Heating and Cooling Curves & Combined Heat Calculations

Heating and Cooling Curves

Understanding Heating Curves

A heating curve is a graphical representation that shows how the temperature of a substance changes as heat is added. It illustrates both temperature changes and phase transitions (such as melting and boiling).

• Diagonal lines indicate temperature changes within a single phase (solid, liquid, or gas).

• Horizontal lines (plateaus) represent phase changes, where temperature remains constant as the substance absorbs heat to change state.

Example: The heating curve for water shows temperature rising as ice melts to liquid, then as liquid water heats to boiling, and finally as water vaporizes to steam.

Understanding Cooling Curves

A cooling curve is the reverse of a heating curve. It shows how the temperature of a substance decreases as heat is removed, including the corresponding phase changes.

• As heat is removed, the substance cools and may undergo condensation (gas to liquid) or freezing (liquid to solid).

• Plateaus on the curve indicate phase changes where temperature remains constant.

Example: The cooling curve for water illustrates the temperature drop as steam condenses to liquid and then freezes to ice.

Combined Heat Calculations

Calculating Total Heat for Phase Changes

To determine the total heat required to convert a substance from one state to another (e.g., liquid to gas), you must account for both the heat needed to change the temperature within a phase and the heat required for the phase change itself.

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

• Heat of vaporization (ΔHvap): The amount of heat required to convert 1 gram of a liquid to gas at its boiling point.

Stepwise Calculation Example: Heating and Vaporizing Ethanol

Problem: Calculate the total heat (in joules) needed to convert 15.0 g of liquid ethanol at 25.0°C to gas at its boiling point of 78.0°C. Given: specific heat of ethanol = 2.46 J/g°C, heat of vaporization = 841 J/g.

1. State the given and needed quantities:

   • Given: 15.0 g ethanol at 25.0°C

   • Needed: Total joules to heat ethanol to 78.0°C and convert to gas

2. Write a plan:

   • Total heat = (heat to warm ethanol from 25.0°C to 78.0°C) + (heat to vaporize ethanol at 78.0°C)

3. Write the heat conversion factors:

   • Specific heat of ethanol: $c = 2.46 \ \mathrm{J/g\ ^\circ C}$

   • Heat of vaporization: $\Delta H_{vap} = 841 \ \mathrm{J/g}$

4. Calculate the temperature change:

   • $\Delta T = 78.0\ ^\circ \mathrm{C} - 25.0\ ^\circ \mathrm{C} = 53.0\ ^\circ \mathrm{C}$

5. Calculate the heat needed to warm ethanol:

   • $q = m \times c \times \Delta T$

   • $q = 15.0\ \mathrm{g} \times 2.46\ \mathrm{J/g\ ^\circ C} \times 53.0\ ^\circ \mathrm{C} = 1960\ \mathrm{J}$

6. Calculate the heat needed to vaporize ethanol:

   • $q = m \times \Delta H_{vap}$

   • $q = 15.0\ \mathrm{g} \times 841\ \mathrm{J/g} = 12\ 600\ \mathrm{J}$

7. Calculate the total energy needed:

   • Total heat = $1960\ \mathrm{J} + 12\ 600\ \mathrm{J} = 14\ 600\ \mathrm{J}$

Summary Table: Steps in Combined Heat Calculations

Step	Process	Equation	Result
1	Heating ethanol (25.0°C to 78.0°C)	$q = m \times c \times \Delta T$	1960 J
2	Vaporizing ethanol at 78.0°C	$q = m \times \Delta H_{vap}$	12 600 J
Total	Sum of both steps		14 600 J

Key Formulas

• Heat for temperature change: $q = m \times c \times \Delta T$

• Heat for phase change (vaporization): $q = m \times \Delta H_{vap}$

Important Concepts

• During a phase change, temperature remains constant even as heat is added or removed.

• Always use the correct specific heat or enthalpy value for the substance and phase involved.

• Significant figures in calculations should reflect the precision of the given data.