Chapter 14: Temperature & Heat

Thermodynamics

Thermodynamics is a fundamental branch of physics concerned with the study of systems containing a very large number of constituents (typically ). It analyzes the bulk or average properties of these systems, such as temperature, pressure, and chemical potential, rather than focusing on individual particles.

• Definition: Thermodynamics is the study of energy, heat, and work in large systems.

• Big Four in Physics: Thermodynamics, classical mechanics, quantum mechanics, electromagnetism.

Temperature

Temperature is a central concept in thermodynamics, representing the average kinetic energy of the particles in a system. It is what is measured with a thermometer and is the property that becomes equal for two objects in thermal contact after sufficient time (thermal equilibrium).

• Operational Definition: Temperature is a measure of the average kinetic energy of the constituents of a system.

• Thermal Equilibrium: Two objects in contact reach the same temperature after a while.

• Heat Transfer: When touching a hot object, energy is transferred to you as heat, raising your skin temperature.

• Historical Note: The connection between heat and energy took about 150 years to be fully understood by physicists.

Temperature Scales

Temperature can be measured using different scales, each with its own reference points and units. The most common are Fahrenheit, Celsius, and Kelvin.

• Fahrenheit: Water freezes at 32°F and boils at 212°F. Linear scale.

• Celsius: Water freezes at 0°C and boils at 100°C. Linear scale.

• Kelvin: Absolute temperature scale, zero at absolute zero.

• Linear Relationship: The scales are linearly related:

  • Using freeze and boil points, or

• Coincidence Point: The temperature at which Celsius and Fahrenheit coincide can be found by solving .

Absolute Zero

Absolute zero is the theoretical temperature at which the average kinetic energy of the particles in a substance becomes zero. However, quantum mechanical effects prevent this from being physically attainable.

• Definition: Absolute zero is the (unreachable) temperature where the average kinetic energy of the constituents is zero.

• Quantum Effects: Quantum mechanics and the Heisenberg Uncertainty Principle prevent particles from having zero momentum.

• Kelvin Scale: Rescaling Celsius so that zero occurs at absolute zero gives the Kelvin scale:

Thermal Expansion

When materials are heated, their particles gain kinetic energy and move more vigorously, causing the material to expand. The type and amount of expansion depend on the material and its geometry.

• Linear Expansion (Thin Objects):

  • If a thin object increases in temperature by , its length changes by

  • is the coefficient of linear expansion, material-dependent.

  • General formula:

• Volumetric Expansion (Thick Objects):

  • If a thick object increases in temperature by , its volume changes by

  • is the coefficient of volume expansion, material-dependent.

  • General formula:

• Applications: Bimetal strips in thermostats, expansion of steel tapes, and the anomalous expansion of water (important for freezing lakes).

Thermal Energy: Heat

Heat is the energy transferred between systems or objects due to a temperature difference. It is not a property contained within an object, but rather energy in transit.

• Definition: Heat flow or heat transfer is energy transfer due to temperature difference.

• Units:

  • 1 cal = 4.186 J

  • 1 kcal = 1000 cal = 4186 J

  • 1 Btu = 778 ft-lb = 252 cal = 1055 J

• Key Point: Heat is only meaningful as energy in transit, not as a property of an object.

Heat & Specific Heat Capacity

The specific heat capacity of a substance quantifies how much heat is required to change its temperature by a certain amount. It is a material property and varies widely among substances.

• Formula:

• Q: Amount of heat transferred

• m: Mass of the substance

• c: Specific heat capacity (J/kg·K)

• Large c: More heat required to change temperature; also, more heat released when cooling.

• Example: Water has a high specific heat capacity ( J/kg·K), making it effective for thermal regulation.

Phase Changes

When a substance changes from one state of matter to another (solid, liquid, gas, plasma), it undergoes a phase change. During this process, the temperature remains constant as all the heat goes into changing the phase.

• Examples: Water ↔ ice, water ↔ steam, gas ↔ plasma.

• Key Point: Temperature does not change during a phase change; heat is used for the phase transition.

Latent Heat

Latent heat is the amount of heat required for a substance to change phase at constant temperature.

• Fusion (Melting/Freezing):

  • Formula:

  • is the latent heat of fusion (J/kg)

  • Water: J/kg

• Vaporization (Boiling/Condensing):

  • Formula:

  • is the latent heat of vaporization (J/kg)

  • Water: J/kg

• Sign Convention: is positive when energy is added (melting/boiling), negative when removed (freezing/condensing).

Heat Transfer Mechanisms

Heat can be transferred by three main mechanisms: conduction, convection, and radiation.

• Conduction: Transfer of heat through direct contact. Governed by thermal conductivity .

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

• Radiation: Transfer of heat via electromagnetic waves, does not require a medium.

Conduction

• Formula:

• is the heat current (rate of heat flow), is the cross-sectional area, is the length, and are the temperatures at each end.

• Thermal Conductivity Table:

Radiation

• Formula:

• is surface area, is emissivity, is the Stefan-Boltzmann constant ( W/(m·K)), is temperature in Kelvin.

• Net Heat Transfer: , where is the temperature of the surroundings.

• Emissivity: for a perfect reflector, for a perfect absorber (blackbody).

Examples & Applications

• Thermal Expansion: Steel tape length increases on a hot day due to linear expansion.

• Bimetal Strips: Used in mechanical thermostats to detect temperature changes.

• Water's Anomalous Expansion: Water expands upon freezing, affecting lake ice formation.

• Heat Capacity: Water's high specific heat makes it useful for temperature regulation.

• Latent Heat: Calculating energy required for melting/freezing and boiling/condensing.

• Heat Transfer: Calculating net power radiated by a heated object using the Stefan-Boltzmann law.

Additional info: Some context and table entries have been inferred and expanded for completeness and clarity. All equations are provided in LaTeX format for academic use.