Change of State: Melting, Boiling & Latent Heat

Hey everyone! Ever wondered why a pot of boiling water stays at 100°C, no matter how high you turn up the fire? Or why you feel so cold after getting out of a swimming pool, even on a warm day? The answers lie in the fascinating physics of changing states. In these notes, we'll explore what happens when solids melt and liquids boil, and we'll uncover the secret of "hidden heat" that makes it all possible. It's a key part of understanding energy in our everyday world, from cooking noodles to understanding the weather. Let's get started!


1. A Quick Review: The Three States of Matter

Before we can change states, let's quickly remember what they are. Everything is made of tiny particles (atoms and molecules) that are always moving.

The Three States:
  • Solid: Particles are packed tightly in a fixed, regular pattern (like a crystal). They vibrate on the spot but can't move around. Think of students sitting in neat rows in a classroom, only able to fidget in their chairs.
  • Liquid: Particles are still close together but can slide past one another. They don't have a fixed shape. Think of the same students during recess, walking around and mingling in the playground.
  • Gas: Particles are far apart and move randomly and quickly in all directions. They fill whatever container they are in. Think of the students after the final school bell rings, running off in all directions!
What holds them together?

There are forces of attraction between these particles. To change a solid to a liquid, or a liquid to a gas, we need to give the particles enough energy to overcome these forces.

Key Takeaway

The state of a substance depends on how its particles are arranged and how they move. Changing state means changing this arrangement and motion by adding or removing energy.


2. The Process of Changing State

When you heat a substance, its temperature usually rises. But something strange happens during melting and boiling. Let's look at what happens when we heat an ice cube until it becomes steam.

Melting and Boiling Points

Changes of state happen at specific temperatures for any given pure substance (at a standard pressure).

  • Melting Point: The specific temperature at which a substance changes from a solid to a liquid. For water, this is 0°C. The reverse process, liquid to solid, is called freezing, and it happens at the same temperature.
  • Boiling Point: The specific temperature at which a substance changes from a liquid to a gas. For water, this is 100°C. The reverse process, gas to liquid, is called condensing, and it also happens at the same temperature.

The Big Surprise: Temperature Stays Constant!

This is the most important concept in this chapter. When a substance is melting or boiling, its temperature DOES NOT CHANGE, even though you are still supplying heat energy to it!

Example: If you put a thermometer in a beaker of melting ice, it will read 0°C until ALL the ice has melted. Only then will the water's temperature start to rise. The same thing happens at 100°C for boiling.

So, where does all that heat energy go? This leads us to the idea of latent heat.

Key Takeaway

Melting and boiling are changes of state that occur at a constant temperature, known as the melting point and boiling point.


3. Latent Heat: The "Hidden" Energy

Don't worry if the last part seemed weird! It's a tricky idea, but we can break it down. The energy you add during a state change isn't "lost"—it's doing a very important job behind the scenes.

Kinetic vs. Potential Energy of Molecules

Remember, the total internal energy of a substance is the sum of its molecules' kinetic and potential energy.

  • Kinetic Energy (KE): Related to how fast the molecules are moving or vibrating. We measure the average KE of the molecules as temperature.
  • Potential Energy (PE): Related to the forces between molecules and their separation. The further apart the molecules are, the higher their potential energy.

So, what happens during a change of state?

When you add heat and the temperature is NOT changing (i.e., at the melting or boiling point):

  • The average Kinetic Energy of the molecules stays the same.
  • The energy you supply is used to overcome the forces holding the molecules together, pushing them further apart.
  • This increases the molecules' Potential Energy.

Analogy Time! Imagine you have a tower of Lego bricks (a solid). Shaking the tower makes the bricks vibrate (increasing KE/temperature). But to change its state, you have to pull the bricks apart. The energy you use to "un-click" the Lego bricks doesn't make them shake faster; it just separates them, increasing their potential to be built into something else (increasing PE). That "un-clicking" energy is like latent heat!

This "hidden" energy that increases potential energy to cause a change of state is called Latent Heat.

Key Takeaway

Latent heat is the energy transferred during a change of state that increases the potential energy of the molecules, not their kinetic energy. This is why the temperature remains constant.


4. Specific Latent Heat: The Formulas

Different substances need different amounts of energy to change state. To compare them, we use the idea of specific latent heat, which is the energy needed per kilogram.

Specific Latent Heat (l) is defined as the energy required to change the state of 1 kg of a substance without any change in temperature. The unit is joules per kilogram (J kg⁻¹).

Two Types of Specific Latent Heat

There are two types, one for melting and one for boiling.

