1.5 Phase Changes

Phase changes are fascinating transformations of matter. They occur when substances shift between solid, liquid, and gas states by absorbing or releasing energy. These transitions happen at constant temperatures as molecules break or form bonds.

Understanding phase changes is crucial for grasping thermodynamics. We'll explore the energy involved, equilibrium between phases, and how to calculate latent heat. We'll also dive into calorimetry and phase diagrams, key tools for analyzing these transitions.

Phase Changes

Process of phase transitions

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• Phase transitions occur when a substance changes from one state of matter to another by absorbing or releasing energy
  • Solid to liquid through melting (ice to water)
  • Liquid to gas through vaporization (water to steam)
  • Gas to liquid through condensation (steam to water)
  • Liquid to solid through freezing (water to ice)
  • Solid to gas through sublimation (dry ice to carbon dioxide gas)
  • Gas to solid through deposition (water vapor to frost)
• During a phase transition, the temperature remains constant as the substance absorbs or releases latent heat energy
• The absorbed or released energy changes the kinetic energy and potential energy of the molecules, allowing them to break or form intermolecular bonds
• Phase transitions often begin with nucleation, where small clusters of molecules in the new phase form and grow

Equilibrium between phases

• Equilibrium between phases occurs when the rate of molecules leaving one phase equals the rate of molecules entering that phase, resulting in no net change in the amount of each phase
  • At equilibrium, the vapor pressure of the liquid equals the pressure of the gas above it (water and water vapor in a closed container)
  • The equilibrium vapor pressure depends on the temperature and the intermolecular forces of the substance
• Factors affecting equilibrium:
  • Temperature: higher temperatures increase the vapor pressure and shift the equilibrium towards the gas phase (boiling water at high altitudes)
  • Pressure: higher pressures shift the equilibrium towards the phase with the smaller volume (liquid) (pressure cookers)
  • Surface area: larger surface areas increase the rate of evaporation and shift the equilibrium towards the gas phase (drying clothes on a clothesline)

Energy changes in phase transitions

• Latent heat is the energy required to change the phase of a substance without changing its temperature
  • Latent heat of fusion ($L_f$) is the energy required to melt or freeze a substance (334 J/g for water)
  • Latent heat of vaporization ($L_v$) is the energy required to vaporize or condense a substance (2260 J/g for water)
• The energy required for a phase change is calculated using the formula: $Q = mL$
  • $Q$ is the energy absorbed or released in joules (J)
  • $m$ is the mass of the substance in kilograms (kg)
  • $L$ is the latent heat of the specific phase transition in joules per kilogram (J/kg)
• The latent heat values are specific to each substance and can be found in reference tables (2108 J/g for ammonia, 58 J/g for mercury)
• The heat of transformation is the energy required for a substance to undergo a phase change, which includes both latent heat and any additional energy needed for structural changes

Latent heat calculations

• To calculate the energy absorbed or released during a phase change, use the formula $Q = mL$
  • Example: Calculate the energy required to melt 500 g of ice at 0℃. $L_f$ for water is 334 J/g. $Q = mL_f = 0.5 kg × 334,000 J/kg = 167,000 J$ or $167 kJ$
• When a substance undergoes both a temperature change and a phase change, calculate the energy for each process separately and add them together
  • Example: Calculate the energy required to heat 200 g of ice at -10℃ to steam at 120℃. Specific heat capacity of ice is 2.09 J/g·℃, specific heat capacity of water is 4.18 J/g·℃, and specific heat capacity of steam is 2.01 J/g·℃.
    1. Heating ice from -10℃ to 0℃: $Q_1 = mc\Delta T = 0.2 kg × 2,090 J/kg·℃ × 10℃ = 4,180 J$
    2. Melting ice at 0℃: $Q_2 = mL_f = 0.2 kg × 334,000 J/kg = 66,800 J$
    3. Heating water from 0℃ to 100℃: $Q_3 = mc\Delta T = 0.2 kg × 4,180 J/kg·℃ × 100℃ = 83,600 J$
    4. Vaporizing water at 100℃: $Q_4 = mL_v = 0.2 kg × 2,260,000 J/kg = 452,000 J$
    5. Heating steam from 100℃ to 120℃: $Q_5 = mc\Delta T = 0.2 kg × 2,010 J/kg·℃ × 20℃ = 8,040 J$ Total energy required: $Q_{total} = Q_1 + Q_2 + Q_3 + Q_4 + Q_5 = 614,620 J$ or $614.62 kJ$

