States of Matter and Changes of State

6.4 Lesson: States of Matter and Changes of State

• States of Matter

6. 4 Changes of States

• Heat transfer occurs during a change in state.
• Solid to liquid: Absorbs thermal energy.
• Liquid to gas: Absorbs thermal energy.
• Gas to liquid: Releases thermal energy.
• Liquid to solid: Releases thermal energy.
• Fusion: The process of liquid changing into a solid.
• Vaporization: The process of a liquid changing into a vapor.

Heating Graph for Water

• The heating graph shows the relationship between temperature and thermal energy absorbed as ice is heated to become water and then steam.
• Ice warms up from -10°C to 0°C.
• Ice melts (at 0°C) into liquid water.
• Liquid water warms up from 0°C to 100°C.
• Liquid water boils (at 100°C) into water vapor.
• Water vapor warms up above 100°C.

Cooling Graph for Water

• The cooling graph illustrates temperature changes as water vapor cools to become liquid water and then ice.
• Water vapor cools down.
• Water vapor condenses into liquid water.
• Liquid water cools down.
• Liquid water freezes into ice.
• Ice cools down.

Latent Heat

• Latent Heat: The total energy absorbed or released during a change of state.
• Specific Latent Heat: The amount of thermal energy required for 1 kg of a substance to change from one state to another, measured in J/kg.

Specific Latent Heat

• Specific latent heat of fusion ($L_f$) is related to melting and freezing.
• Specific latent heat of vaporization ($L_v$) is related to boiling and condensing.

Heat Capacity Formulas

• $Q<em>f = mL</em>f$ where:
  • $Q_f$ = Latent heat of fusion (in J)
  • $m$ = mass (in kg)
  • $L_f$ = specific latent heat of fusion (in J/kg)
  • Note: $Q_f$ is used for both melting and freezing.
• $Q<em>v = mL</em>v$ where:
  • $Q_v$ = Latent heat of vaporization (in J)
  • $m$ = mass (in kg)
  • $L_v$ = specific latent heat of vaporization (in J/kg)
  • Note: $Q_v$ is used for both boiling and condensing.

Example #1

• How much heat is required to bring 10 kg of 100°C liquid water to 100°C steam?

Example #1 Solution

• Given:
  • $m = 10 \text{kg}$
  • Water at 100°C converting to steam at 100°C
  • $L_v = 2.3 \times 10^6 \text{ J/kg}$ (from a table)
• Formula:
  • $Q<em>v = mL</em>v$
• Calculation:
  • $Q_v = (10 \text{kg}) (2.3 \times 10^6 \text{ J/kg}) = 2.3 \times 10^7 \text{ J}$
• The latent heat of $2.3 \times 10^7 \text{ J}$ is needed.

Example #2

• How much thermal energy is required to raise 5.0 kg of -30°C ice to a temperature of 140°C?
  • [Note: $c<em>{\text{ice}} = 2100 \text{J}/(°\text{C} \cdot \text{kg})$, $c</em>{\text{water}} = 4180 \text{J}/(°\text{C} \cdot \text{kg})$, $c<em>{\text{water vapour}} = 2080 \text{ J}/(°\text{C} \cdot \text{kg})$, $L</em>v = 2255000 \text{J/kg}$, $L_f = 333000 \text{J/kg}$]

Example #2 solution

• Heating stages:
  • Ice: -30°C → 0°C
  • Ice to water (at 0°C)
  • Water: 0°C → 100°C
  • Water to steam (at 100°C)
  • Steam: 100°C → 140°C
• Calculations:
  • Heat to warm ice from -30°C to 0°C: $Q<em>1 = m \cdot c</em>{\text{ice}} \cdot \Delta T_{\text{ice}} = (5.0 \text{ kg}) (2.1 \times 10^3 \text{ J/(kg} \cdot °\text{C)}) (0°\text{C} - (-30°\text{C}))$
  • Heat for ice to water: $Q<em>2 = m L</em>f = (5.0 \text{ kg}) (3.4 \times 10^5 \text{ J/kg})$
  • Heat to warm water from 0°C to 100°C: $Q<em>3 = m \cdot c</em>{\text{w}} \cdot \Delta T_w = (5.0 \text{ kg}) (4.18 \times 10^3 \text{ J/(kg} \cdot °\text{C)}) (100°\text{C} - 0°\text{C})$
  • Heat for water to steam: $Q<em>4 = m L</em>v = (5.0 \text{ kg}) (2.3 \times 10^6 \text{ J/kg})$
  • Heat to warm steam from 100°C to 140°C: $Q<em>5 = m \cdot c</em>{\text{steam}} \cdot \Delta T_{\text{steam}} = (5.0 \text{ kg}) (2.08 \times 10^3 \text{ J/(kg} \cdot °\text{C)}) (140°\text{C} - 100°\text{C})$
• Total heat required:
  • $Q = Q<em>1 + Q</em>2 + Q<em>3 + Q</em>4 + Q_5$
  • $Q = 315000 \text{ J} + 1700000 \text{ J} + 2090000 \text{ J} + 11500000 \text{ J} + 416000 \text{ J} = 16021000 \text{ J}$
• The total thermal energy is $1.6 \times 10^7 \text{ J}$.

Practice Questions

• Page 293 Q1-3
• Page 295 Q6-9
• Page 283 Q1-3
• Page 286 Q1,2
• Page 287 Q1-9

Unit Review Questions

• Ch. 5 Review: Page 261 Q1-5,8-11,13,15; Page 262 Q1-4,8-12,15,16,23,24a,29-32,42,44,47,49,50,53,57
• Ch. 6 Review: Page 309 Q3-6,13-16; Page 310 Q1-5,8,18,19,28,29,33-35,40,41,44,45,66,67