Temperature, Thermal Expansion, and Ideal Gas Law

Temperature and Scales

Temperature is a measure of the average kinetic energy of particles in a substance. Common temperature scales include Celsius (°C), Fahrenheit (°F), and Kelvin (K).

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

• Conversion:

Thermal Expansion

• Linear Expansion: Change in length due to temperature change. where is the coefficient of linear expansion.

• Volume Expansion: Change in volume due to temperature change. where is the coefficient of volume expansion.

Ideal Gas Law

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

• Where = pressure, = volume, = number of moles, = universal gas constant, = temperature in Kelvin.

Avogadro's Number and Moles

• Avogadro's number: particles/mol

• Number of molecules:

Kinetic Theory of Gases

Basic Assumptions

• Gases consist of a large number of molecules in random motion.

• Collisions between molecules and with container walls are elastic.

• Volume of molecules is negligible compared to container volume.

Average Kinetic Energy

• For a monatomic ideal gas: where is Boltzmann's constant.

Root-Mean-Square Speed

Maxwell-Boltzmann Distribution

• Describes the probability distribution of speeds in a gas.

Heat and the First Law of Thermodynamics

Heat and Internal Energy

• Heat (Q): Energy transferred due to temperature difference.

• Internal Energy (U): Total energy of all molecules in a system.

• For a monatomic ideal gas:

Specific Heat

• Amount of heat required to change temperature of 1 kg of substance by 1 K.

Phase Changes

• Heat of fusion (): solid ↔ liquid

• Heat of vaporization (): liquid ↔ gas

First Law of Thermodynamics

• Energy conservation for thermodynamic systems.

• Where is work done by the system.

Thermodynamic Processes

• Isothermal: , ,

• Adiabatic: ,

• Isochoric: , ,

• Isobaric: ,

Second Law of Thermodynamics

Heat Engines and Efficiency

• Heat engines convert heat into work in a cyclic process.

• Efficiency:

• Carnot efficiency:

Entropy

• Entropy () measures disorder or randomness.

• Change in entropy:

• For reversible processes:

Second Law Statements

• Natural processes tend to increase the total entropy of the universe.

• Energy spontaneously disperses from being localized to becoming spread out if it is not hindered from doing so.

Electric Charge and Electric Field

Charge and Coulomb's Law

• Charge is quantized and conserved.

• Coulomb's Law:

• Where

Electric Field

• Electric field due to point charge:

• Direction: Away from positive, toward negative charges.

Gauss's Law

• Relates electric flux through a closed surface to the charge enclosed.

Electric Potential

• Potential energy per unit charge.

• Potential difference:

Capacitance, Dielectrics, and Electric Energy Storage

• Capacitance:

• Parallel plate capacitor:

• Energy stored:

• Dielectrics increase capacitance by a factor (dielectric constant).

Electric Current and Resistance

• Current:

• Ohm's Law:

• Resistance:

• Power:

DC Circuits

• Series:

• Parallel:

• Kirchhoff's Laws: Conservation of charge and energy in circuits.

Magnetism

• Magnetic force on moving charge:

• Magnetic field due to current: (long straight wire)

• Right-hand rule for direction of field.

Sources of Magnetic Field

• Biot-Savart Law:

• Ampère's Law:

Electromagnetic Induction and Faraday's Law

• Faraday's Law:

• Lenz's Law: Induced emf opposes the change in magnetic flux.

Inductance, Electromagnetic Oscillations, and AC Circuits

• Inductance:

• Energy in inductor:

• LC Oscillator: , ,

Additional info: These notes cover core topics from thermodynamics, kinetic theory, and electromagnetism, following the standard sequence of a college-level Physics II course.