Thermal Physics: Temperature, Heat Transfer, and Phase Changes – Study Notes

Thermal Physics: Temperature, Heat Transfer, and Phase Changes

Non-Thermal Equilibrium Relationships

Thermal equilibrium is a state in which two objects in contact with each other no longer transfer heat, meaning they are at the same temperature. However, systems can have other types of equilibrium or relationships that are not thermal in nature.

• Non-thermal equilibrium: A situation where two systems share a property (such as pressure or chemical potential) but are not at the same temperature.

• Example: Consider three objects: A, B, and C. A and B are in mechanical equilibrium (no net force between them), and B and C are also in mechanical equilibrium, but A and C are not in thermal equilibrium (they are at different temperatures).

• Key Point: The transitive property of equilibrium (if A is in equilibrium with B, and B with C, then A is with C) only holds for thermal equilibrium, not necessarily for other types.

Temperature Scales and Measurement Errors

Temperature can be measured in different scales, most commonly Celsius (°C) and Fahrenheit (°F). Errors in reading or converting temperatures can lead to incorrect results.

• Celsius to Fahrenheit conversion: The formula is $F = \frac{9}{5}C + 32$.

• Common mistakes: Omitting the negative sign or misapplying the conversion formula can lead to errors.

• Example: If a temperature is -x°C, but the negative sign is omitted and the conversion is done as if it were x°C, the result may coincidentally match the correct Fahrenheit value for -x°C under certain conditions. This is a mathematical curiosity and not generally true.

• Significance: Always check the sign and apply the correct formula when converting temperatures.

Bimetallic Thermometers

Bimetallic thermometers use two metals with different coefficients of thermal expansion bonded together. As temperature changes, the metals expand at different rates, causing the strip to bend or coil, which moves a pointer to indicate temperature.

• Structure: A bimetallic strip is often shaped into a spiral or coil to amplify the movement.

• Why two metals? The difference in expansion rates causes the strip to bend; a single metal would not bend.

• Temperature response: The strip bends more as the temperature increases. The smallest spiral radius occurs at the lowest temperature, and the largest at the highest temperature.

• Applications: Used in household thermometers, thermostats, and other temperature-sensing devices.

Heat Transfer: Conduction and Convection

Heat can be transferred by conduction (through solids), convection (through fluids), and radiation. The rate of heat transfer depends on material properties and temperature differences.

• Conduction: The process by which heat energy is transmitted through collisions between neighboring atoms or molecules.

• Formula for heat conduction: $Q = \frac{kA\Delta T t}{d}$, where:

  • $Q$ = heat transferred (Joules)

  • $k$ = thermal conductivity (W/m·K)

  • $A$ = area (m²)

  • $\Delta T$ = temperature difference (K or °C)

  • $t$ = time (s)

  • $d$ = thickness of material (m)

• Convection: The transfer of heat by the movement of fluids (liquids or gases).

• Example: Double-paned windows reduce heat loss by trapping air (a poor conductor) between glass panes, reducing conduction and increasing insulation.

Phase Changes and Pressure-Temperature Diagrams

Phase diagrams show the state of a substance (solid, liquid, gas) at different temperatures and pressures. The lines on the diagram indicate conditions where two phases coexist (e.g., melting/freezing, boiling/condensing).

• Melting of ice under pressure: Applying pressure can lower the melting point of ice, causing it to melt at temperatures below 0°C.

• Clausius-Clapeyron relation: Describes the slope of the phase boundary between two phases.

• Example: An ice skater exerts pressure on the ice, causing it to melt and form a thin layer of water, reducing friction and allowing smooth gliding.

• Formula for pressure: $P = \frac{F}{A}$, where $F$ is force and $A$ is area.

Sample Table: Comparison of Heat Transfer Methods

Method	Medium	Mechanism	Example
Conduction	Solids	Direct molecular collisions	Metal rod heated at one end
Convection	Liquids/Gases	Bulk movement of fluid	Boiling water
Radiation	Vacuum or any medium	Electromagnetic waves	Sunlight warming the Earth

Additional info:

• For the bimetallic thermometer, the spiral is smallest at the lowest temperature and largest at the highest temperature because the metal with the higher expansion rate causes the coil to tighten or loosen as temperature changes.

• In the ice skating example, the pressure exerted by the skate blade is sufficient to lower the melting point of ice, creating a lubricating layer of water.