General Principles of Thermodynamics

Laws of Thermodynamics

The laws of thermodynamics govern the behavior of energy and entropy in physical systems, especially those involving heat and temperature.

• First Law of Thermodynamics: States the conservation of energy for systems where only thermal energy changes. The change in thermal energy () is equal to the work () done on the system plus the heat () added to the system:

• Second Law of Thermodynamics: Specifies the direction of spontaneous processes. The entropy of an isolated system never decreases; energy spontaneously flows from hot to cold, and energy transformations are not 100% efficient.

• Third Law of Thermodynamics: (For curiosity) It is impossible to cool a system to absolute zero (0 K) in a finite number of steps.

Heat is energy transferred between objects due to a temperature difference. Transfer continues until thermal equilibrium is reached.

Important Concepts in Thermal Physics

Thermal Energy

For a gas, thermal energy is the total kinetic energy of motion of its atoms or molecules. This energy is random and associated with entropy.

• Random kinetic energy contributes to the disorder (entropy) of the system.

Temperature

Temperature is related to the average kinetic energy of the particles in a system. Two systems are in thermal equilibrium if they are at the same temperature, meaning no net heat energy is transferred between them.

Heat Engines and Heat Pumps

• Heat Engine: Converts thermal energy from a hot reservoir into useful work, exhausting heat to a cold reservoir. Efficiency is limited by the second law of thermodynamics. Maximum efficiency:

• Heat Pump: Uses energy input to transfer heat from a cold side to a hot side. The coefficient of performance (COP) is analogous to efficiency. For cooling:

Atomic Model of Matter

Phases of Matter

The atomic model describes matter as composed of basic particles (atoms or molecules). The arrangement and interaction of these particles define the phase:

• Solid: Particles are connected by stiff, spring-like bonds, giving solids a definite shape and low compressibility.

• Liquid: Weak bonds allow motion while keeping particles close together.

• Gas: Particles move freely and collide with each other and container walls.

Atomic Mass and Atomic Mass Number

• Atomic Mass Number (A):

• Atomic Mass Unit (u):

• Molecular Mass: Sum of atomic masses in a molecule (e.g., has molecular mass )

The Mole and Avogadro's Number

• Mole (mol): A way to specify the amount of substance; basic particles (Avogadro's number, ).

• Monatomic Gas: Basic particles are atoms (e.g., He, Ne, Ar).

• Diatomic Gas: Basic particles are molecules with two atoms (e.g., , , ).

• Moles from number of particles:

• Moles from mass: , where is molar mass in grams.

Atomic Model of an Ideal Gas

Properties of Ideal Gases

Ideal gases are highly compressible, and their temperature is directly proportional to the average kinetic energy per atom.

• Boltzmann's constant:

• Thermal energy of N atoms:

• Change in thermal energy:

At high altitudes, even with high temperatures, the low density of air means low thermal energy.

Molecular Speeds and Temperature

• Average kinetic energy:

• Root-mean-square (rms) speed:

• Relationship to temperature:

• Rms speed formula:

Temperature must be in kelvin for these calculations.

Pressure in Gases

• Gas particles colliding with container walls exert a force, resulting in pressure.

• Definition of pressure:

• SI unit: Pascal ()

• Standard atmosphere:

• Net pressure force is exerted only where there is a pressure difference.

• Absolute pressure: Total pressure exerted.

• Gauge pressure: Difference between absolute pressure and atmospheric pressure.

The Ideal-Gas Law

Formulation

The ideal-gas law relates pressure, volume, and temperature for a sample of gas.

• Version 1 (number of molecules):

• Version 2 (number of moles):

• Gas constant:

For a sealed container, the relationship between initial and final states is:

Ideal-Gas Processes

Types of Processes

• Constant-Volume (Isochoric) Process: Volume remains constant; pressure changes with temperature. Appears as a vertical line on a pV diagram.

• Constant-Pressure (Isobaric) Process: Pressure remains constant; volume changes. Appears as a horizontal line on a pV diagram.

• Constant-Temperature (Isothermal) Process: Temperature remains constant; is constant. Appears as a hyperbola on a pV diagram.

• Adiabatic Process: No heat is transferred (); temperature changes due to work done.

Work and Energy in Gas Processes

• Work done by a gas at constant pressure:

• For other processes, work is the area under the pV curve.

• First Law of Thermodynamics (for ideal gases):

• Change in thermal energy:

Work is positive if the gas expands (), negative if compressed ().

Thermal Expansion

Volume and Linear Expansion

Thermal expansion is the increase in size of a material when heated.

• Volume expansion:

• Linear expansion:

• Coefficients (linear) and (volume) depend on material and have units of .

Thermal expansion must be considered in engineering design to prevent structural damage.

Summary

• The atomic model explains phases of matter, thermal expansion, and heat transfer.

• The ideal-gas law relates pressure, volume, and temperature for gases.

• pV diagrams are useful for visualizing gas processes.

• Thermal expansion affects the dimensions of materials and must be accounted for in design.