Heating and Cooling Curves

Introduction to Heating and Cooling Curves

Heating and cooling curves are graphical representations of the amount of heat absorbed or released by a substance during phase changes. These curves help visualize how temperature changes as a substance transitions between solid, liquid, and gas phases.

• Heating Curve: Shows temperature increase as heat is added, including plateaus during phase changes.

• Cooling Curve: Shows temperature decrease as heat is removed, with plateaus during phase changes.

Key Concepts

• Temperature remains constant during phase changes (e.g., melting, boiling) because energy is used to break or form intermolecular forces rather than changing kinetic energy.

• Sloped segments: Temperature changes as heat is added or removed; the substance remains in a single phase.

• Plateau segments: Phase changes occur (solid-liquid, liquid-gas); temperature remains constant.

• Endothermic process: Heat is absorbed (e.g., melting, vaporization).

• Exothermic process: Heat is released (e.g., freezing, condensation).

Formulas Used in Heating and Cooling Curves

• Specific Heat Equation:

• q: Heat absorbed or released (J)

• m: Mass (g)

• c: Specific heat capacity (J/g·°C)

• \Delta T: Change in temperature (°C)

• Heat of Fusion (melting/freezing):

• \Delta H_f: Heat of fusion (J/g)

• Heat of Vaporization (boiling/condensation):

• \Delta H_v: Heat of vaporization (J/g)

Heating and Cooling Curve Diagrams

• Heating Curve: Temperature increases with time, with flat regions at melting and boiling points.

• Cooling Curve: Temperature decreases with time, with flat regions at freezing and condensation points.

Table: Specific Heats and Heats of Phase Change

Additional info: Table values are typical for water; other substances have different values.

Example Problem: Calculating Heat for Phase Change

Example: How much energy (kJ) is required to convert 7.64 g acetone (molar mass = 58.08 g/mol) as a liquid at -30°C to a solid at -115°C?

• Use the specific heat of liquid and solid, and the heat of fusion for acetone.

• Calculate energy for each step: cooling liquid, freezing, cooling solid.

Solution Steps:

1. Calculate energy to cool liquid from -30°C to freezing point.

2. Calculate energy for freezing (phase change).

3. Calculate energy to cool solid from freezing point to -115°C.

4. Add all energies for total heat required.

Additional info: Always use correct specific heat and phase change values for the substance in question.

Practice Problem: Heat Added to Ice

Practice: If 31.2 kJ of heat are added to 11.5 g ice cube at -5.0°C, what will be the resulting state and temperature of the substance?

• Calculate energy to warm ice to 0°C.

• Calculate energy to melt ice at 0°C.

• Calculate energy to warm resulting water, if any heat remains.

Answer: 36.82°C, liquid

Summary Table: Steps in Heating/Cooling Curve Calculations