Thermodynamics Laws

Thermodynamics

Laws of Thermodynamics

• Zeroth Law: If two systems are in thermal equilibrium with a third system, they are also in thermal equilibrium with each other.
• First Law: Energy cannot be created or destroyed, only converted from one form to another. ΔU = Q - W
• Second Law: The total entropy of an isolated system always increases over time. ΔS = ΔQ / T
• Third Law: As the temperature of a system approaches absolute zero, its entropy approaches a minimum value.

Thermodynamic Systems

• Isolated System: No energy or matter can be exchanged with the surroundings.
• Closed System: Energy can be exchanged with the surroundings, but not matter.
• Open System: Both energy and matter can be exchanged with the surroundings.

Thermodynamic Properties

• Internal Energy (U): The total energy of a system, including kinetic energy, potential energy, and potential energy associated with the molecular structure.
• Enthalpy (H): A measure of the total energy of a system, including internal energy and the energy associated with the pressure and volume of a system. H = U + pV
• Entropy (S): A measure of the disorder or randomness of a system.

Quantum Mechanics

Key Principles

• Wave-Particle Duality: Quantum objects, such as electrons, can exhibit both wave-like and particle-like behavior.
• Uncertainty Principle: It is impossible to know certain properties of a quantum object, such as position and momentum, simultaneously with infinite precision.
• Superposition: A quantum object can exist in multiple states simultaneously.
• Entanglement: The properties of two or more quantum objects can be connected in such a way that the state of one object is dependent on the state of the other.

Quantum Systems

• Schrödinger Equation: A mathematical equation that describes the time-evolution of a quantum system. iℏ(∂ψ/∂t) = Hψ
• Wave Function (ψ): A mathematical function that describes the quantum state of a system.
• Hamiltonian (H): A mathematical operator that represents the total energy of a quantum system.

Quantum Mechanics and Measurement

• Observables: Quantities that can be measured, such as position, momentum, and energy.
• Measurement: The act of observing a quantum system, which causes the system to collapse from a superposition of states to a single state.
• Probabilistic Nature: Quantum mechanics predicts the probability of different outcomes for a measurement, rather than a definite outcome.

Thermodynamics

Laws of Thermodynamics

• Zeroth Law of Thermodynamics: Thermal equilibrium is a transitive property, meaning that if systems A and B are in thermal equilibrium with system C, then A and B are also in thermal equilibrium with each other.
• First Law of Thermodynamics: Energy is conserved, but can be converted from one form to another, and is expressed as ΔU = Q - W, where U is internal energy, Q is heat added, and W is work done.
• Second Law of Thermodynamics: The total entropy of an isolated system always increases over time, and is expressed as ΔS = ΔQ / T, where S is entropy, Q is heat added, and T is temperature.
• Third Law of Thermodynamics: As the temperature of a system approaches absolute zero, its entropy approaches a minimum value.

Thermodynamic Systems

• Isolated System: A system that does not exchange energy or matter with its surroundings.
• Closed System: A system that exchanges energy but not matter with its surroundings.
• Open System: A system that exchanges both energy and matter with its surroundings.

Thermodynamic Properties

• Internal Energy (U): The total energy of a system, including kinetic energy, potential energy, and potential energy associated with the molecular structure.
• Enthalpy (H): A measure of the total energy of a system, including internal energy and the energy associated with the pressure and volume of a system, expressed as H = U + pV.
• Entropy (S): A measure of the disorder or randomness of a system.

Quantum Mechanics

Key Principles

• Wave-Particle Duality: Quantum objects exhibit both wave-like and particle-like behavior, such as electrons behaving as both waves and particles.
• Uncertainty Principle: It is impossible to know certain properties of a quantum object, such as position and momentum, simultaneously with infinite precision.
• Superposition: A quantum object can exist in multiple states simultaneously, such as spinning both clockwise and counterclockwise.
• Entanglement: The properties of two or more quantum objects are connected in such a way that the state of one object is dependent on the state of the other.

Quantum Systems

• Schrödinger Equation: A mathematical equation that describes the time-evolution of a quantum system, expressed as iℏ(∂ψ/∂t) = Hψ.
• Wave Function (ψ): A mathematical function that describes the quantum state of a system.
• Hamiltonian (H): A mathematical operator that represents the total energy of a quantum system.

Quantum Mechanics and Measurement

• Observables: Quantities that can be measured, such as position, momentum, and energy.
• Measurement: The act of observing a quantum system, which causes the system to collapse from a superposition of states to a single state.
• Probabilistic Nature: Quantum mechanics predicts the probability of different outcomes for a measurement, rather than a definite outcome.