Cooling Curve Notes (Gas to Liquid to Solid)

A cooling curve is a plot of temperature versus time, illustrating how a substance loses heat as it cools. The x-axis represents time (e.g., seconds, minutes), and the y-axis represents temperature (typically in degrees Celsius, $^ ext{o}$C). Temperature is a direct measure of the average kinetic energy of the particles within the system. The curve's overall shape reflects phase changes as energy is transferred to the surroundings. A key characteristic is that temperature remains constant during phase changes, as energy is utilized for phase conversion rather than altering molecular kinetic energy.

The process typically begins with the substance in a gas phase at a high temperature (e.g., water at 120 $^ ext{o}$C). As energy is removed from the gas, through mechanisms like ice packs, the molecular speeds decrease, causing the temperature to drop. When the substance reaches a phase change temperature, the curve's behavior changes dramatically.

For water at 1 atm, the critical phase change temperatures are:

• Condensation (gas $<br>ightleftharpoons$ liquid) occurs at 100 $^ ext{o}$C.

• Freezing (liquid $<br>ightleftharpoons$ solid) occurs at 0 $^ ext{o}$C.

Step-by-Step Process (A-F) on the Cooling Curve:

1. A. Gas at 120 $^ ext{o}$C: We start with a hot gas. As it loses heat, its particles slow down, and the temperature drops from 120 $^ ext{o}$C to 100 $^ ext{o}$C.

2. B. Gas at 100 $^ ext{o}$C: The gas has reached 100 $^ ext{o}$C, which is its condensation point. It's still a gas, but it's ready to change into a liquid.

3. C. Condensation at 100 $^ ext{o}$C (Gas ext{>} Liquid): Even though heat is still being removed, the temperature stays at 100 $^ ext{o}$C. This is because the gas particles are coming closer to form a liquid, releasing energy (called latent heat). This release of energy keeps the temperature constant until all the gas becomes liquid. This flat section on the curve is called a plateau.

4. D. Liquid Cooling from 100 $^ ext{o}$C to 0 $^ ext{o}$C: Now that it's all liquid, the water continues to lose heat. Its particles slow down further, and the temperature drops from 100 $^ ext{o}$C to 0 $^ ext{o}$C.

5. E. Freezing at 0 $^ ext{o}$C (Liquid ext{>} Solid): At 0 $^ ext{o}$C, the liquid starts to freeze into a solid. Again, the temperature stays constant here because as the liquid turns to solid, it forms stronger bonds and releases heat (latent heat), which prevents the temperature from dropping. This is another plateau.

6. F. Solid Cooling Below 0 $^ ext{o}$C: Once all the water has become a solid (ice), it continues to lose heat, and its temperature drops below 0 $^ ext{o}$C.

Key Concepts:

• Temperature and Movement: Temperature tells us how fast the particles in a substance are moving on average. When a substance cools, its particles slow down, and its temperature drops. But this isn't true when a substance is changing its phase.

• Phase Changes and Hidden Heat (Latent Heat): When a substance changes from a gas to a liquid (condensation) or a liquid to a solid (freezing), it releases what's called "latent heat" or "hidden heat." During these times, the temperature doesn't change, even though heat is being removed. This is why you see flat sections (plateaus) on the cooling curve. The energy released as particles get closer balances the energy being taken away.

• Forces Between Particles (Intermolecular Forces): Particles in a gas have very weak forces between them. These forces get stronger when a gas turns into a liquid, and even stronger when a liquid turns into a solid. Forming these stronger forces releases energy, which is why the temperature stays constant during phase changes (the plateaus).

Mathematical Formulas:

• Heat change without phase change: To find out how much heat (Q) is added or removed when a substance changes temperature but stays in the same phase, we use: $Q = m \, c \, \Delta T$

  • Here, $m$ is the mass of the substance.

  • $c$ is how easily the substance heats up or cools down (its specific heat capacity).

  • $\Delta T$ is the change in temperature.

• Heat change during a phase change: To find out how much heat (Q) is released or absorbed when a substance changes phase (like freezing or boiling), we use: $Q = m \, L$

  • $m$ is the mass of the substance.

  • $L$ is the 'latent heat' specific to that phase change (e.g., latent heat of fusion for freezing/melting, or latent heat of vaporization for boiling/condensing).

Latent Heats for Water at 1 atm (approximate values):

• For Freezing/Melting (solid $ightleftharpoons$ liquid): $L_f \approx 333.55\;\text{kJ/kg}$

• For Condensing/Boiling (gas $ightleftharpoons$ liquid): $L_v \approx 2257\;\text{kJ/kg}$

The cooling curve helps us see how a substance releases heat and changes phases over time. It shows us both when the temperature changes and when it stays constant during important phase changes.