Grade 9

Intermediate

8 min

Lesson 9 of 12

Phase Changes and Latent Heat

Not Started

Examining why temperature stays constant while a substance is melting or boiling.

Why does a pot of boiling water stay at exactly $100^\circ C$ even if you turn the burner to its highest setting? It seems like the temperature should keep rising, but the thermometer won't budge until the water is completely gone.

Learning Objectives

1.Identify the plateau regions on a heating curve where phase changes occur.
2.Distinguish between the latent heat of fusion ( $L_f$ ) and the latent heat of vaporization ( $L_v$ ).
3.Calculate the energy required for a substance to change state using the formula $Q = mL$ .

The Mystery of the Plateau

When you heat a solid, its temperature rises because the molecules move faster. However, once it reaches its melting point, the temperature stops rising. On a graph, this appears as a flat line called a plateau. Even though you are still adding heat, the temperature remains constant until every bit of the solid has turned into a liquid. This is because the energy is no longer being used to increase the speed of the molecules (which we measure as temperature). Instead, the energy is being used to break the intermolecular bonds holding the solid together. This 'hidden' energy is called Latent Heat.

Quick Check

What is happening to the energy being added to a substance during a plateau on a heating curve?

Think about what 'latent' or 'hidden' means in this context.

Answer

The energy is being used to break molecular bonds to change the state of the substance, rather than increasing its temperature.

Fusion vs. Vaporization

There are two main types of latent heat you need to know. **Latent Heat of Fusion ( $L_f$ ) is the energy required to change a substance from a solid to a liquid (melting). Latent Heat of Vaporization ( $L_v$ )** is the energy required to change a liquid into a gas (boiling). For most substances, $L_v$ is much larger than $L_f$ . This is because it takes significantly more energy to completely pull molecules apart into a gas than it does to simply loosen them enough to slide past each other as a liquid.

How much energy is required to melt $2\text{ kg}$ of ice at $0^\circ C$ ? The latent heat of fusion for water is $L_f = 3.34 \times 10^5\text{ J/kg}$ .

1. Identify the formula: $Q = mL_f$ 2. Plug in the values: $Q = (2\text{ kg}) \times (3.34 \times 10^5\text{ J/kg})$ 3. Calculate the result: $Q = 6.68 \times 10^5\text{ J}$ or $668,000\text{ Joules}$ .

Quick Check

Which usually requires more energy: melting a kilogram of a substance or boiling that same kilogram?

Compare

L_f

and

L_v

Answer

Boiling (Vaporization) usually requires more energy because the molecules must be completely separated.

The Latent Heat Formula

To calculate the total heat (

Q

) absorbed or released during a phase change, we use the mass (

m

) of the substance and its specific latent heat (

L

). The formula is:

Q = mL

Note that there is no

\Delta T

(change in temperature) in this formula! This is because, as we've learned, the temperature does not change during the phase transition itself. The units for

L

are typically Joules per kilogram (

\text{J/kg}

) or Joules per gram (

\text{J/g}

A chef boils away $0.5\text{ kg}$ of water to reduce a sauce. If the latent heat of vaporization for water is $L_v = 2.26 \times 10^6\text{ J/kg}$ , how much energy was transferred to the water?

1. Identify the mass: $m = 0.5\text{ kg}$ 2. Identify the constant: $L_v = 2,260,000\text{ J/kg}$ 3. Apply the formula: $Q = 0.5 \times 2,260,000$ 4. Final Answer: $Q = 1,130,000\text{ J}$ or $1.13\text{ MJ}$ .

How much total energy is needed to take $1\text{ kg}$ of ice at $0^\circ C$ and turn it into liquid water at $20^\circ C$ ? (Specific heat of water $c = 4186\text{ J/kg}^\circ C$ ; $L_f = 3.34 \times 10^5\text{ J/kg}$ ).

1. Step 1: Melt the ice. Use $Q_1 = mL_f$ $Q_1 = 1 \times 334,000 = 334,000\text{ J}$ 2. Step 2: Heat the water. Use $Q_2 = mc\Delta T$ $Q_2 = 1 \times 4186 \times (20 - 0) = 83,720\text{ J}$ 3. Step 3: Add them together. $Q_{total} = Q_1 + Q_2$ $Q_{total} = 334,000 + 83,720 = 417,720\text{ J}$ .

Key Takeaways

1Temperature remains constant during a phase change, creating a plateau on a heating curve.
2Latent heat is the energy used to break or form molecular bonds during a state change.
3The formula for phase change energy is $Q = mL$ .
4Latent heat of vaporization ( $L_v$ ) is typically much higher than latent heat of fusion ( $L_f$ ).

Quick Check

Multiple Choice

On a heating curve graph, what does a horizontal line represent?

Multiple Choice

Which formula would you use to find the energy needed to turn $100^\circ C$ water into $100^\circ C$ steam?

True/False

The temperature of a substance increases while it is in the process of melting.

What's Next?

Review Tomorrow

In 24 hours, try to sketch a heating curve for water from memory and label where $Q = mc\Delta T$ applies and where $Q = mL$ applies.

Practice Activity

Look at a bag of frozen peas in your freezer. Estimate their mass and calculate how many Joules of energy it would take just to melt them (using $L_f = 334,000\text{ J/kg}$ ).

Browse

Browse

Phase Changes and Latent Heat

Learning Objectives

The Mystery of the Plateau

Fusion vs. Vaporization

The Latent Heat Formula

Key Takeaways

Quick Check

What's Next?

Phase Changes and Latent Heat

Learning Objectives

The Mystery of the Plateau

Fusion vs. Vaporization

The Latent Heat Formula

Key Takeaways

Quick Check

What's Next?