Temperature and Temperature Scales

Definition and Measurement

Temperature is a measure of the average translational kinetic energy of molecules in a substance. It is a fundamental concept in thermodynamics and kinetic theory.

• Temperature Scales: Common scales include Celsius (°C), Fahrenheit (°F), and Kelvin (K).

• Kelvin Scale: The absolute temperature scale, where 0 K is absolute zero.

• Conversion:

• Example: Room temperature: , K

Thermal Equilibrium

When two systems are in thermal contact and have the same temperature, they are in thermal equilibrium and no net thermal energy flows between them.

• Key Point: Thermal equilibrium is the basis for temperature measurement.

Thermal Expansion

Expansion of Solids and Liquids

Most materials expand when heated due to increased molecular motion. The change in length or volume is proportional to the temperature change.

• Linear Expansion:

• Volume Expansion:

• Coefficients: is the linear expansion coefficient; is the volume expansion coefficient ( for solids).

• Example: Brass:

• Exceptions: Polymers (plastic, rubber) have small expansion effects.

Expansion of Gases

Gases expand much more than solids or liquids for a given temperature change, governed by the ideal gas law.

• Key Point: Volume expansion in gases is typically described by

Ideal Gas Law and Gas Processes

Ideal Gas Law

The ideal gas law relates pressure, volume, temperature, and the number of moles of gas.

• Equation:

• Variables: = pressure, = volume, = moles, = universal gas constant ( J/mol·K), = temperature in Kelvin.

• Boltzmann Constant: J/K

• Example: Weather balloon at , Pa

Gas Processes

• Isochoric: Constant volume ()

• Isobaric: Constant pressure ()

• Isothermal: Constant temperature ()

• Adiabatic: No heat exchange ()

Partial Pressures

In a mixture of gases, the total pressure is the sum of the partial pressures of each component.

• Law of Partial Pressures:

• Example: Air: , ,

Kinetic Theory of Gases

Basic Principles

The kinetic theory describes gases as collections of particles obeying Newton's laws, with pressure arising from collisions with container walls.

• Average Kinetic Energy: per particle

• Root Mean Square Speed:

• Pressure:

• Example: for at

Brownian Motion and Diffusion

Brownian motion is the random movement of particles suspended in a fluid, resulting from collisions with molecules. Diffusion is the net flow of particles from regions of higher concentration to lower concentration.

• Diffusion Equation:

• Diffusion Coefficient: depends on particle nature, background, and temperature.

• Example: A particle diffuses 1 mm in 1 hour; to diffuse 2 mm, it takes 4 hours ().

Osmosis and Osmotic Pressure

Osmosis

Osmosis is the selective diffusion of water through a semipermeable membrane from a region of higher water potential to lower water potential.

• Osmotic Pressure:

• Variables: = molar concentration, = gas constant, = temperature

• Example: Find osmotic pressure for a mol/L salt solution at $300$ K

Heat, Specific Heat, and Calorimetry

Heat Capacity and Specific Heat

Heat capacity is the ratio of heat added to a system to the corresponding temperature change. Specific heat is the heat capacity per unit mass.

• Heat Capacity:

• Specific Heat:

• Example: Water: J/kg·°C

• Calorimetry Equation:

Phase Changes

During phase changes (melting, boiling), temperature remains constant while heat is supplied.

• Latent Heat:

• Fusion (melting):

• Vaporization (boiling):

• Example: Mixing ice and water, calculating final temperature using

First Law of Thermodynamics

Energy Conservation

The first law states that the change in internal energy of a system equals the heat added to the system minus the work done by the system.

• Equation:

• Internal Energy: For an ideal gas,

• Work: (for constant pressure)

• Example: Isobaric expansion:

Degrees of Freedom and Equipartition

Energy is distributed among degrees of freedom (translational, rotational, vibrational) according to the equipartition theorem.

• Monatomic Gas: 3 translational degrees ()

• Diatomic Gas: 5 degrees (3 translational + 2 rotational)

• Solids: 6 degrees (3 translational + 3 vibrational)

Heat Transfer Mechanisms

Conduction, Convection, and Radiation

Heat can be transferred by conduction (through materials), convection (bulk motion of fluids), and radiation (electromagnetic waves).

• Conduction: , where is thermal conductivity

• Convection: Transfer by movement of thermal mass

• Radiation: , where is emissivity, W/m2·K4

• Example: Insulating a window with plastic reduces conduction

Summary Table: Gas Processes

Additional info:

• Some equations and values were inferred from context and standard physics knowledge.

• Examples and applications were expanded for clarity.

• Table entries were logically grouped and completed for completeness.