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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 . We'll also dive into and phase diagrams, key tools for analyzing these transitions.

Phase Changes

Process of phase transitions

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  • occur when a substance changes from one state of matter to another by absorbing or releasing energy
    • Solid to liquid through (ice to water)
    • Liquid to gas through vaporization (water to steam)
    • Gas to liquid through (steam to water)
    • Liquid to solid through (water to ice)
    • Solid to gas through ( to carbon dioxide gas)
    • Gas to solid through (water 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 , 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 of the liquid equals the pressure of the gas above it (water and water vapor in a closed container)
    • The depends on the temperature and the intermolecular forces of the substance
  • Factors affecting equilibrium:
    • Temperature: higher temperatures increase the 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 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
    • (LfL_f) is the energy required to melt or freeze a substance (334 J/g for water)
    • (LvL_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=mLQ = mL
    • QQ is the energy absorbed or released in joules (J)
    • mm is the mass of the substance in kilograms (kg)
    • LL 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 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=mLQ = mL
    • Example: Calculate the energy required to melt 500 g of ice at 0℃. LfL_f for water is 334 J/g. Q=mLf=0.5kg×334,000J/kg=167,000JQ = mL_f = 0.5 kg × 334,000 J/kg = 167,000 J or 167kJ167 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℃. capacity of ice is 2.09 J/g·℃, 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℃: Q1=mcΔT=0.2kg×2,090J/kg⋅℃×10℃=4,180JQ_1 = mc\Delta T = 0.2 kg × 2,090 J/kg·℃ × 10℃ = 4,180 J
      2. Melting ice at 0℃: Q2=mLf=0.2kg×334,000J/kg=66,800JQ_2 = mL_f = 0.2 kg × 334,000 J/kg = 66,800 J
      3. Heating water from 0℃ to 100℃: Q3=mcΔT=0.2kg×4,180J/kg⋅℃×100℃=83,600JQ_3 = mc\Delta T = 0.2 kg × 4,180 J/kg·℃ × 100℃ = 83,600 J
      4. Vaporizing water at 100℃: Q4=mLv=0.2kg×2,260,000J/kg=452,000JQ_4 = mL_v = 0.2 kg × 2,260,000 J/kg = 452,000 J
      5. Heating steam from 100℃ to 120℃: Q5=mcΔT=0.2kg×2,010J/kg⋅℃×20℃=8,040JQ_5 = mc\Delta T = 0.2 kg × 2,010 J/kg·℃ × 20℃ = 8,040 J Total energy required: Qtotal=Q1+Q2+Q3+Q4+Q5=614,620JQ_{total} = Q_1 + Q_2 + Q_3 + Q_4 + Q_5 = 614,620 J or 614.62kJ614.62 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=mcΔT+mLQ = mc\Delta T + mL
    • QQ is the energy absorbed or released in joules (J)
    • mm is the mass of the substance in kilograms (kg)
    • cc is the specific heat capacity of the substance in joules per kilogram per kelvin (J/kg·K)
    • ΔT\Delta T is the change in temperature in kelvins (K) or degrees Celsius (℃)
    • LL 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=mcΔT+mLQ = 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 TfT_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 for water is 334 J/g.
    • Energy lost by water: Qw=mwcw(Ti−Tf)=300g×4.18J/g⋅℃×(50℃−Tf)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℃: Q1=miciΔT=100g×2.09J/g⋅℃×5℃=1,045JQ_1 = m_ic_i\Delta T = 100 g × 2.09 J/g·℃ × 5℃ = 1,045 J
      2. Melting ice at 0℃: Q2=miLf=100g×334J/g=33,400JQ_2 = m_iL_f = 100 g × 334 J/g = 33,400 J
      3. Heating melted ice (water) from 0℃ to TfT_f: Q3=mwcwΔT=100g×4.18J/g⋅℃×(Tf−0℃)Q_3 = m_wc_w\Delta T = 100 g × 4.18 J/g·℃ × (T_f - 0℃)
    • Applying conservation of energy: Qw=Q1+Q2+Q3Q_w = Q_1 + Q_2 + Q_3 300g×4.18J/g⋅℃×(50℃−Tf)=1,045J+33,400J+100g×4.18J/g⋅℃×(Tf−0℃)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 TfT_f: 62,700J−1,254J/℃×Tf=34,445J+418J/℃×Tf62,700 J - 1,254 J/℃ × T_f = 34,445 J + 418 J/℃ × T_f 28,255J=1,672J/℃×Tf28,255 J = 1,672 J/℃ × T_f Tf=16.9℃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 is a unique state where the distinction between liquid and gas phases disappears
  • Near the , substances can exhibit unusual behavior, such as rapid fluctuations between phases
  • The 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
  • occurs when a system's behavior depends on its history, often observed in phase transitions of certain materials

