Thermodynamics Review

Introduction and Review of Classical Thermodynamics

• The universe is enormous, with a vast number of particles, making it necessary to learn how to count the number of states a system can have or avoid counting them.
• A small cup of tea contains about 5 moles of water, equivalent to 3 × 10^24 molecules of water.

Laws of Thermodynamics

• Zeroth Law of Thermodynamics: introduces the concept of thermal equilibrium and allows for the definition of a temperature scale.
• 1st Law of Thermodynamics: states that energy cannot be created or destroyed, only converted from one form to another.
• 2nd Law of Thermodynamics: describes the direction of spontaneous processes, introducing the concept of entropy.

Thermodynamic Potentials

• Free energies and thermodynamic potentials: describe the energy available to do work in a system.
• Maxwell Relations: provide a set of equations that relate the thermodynamic potentials to each other.
• Heat capacity and specific heat: measure the amount of heat energy required to change the temperature of a system.

Chemical Potential

• Chemical potential: a measure of the energy associated with the addition or removal of particles from a system.

Intensive/Extensive Variables and Conjugacy

• Intensive variables: independent of the system size, such as temperature and pressure.
• Extensive variables: dependent on the system size, such as energy and volume.
• Conjugacy: the relationship between intensive and extensive variables.

Statistical Ensembles

• Phase space of microstates: a mathematical representation of all possible states of a system.
• Microcanonical ensemble: a statistical ensemble that describes a system with a fixed energy and number of particles.
• Canonical ensemble: a statistical ensemble that describes a system in thermal equilibrium with a heat bath.
• Boltzmann Distribution: a probability distribution that describes the likelihood of a system being in a particular state.
• Partition function: a mathematical function that describes the probability of a system being in a particular state.

Classical Gas

• Ideal gas: a hypothetical gas that obeys the ideal gas law, which describes the relationship between pressure, volume, and temperature.
• Equipartition Theorem: states that the energy is evenly distributed among the available degrees of freedom.
• Maxwell-Boltzmann distribution: a probability distribution that describes the velocity of particles in a gas.

Quantum Gas

• Quantum states vs classical particles: quantum states are distinct from classical particles, with properties that are governed by quantum mechanics.
• Density of states: a mathematical function that describes the number of available states in a system.
• Relativistic vs non-relativistic particles: particles can be described as either relativistic or non-relativistic, depending on their velocity.
• Indistiguishability: particles can be either distinguishable or indistinguishable, depending on their properties.