water's surface tension would prevent boiling!

Superheating is very dangerous! Even the slightest change disrupts the surface tension. So, the liquid boils violently. Sometimes it is so violent that hot water sprays across the room.

Supercooling is the opposite of superheating. Supercooling is when we cool a liquid below its freezing point. For crystalization, a fluid needs a nucleation site. If we have a pure substance and a smooth container, we can initiate supercooling.

(Video) How Much Thermal Energy Is Required To Heat Ice Into Steam - Heating Curve Chemistry Problems

by The Organic Chemistry Tutor

In this video, The Organic Chemistry Tutor walks you through a heating and cooling curve example problem. The problem asks you to heat ice to steam. So, it has six different steps. He shows you how to do each step to find the total energy required. Do you want a better understanding of heating and cooling curves? This is a great video.