Thermal Equilibrium and the Zeroth Law

Thermal Equilibrium

Thermal equilibrium is a fundamental concept in thermodynamics describing the state in which two bodies in contact no longer exchange heat energy. This occurs when both bodies reach the same temperature.

• Heat Flow (Q): Heat naturally flows from a hotter object to a colder one until equilibrium is reached.

• Equilibrium Condition: When heat flow stops (Q = 0), both bodies have the same temperature.

• Analogy: Similar to static equilibrium in mechanics, where the sum of forces and torques is zero (, ).

Zeroth Law of Thermodynamics

The Zeroth Law establishes the basis for temperature measurement and thermal equilibrium.

• Statement: If Body A is in thermal equilibrium with Body B, and Body B is in equilibrium with Body C, then Body A is in equilibrium with Body C.

• Mathematical Expression: and

Microscopic Perspective

Thermal energy is the microscopic mechanical energy of molecules. Even when a body is at rest, its molecules vibrate and possess kinetic energy.

• Random Motion: Molecules move randomly, contributing to the body's internal energy.

Temperature Scales and Thermometers

Temperature Measurement

Temperature quantifies the state of thermal equilibrium. Thermometers are devices that measure temperature by reaching equilibrium with the object being measured.

• Gas Thermometer: Measures temperature based on the pressure of a gas at constant volume. The relationship is linear.

Temperature Scales

Different scales are used to measure temperature, each with its own reference points.

• Celsius (°C): Defined by the freezing point (0°C) and boiling point (100°C) of water.

• Kelvin (K): The absolute scale, where 0 K is absolute zero—the point at which all molecular motion ceases.

• Conversion Equation:

• Graphical Representation: Pressure vs. temperature graphs show all gas lines converging at C (absolute zero).

Thermal Expansion

Expansion of Materials

Most materials expand when heated and contract when cooled. The degree of expansion depends on the material and its state (solid, liquid, gas).

• General Rule: Increasing temperature causes expansion; decreasing temperature causes contraction.

• Material Dependence: Expansion is characterized by coefficients:

  • Linear Expansion Coefficient (\alpha): For length changes.

  • Volume Expansion Coefficient (\beta): For volume changes.

• State of Matter: Gases expand much more than solids or liquids with temperature changes.

Heat Capacity and Specific Heat

Heat Capacity

Heat capacity is a measure of how much heat energy is required to change an object's temperature.

• Definition: The amount of heat needed to raise the temperature of a body by one degree.

• Equation:

• Dependence: Depends on both the material and the mass of the object.

Specific Heat

Specific heat is the heat capacity per unit mass, an intrinsic property of the material.

• Equation:

• Specific Heat of Water:

• Units: 1 calorie = heat required to raise 1g of water by 1°C = 4.186 J

• Sign Convention: if heat enters the system; if heat leaves.

Mechanisms of Heat Transfer

Conduction

Conduction is the transfer of heat through a material without the material itself moving. It occurs via molecular collisions and vibrations.

• Power Equation:

• Thermal Conductivity (k): High for conductors (metals), low for insulators (styrofoam, vacuum).

• Example: Heat traveling from a stove burner through the base of a pot.

Convection

Convection is the transfer of heat by the movement of fluids (liquids or gases). Warm fluid rises and cool fluid sinks, creating convection currents.

• Mechanism: Actual motion of material transports heat.

• Example: Air heated by a radiator rises, cools, and falls, forming a circular current in a room.

Radiation

Radiation is the transfer of heat via electromagnetic waves, primarily in the infrared spectrum. It does not require a medium.

• Stefan-Boltzmann Law:

• Emissivity (e): Dimensionless value between 0 and 1; a black body () is an ideal radiator.

• Example: Heat from the Sun reaching Earth through the vacuum of space.

Summary Table: Temperature Scales and Properties

Summary Table: Mechanisms of Heat Transfer

Additional info: Academic context and equations have been expanded for clarity and completeness. Visual descriptions have been translated into examples and summary tables.