1. Specific Latent Heat of Fusion (l_f)

This is for the solid-liquid change (melting or freezing).

The energy (Q) needed to melt a mass (m) of a solid at its melting point is given by:

$$Q = m l_f$$

Where:

  • Q = Heat energy supplied (in Joules, J)
  • m = mass of the substance (in kilograms, kg)
  • l_f = specific latent heat of fusion (in J kg⁻¹)

For water, l_f = 3.34 x 10⁵ J kg⁻¹. This means you need 334,000 Joules of energy just to melt 1 kg of ice at 0°C!

2. Specific Latent Heat of Vaporization (l_v)

This is for the liquid-gas change (boiling or condensing).

The energy (Q) needed to boil a mass (m) of a liquid at its boiling point is given by:

$$Q = m l_v$$

Where:

  • Q = Heat energy supplied (in Joules, J)
  • m = mass of the substance (in kilograms, kg)
  • l_v = specific latent heat of vaporization (in J kg⁻¹)

For water, l_v = 2.26 x 10⁶ J kg⁻¹. This means you need a massive 2,260,000 Joules to turn 1 kg of water into steam at 100°C.

Did you know?

The specific latent heat of vaporization of water is much larger than its specific latent heat of fusion. It takes way more energy to separate molecules completely into a gas than to just loosen them into a liquid. This is also why a burn from steam at 100°C is much more severe than a burn from boiling water at 100°C. The steam releases a huge amount of latent heat when it condenses on your skin!


5. Solving Problems with Latent Heat

In exams, you'll often get multi-step problems. The key is to break the problem down and ask yourself: "Is the temperature changing, or is the state changing?"

The Two Key Formulas
  1. If temperature is changing (heating a solid, liquid, or gas): Use $$Q = mc\Delta T$$
  2. If state is changing (melting, freezing, boiling, condensing): Use $$Q = ml$$
Step-by-Step Guide to Solving Problems

Let's try a classic example: Calculate the total energy required to change 0.5 kg of ice at -10°C to steam at 100°C.

(Given: c_ice = 2100 J kg⁻¹ °C⁻¹, l_f = 3.34 x 10⁵ J kg⁻¹, c_water = 4200 J kg⁻¹ °C⁻¹, l_v = 2.26 x 10⁶ J kg⁻¹)

Step 1: Break it down into stages. A simple diagram helps!

Ice at -10°C → Ice at 0°C → Water at 0°C → Water at 100°C → Steam at 100°C

This gives us 4 separate energy calculations to do.

Stage A: Heat the ice from -10°C to 0°C

Temperature is changing, so use Q = mcΔT.

$$Q_A = (0.5 \text{ kg}) \times (2100 \text{ J kg}^{-1} \text{°C}^{-1}) \times (0 - (-10)) \text{°C} = 10500 \text{ J}$$

Stage B: Melt the ice at 0°C

State is changing, so use Q = ml_f.

$$Q_B = (0.5 \text{ kg}) \times (3.34 \times 10^5 \text{ J kg}^{-1}) = 167000 \text{ J}$$

Stage C: Heat the water from 0°C to 100°C

Temperature is changing, so use Q = mcΔT.

$$Q_C = (0.5 \text{ kg}) \times (4200 \text{ J kg}^{-1} \text{°C}^{-1}) \times (100 - 0) \text{°C} = 210000 \text{ J}$$

Stage D: Boil the water at 100°C

State is changing, so use Q = ml_v.

$$Q_D = (0.5 \text{ kg}) \times (2.26 \times 10^6 \text{ J kg}^{-1}) = 1130000 \text{ J}$$

Step 2: Add up all the energies.

$$Q_{\text{total}} = Q_A + Q_B + Q_C + Q_D$$

$$Q_{\text{total}} = 10500 + 167000 + 210000 + 1130000 = 1517500 \text{ J}$$

So, the total energy required is 1,517,500 J (or 1.52 MJ).

Common Mistakes to Avoid
  • Units: Always make sure your mass is in kg, not grams!
  • Wrong Formula: Don't mix up $$Q = mc\Delta T$$ and $$Q = ml$$. Remember: If there's a ΔT (change in temp), use the first one. If the temperature is constant, use the second.
  • Missing Steps: Forgetting one of the stages is very common. Always draw a quick temperature-energy sketch to make sure you have all the parts.

Final Key Takeaway

You are now equipped with the main tools for this topic! The key is to identify whether energy is being used to change kinetic energy (temperature) or potential energy (state), and then apply the correct formula. Practice makes perfect. You've got this!