Phase changes and latent heat Knowledge-Based Study

Study notes

1. States of Matter and Phase Transitions

   Matter commonly exists in three macroscopic states: solid, liquid, and gas. A phase change is a physical transition from one state of aggregation to another, occurring when energy is added or removed under constant pressure.

   • Melting (Fusion): Transition from solid to liquid.
   • Freezing (Solidification): Transition from liquid to solid.
   • Vaporization: Transition from liquid to gas (via boiling throughout the liquid or evaporation at the surface).
   • Condensation: Transition from gas to liquid.
   • Sublimation: Direct transition from solid to gas without entering the liquid phase.
   • Deposition: Direct transition from gas to solid.

   For a pure substance at a given pressure, phase changes occur at characteristic fixed temperatures, such as the melting point and the boiling point.

   Kinetic vs. Potential Energy

   A crucial observation in thermal physics is that the temperature of a pure substance remains strictly constant during an entire phase transition, provided the pressure is kept constant.

   Temperature is a direct measure of the average translational kinetic energy of the constituent particles:

   • When heat is supplied and temperature rises, the added energy increases the average kinetic energy of the molecules.
   • During a phase transition, added heat does not increase the particles' average kinetic energy. Instead, it is used to overcome or loosen intermolecular forces (electrostatic attractions between particles), thereby increasing their potential energy.

   Conversely, during an exothermic phase change (such as freezing or condensation), thermal energy is released to the surroundings as intermolecular bonds form or strengthen, while the temperature remains unchanged until the transition is complete.

   Specific Latent Heat

   The term latent heat originates from the Latin word for 'hidden', because thermal energy is transferred without causing an observable temperature change on a thermometer.

   The amount of heat energy $Q$ required to change the phase of a mass $m$ of a pure substance without a change in temperature is given by:

   $$Q = m L$$

   Here:

   • $Q$ is the thermal energy absorbed or released (measured in joules, $\text{J}$).
   • $m$ is the mass of the substance (measured in kilograms, $\text{kg}$).
   • $L$ is the specific latent heat of the substance (measured in $\text{J/kg}$).

   Types of Specific Latent Heat

   • Specific Latent Heat of Fusion ($L_f$): The energy required per unit mass to melt a solid at its melting point. For water, $L_f \approx 3.34 \times 10^5\text{ J/kg}$.
   • Specific Latent Heat of Vaporization ($L_v$): The energy required per unit mass to vaporize a liquid at its boiling point. For water, $L_v \approx 2.26 \times 10^6\text{ J/kg}$.

   Notice that for water, $L_v$ is significantly larger than $L_f$. This difference occurs because melting only partially weakens the intermolecular bonds, whereas vaporization requires completely breaking intermolecular bonds and separating molecules against atmospheric pressure.

   Interpreting Temperature-Time Graphs

   When a solid substance is heated at a constant rate, a plot of temperature versus time (or added heat) exhibits distinct regions:

   1. Single-phase heating segments (sloped regions): The substance exists in a single state (solid, liquid, or gas). Temperature increases according to $Q = mc\Delta T$. The slope of each region is inversely proportional to the heat capacity of that phase ($\Delta T / \Delta t = P / (mc)$, where $P$ is heating power).
   2. Phase coexistence segments (horizontal plateaus): Two phases coexist in dynamic thermal equilibrium (e.g., solid and liquid during melting). Temperature stays flat at the transition temperature while heat is absorbed according to $Q = mL$. The length of the plateau is directly proportional to the latent heat of that phase transition.

   Key Distinction

   Remember to select the correct formula based on the process:

   • Use $Q = mc\Delta T$ when there is a temperature change within a single phase.
   • Use $Q = mL$ when there is a phase change occurring at a constant temperature.