Key Terms to Review (42)

Calorimetry: Calorimetry is the experimental technique used to measure the amount of heat absorbed or released during a physical, chemical, or biological process. It is a fundamental concept in understanding heat transfer, specific heat, and phase changes in thermodynamics.
Clausius-Clapeyron equation: The Clausius-Clapeyron equation is a fundamental relationship that describes the equilibrium vapor pressure of a substance as a function of temperature. It is a crucial tool for understanding phase changes and the behavior of substances as they transition between different states of matter, such as solid, liquid, and gas.
Condensation: Condensation is the phase change from a gas to a liquid. It occurs when a gas is cooled to its dew point or comes into contact with a cooler surface.
Critical point: The critical point is the temperature and pressure at which the liquid and gas phases of a substance become indistinguishable. At this point, the properties of the liquid and gas phases converge into a single phase called a supercritical fluid.
Critical Point: The critical point is the specific temperature and pressure at which a substance's gas and liquid phases become indistinguishable, resulting in a supercritical fluid. At this point, the properties of the liquid and gas phases converge, leading to unique behaviors not found in either state alone. This phenomenon is crucial in understanding phase changes and the behavior of materials under varying conditions.
Critical pressure: Critical pressure is the minimum pressure required to liquefy a substance at its critical temperature. It is a specific point where the distinction between liquid and gas phases ceases to exist.
Critical temperature: The critical temperature is the temperature above which a gas cannot be liquefied, regardless of the pressure applied. It represents the highest temperature at which a substance can exist as a liquid.
Deposition: Deposition is the process by which a substance, typically in the gaseous or liquid state, transforms directly into the solid state without first passing through the intermediate liquid phase. This phase change occurs when the substance's vapor pressure equals the surrounding pressure, causing it to condense and settle out of the gas phase.
Dry ice: Dry ice is the solid form of carbon dioxide ($CO_2$) and sublimates directly into gas at $-78.5\degree C$. It is commonly used as a cooling agent due to its extremely low temperature.
Enthalpy: Enthalpy is a thermodynamic property that represents the total heat content of a system, combining internal energy with the product of pressure and volume. It plays a crucial role in understanding energy changes during phase transitions and chemical reactions, as it accounts for both the energy needed to change temperature and the energy required for changes in phase at constant pressure.
Equilibrium Vapor Pressure: Equilibrium vapor pressure is the pressure exerted by a vapor in thermodynamic equilibrium with its condensed phases (solid or liquid) at a given temperature. It is a fundamental concept in understanding phase changes and the behavior of substances as they transition between different states of matter.
Evaporation: Evaporation is the process where molecules at the surface of a liquid gain sufficient energy to enter the gaseous phase. This typically occurs at temperatures below the boiling point of the liquid.
First-order transition: A first-order transition is a type of phase change that occurs when a system undergoes a discontinuous change in its properties, such as density or entropy, at a specific temperature and pressure. This transition involves latent heat, which is the energy absorbed or released during the phase change, and is characterized by the coexistence of two different phases in equilibrium. First-order transitions can be observed in processes like melting, boiling, and sublimation.
Freezing: Freezing is the phase transition in which a liquid turns into a solid when its temperature is lowered to or below its freezing point. This process involves the release of latent heat and occurs at a specific temperature for pure substances.
Gibbs Free Energy: Gibbs free energy is a thermodynamic quantity that combines the concepts of energy, entropy, and temperature to determine the spontaneity and feasibility of a chemical process. It is a measure of the useful work that can be extracted from a system at constant temperature and pressure.
Heat of fusion: Heat of fusion is the amount of energy required to change a substance from the solid phase to the liquid phase at its melting point. It is usually expressed in joules per gram (J/g) or kilojoules per mole (kJ/mol).
Heat of sublimation: Heat of sublimation is the energy required to change a substance from a solid to a gas without passing through the liquid phase. It is a specific type of latent heat associated with phase changes.
Heat of Transformation: The heat of transformation is the amount of energy released or absorbed during a phase change, such as the transition from solid to liquid (melting) or liquid to gas (vaporization). This energy is associated with the changes in the intermolecular forces and the rearrangement of molecules that occur during the phase transformation.
Heat of vaporization: Heat of vaporization is the amount of heat energy required to convert a unit mass of a liquid into vapor without a change in temperature. It is usually expressed in joules per gram (J/g) or kilojoules per kilogram (kJ/kg).
Hysteresis: Hysteresis is the lag between an input and output in a system, often observed in magnetic materials where the magnetization lags behind the applied magnetic field. This phenomenon results in a looped curve when plotting magnetization against the magnetic field strength.
Hysteresis: Hysteresis is a phenomenon where the response of a system depends on its past history and experiences. It describes the lagging of an effect behind its cause, or the inability of a system to return to its original state when the forces acting on it are removed.