Calorimetry for phase changes

• Calorimetry is the study of heat transfer and the measurement of specific heat capacities and latent heats
• The first law of thermodynamics states that energy is conserved in a closed system, so the energy lost by one object equals the energy gained by another object
• When a substance undergoes a phase change in a calorimeter, the energy absorbed or released can be calculated using the equation: $Q = mc\Delta T + mL$
  • $Q$ is the energy absorbed or released in joules (J)
  • $m$ is the mass of the substance in kilograms (kg)
  • $c$ is the specific heat capacity of the substance in joules per kilogram per kelvin (J/kg·K)
  • $\Delta T$ is the change in temperature in kelvins (K) or degrees Celsius (℃)
  • $L$ is the latent heat of the specific phase transition in joules per kilogram (J/kg)
• To solve calorimetry problems involving phase changes:
  1. Identify the substances involved and their initial and final states
  2. Determine the specific heat capacities and latent heats of the substances
  3. Apply the conservation of energy principle: energy lost by one substance = energy gained by the other substance
  4. Set up equations for each substance using $Q = mc\Delta T + mL$
  5. Solve for the unknown variable (usually the final temperature or the mass of one substance)
• Example: 100 g of ice at -5℃ is added to 300 g of water at 50℃ in a calorimeter. Calculate the final temperature of the mixture assuming no heat loss to the surroundings.
  • Let the final temperature be $T_f$. The specific heat capacity of ice is 2.09 J/g·℃, the specific heat capacity of water is 4.18 J/g·℃, and the latent heat of fusion for water is 334 J/g.
  • Energy lost by water: $Q_w = m_wc_w(T_i - T_f) = 300 g × 4.18 J/g·℃ × (50℃ - T_f)$
  • Energy gained by ice:
    1. Heating ice from -5℃ to 0℃: $Q_1 = m_ic_i\Delta T = 100 g × 2.09 J/g·℃ × 5℃ = 1,045 J$
    2. Melting ice at 0℃: $Q_2 = m_iL_f = 100 g × 334 J/g = 33,400 J$
    3. Heating melted ice (water) from 0℃ to $T_f$: $Q_3 = m_wc_w\Delta T = 100 g × 4.18 J/g·℃ × (T_f - 0℃)$
  • Applying conservation of energy: $Q_w = Q_1 + Q_2 + Q_3$ $300 g × 4.18 J/g·℃ × (50℃ - T_f) = 1,045 J + 33,400 J + 100 g × 4.18 J/g·℃ × (T_f - 0℃)$
  • Solving for $T_f$: $62,700 J - 1,254 J/℃ × T_f = 34,445 J + 418 J/℃ × T_f$ $28,255 J = 1,672 J/℃ × T_f$ $T_f = 16.9℃$

Phase diagrams and critical phenomena

• Phase diagrams represent the equilibrium states of a substance as a function of temperature and pressure
• Phase boundaries on the diagram indicate where two phases coexist in equilibrium
• The critical point is a unique state where the distinction between liquid and gas phases disappears
• Near the critical point, substances can exhibit unusual behavior, such as rapid fluctuations between phases
• The order parameter is a quantity that describes the degree of order in a system and can be used to characterize phase transitions
• Some systems can exist in metastable states, which are temporarily stable but not at the lowest energy configuration
• Hysteresis occurs when a system's behavior depends on its history, often observed in phase transitions of certain materials