Heating and Cooling Curves

Introduction to Heating and Cooling Curves

Heating and cooling curves graphically represent the temperature changes of a substance as it absorbs or releases heat, illustrating the energy involved during phase changes (solid, liquid, gas). These curves are essential for understanding how heat energy is distributed between raising temperature and changing phases.

Heating Curve

The heating curve shows how the temperature of a substance changes as heat is added. It includes both temperature increases and phase changes.

• During phase changes (segments 2 and 4):

  • Temperature remains constant.

  • Average kinetic energy remains constant.

  • Heat is transformed into potential energy, breaking intermolecular forces.

• During temperature increases (sloped segments):

  • Heat energy is converted into kinetic energy, raising the temperature.

  • Temperature increases as the average kinetic energy of particles increases.

Key Point: The flat portions of the curve correspond to phase changes (melting, boiling), while the sloped portions correspond to temperature changes within a single phase.

Cooling Curve

The cooling curve is the reverse of the heating curve, showing how a substance releases heat and undergoes phase changes as it cools. The same principles apply: temperature remains constant during phase changes, and decreases during cooling within a phase.

• Phase changes: Energy is released as potential energy decreases, but temperature remains constant.

• Temperature decreases: Kinetic energy decreases, lowering the temperature.

Specific Heat and Enthalpy Changes

Definitions

• Specific Heat (c): The amount of heat required to raise the temperature of 1 gram of a substance by 1°C. Units:

• Enthalpy of Fusion (): The heat required to convert 1 mole of a solid to a liquid at its melting point. Units:

• Enthalpy of Vaporization (): The heat required to convert 1 mole of a liquid to a gas at its boiling point. Units:

Common Values (from tables in the notes)

Additional info: Table values for acetone are inferred from context and typical data.

Calculations Involving Heating and Cooling Curves

Key Formulas

• Heat for temperature change:

  • Where q is heat (J), m is mass (g), c is specific heat (), and is the temperature change (°C).

• Heat for phase change (melting/freezing):

  • Where n is moles, is enthalpy of fusion ().

• Heat for phase change (vaporization/condensation):

  • Where n is moles, is enthalpy of vaporization ().

Example Problem

How much energy (kJ) is required to convert 76.4 g of acetone (molar mass = 58.08 g/mol) as a liquid at -30°C to a solid at -115.0°C?

• Step 1: Calculate moles of acetone:

• Step 2: Cool liquid from -30°C to melting point (-95°C):

• Step 3: Freeze at -95°C: (negative, since freezing)

• Step 4: Cool solid from -95°C to -115°C:

• Step 5: Add all q values (accounting for sign) to get total energy required.

Answer: 1,543 J (as given in the notes; actual calculation steps omitted for brevity).

Practice Problem

If 5.32 kJ of heat are added to a 15.5 g ice cube at -5.00°C, what will be the resulting state and temperature of the substance?

• Step 1: Calculate energy needed to warm ice to 0°C:

• Step 2: Calculate energy needed to melt ice:

• Step 3: If energy remains, calculate temperature increase of water:

• Step 4: Compare total energy supplied (5.32 kJ) to sum of and to determine final state and temperature.

Answer: 209 (as given in the notes; actual calculation steps omitted for brevity).

Summary Table: Steps in Heating/Cooling Curve Calculations

Additional info: For more complex problems, repeat steps for each phase and phase change, summing all energy values to find the total heat absorbed or released.