Latent Heat: Latent heat refers to the energy released or absorbed by a substance during a phase change, such as the transition from a solid to a liquid or from a liquid to a gas, without a change in temperature. It is the energy required to change the state of a substance without altering its temperature.
Latent heat coefficient: The latent heat coefficient is the amount of heat energy required to change the phase of a unit mass of a substance without changing its temperature. It is typically measured in units of J/kg.
Latent Heat of Fusion: Latent heat of fusion is the amount of energy required to change a substance from a solid state to a liquid state at its melting point, without changing the temperature of the substance. It represents the energy required to overcome the intermolecular forces that hold the solid structure together, allowing the transition to the liquid phase.
Latent Heat of Vaporization: The latent heat of vaporization is the amount of energy required to transform a substance from a liquid state to a gaseous state at a constant temperature and pressure. It represents the energy needed to overcome the intermolecular forces that hold the liquid molecules together, allowing them to transition into a less-dense gas phase.
Melting: Melting is the phase transition from a solid to a liquid. It occurs when a substance absorbs enough heat to overcome its molecular bonds.
Metastable State: A metastable state is a temporary, higher-energy state of a system that is not the most stable configuration, but persists for a significant period of time before transitioning to a more stable state. This concept is particularly important in the context of phase changes, where a substance may exist in a metastable phase before eventually reaching its most stable phase.
Nucleation: Nucleation is the initial step in the formation of a new thermodynamic phase, such as the formation of a solid from a liquid or gas. It involves the spontaneous appearance of a small, stable cluster of atoms or molecules that can then grow into a new phase.
Order Parameter: The order parameter is a measure of the degree of order in a system undergoing a phase transition, such as the transition from a disordered, liquid state to an ordered, solid state. It quantifies the extent to which the system has transitioned from a random, disorganized state to a more structured, organized state.
Phase boundary: A phase boundary is a surface or line that separates different phases of matter, such as solid, liquid, and gas. This boundary is crucial in understanding phase changes, as it marks the conditions under which one phase transitions to another, like melting or boiling. Recognizing these boundaries helps to predict how substances behave when they encounter varying temperature and pressure conditions.
Phase diagram: A phase diagram is a graphical representation that shows the conditions at which distinct phases (such as solid, liquid, and gas) occur and coexist at equilibrium. It typically plots pressure against temperature.
Phase Diagram: A phase diagram is a graphical representation that shows the relationships between the different phases of a substance, such as solid, liquid, and gas, as a function of variables like temperature and pressure. It provides a comprehensive overview of the conditions under which a substance can exist in different states.
Phase transitions: Phase transitions are the processes by which a substance changes from one state of matter (solid, liquid, gas) to another. These changes occur due to variations in temperature and pressure.
Specific heat: Specific heat is the amount of heat required to raise the temperature of one gram of a substance by one degree Celsius. It is a material-specific property and is measured in units of $\text{J/g} \cdot ^\circ \text{C}$.
Specific Heat: Specific heat, also known as specific heat capacity, is a measure of the amount of energy required to raise the temperature of a substance by one degree. It is a fundamental property that describes how much heat a material can absorb or release per unit mass and per unit temperature change.
Sublimation: Sublimation is the phase change where a substance transitions directly from a solid to a gas without passing through the liquid state. It occurs when the molecules in the solid phase gain enough energy to overcome intermolecular forces and enter the gas phase.
Sublimation: Sublimation is the process by which a solid substance transitions directly into a gaseous state, bypassing the liquid phase. This phase change occurs without the material going through the typical melting process, where a solid would first become a liquid before evaporating into a gas.
Supercritical Fluid: A supercritical fluid is a substance at a temperature and pressure above its critical point, where distinct liquid and gas phases do not exist. It exhibits properties between those of a liquid and a gas, making it a unique state of matter with diverse applications.
Triple Point: The triple point is the temperature and pressure at which the three phases of a substance (solid, liquid, and gas) can coexist in equilibrium. It is a unique point on a substance's phase diagram where the solid, liquid, and vapor phases meet.
Vapor: Vapor is the gaseous phase of a substance that is typically liquid or solid under standard conditions. It forms when the substance undergoes a phase change due to heating or pressure reduction.
Vapor pressure: Vapor pressure is the pressure exerted by a vapor in thermodynamic equilibrium with its condensed phases at a given temperature. It indicates the tendency of a substance to evaporate.
Vapor Pressure: Vapor pressure is the pressure exerted by a vapor in equilibrium with its liquid or solid phase at a given temperature. It is a fundamental property that governs the phase changes of substances and plays a crucial role in various physical and chemical processes.
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Glossary
Glossary
1.6 Mechanisms of Heat Transfer