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16.2 Entropy

3 min read•june 25, 2024

measures in thermodynamic systems. It's key to understanding why processes happen spontaneously. Higher entropy means more disorder, like in gases, while lower entropy means more order, like in solids.

Entropy relates to , which are possible particle arrangements. More microstates mean higher entropy. This concept helps explain why some processes occur naturally and others don't, connecting to the idea of spontaneity in reactions.

Entropy and Thermodynamics

Entropy in thermodynamic systems

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  • Entropy (SS) thermodynamic state function measures degree of disorder or randomness in a system
    • Higher entropy indicates greater disorder or randomness (gas phase)
    • Lower entropy indicates greater order or predictability (solid phase)
  • Entropy plays crucial role in determining spontaneity of processes in thermodynamic systems
    • Spontaneous processes tend to increase total entropy of universe (system + surroundings) (ice melting at room temperature)
    • Non-spontaneous processes decrease total entropy of universe (water freezing at room temperature)
  • states total entropy of universe always increases in spontaneous processes ( transfer from hot to cold object)
    • This principle is closely related to the concept of in natural processes

Entropy's relation to microstates

  • Entropy directly related to number of microstates () accessible to a system
    • Microstates different possible arrangements of particles in a system that correspond to a given macrostate (different ways to arrange cards in a deck)
    • relates entropy to number of microstates: S=[k](https://www.fiveableKeyTerm:K)ln⁡WS = [k](https://www.fiveableKeyTerm:K) \ln W, where kk is
  • Systems with larger number of microstates have higher entropy (gas vs. solid at same temperature)
  • Disorder refers to lack of predictability or randomness in a system
    • Systems with more disorder have larger number of microstates and higher entropy (shuffled vs. ordered deck of cards)
  • provides a framework for understanding entropy at the molecular level

Entropy changes in reactions

  • Entropy changes (ΔS\Delta S) can be predicted for various chemical reactions and physical processes
  • Phase changes:
    1. Entropy increases during phase changes that go from more ordered to less ordered states
      • Solid to liquid (melting): ΔS>0\Delta S > 0 (ice to water)
      • Liquid to gas (vaporization): ΔS>0\Delta S > 0 (water to steam)
    2. Entropy decreases during phase changes that go from less ordered to more ordered states
      • Gas to liquid (condensation): ΔS<0\Delta S < 0 (steam to water)
      • Liquid to solid (freezing): ΔS<0\Delta S < 0 (water to ice)
  • Temperature changes:
    • Entropy increases when temperature of a system increases: ΔS>0\Delta S > 0 (heating a substance)
    • Entropy decreases when temperature of a system decreases: ΔS<0\Delta S < 0 (cooling a substance)
  • Chemical reactions:
    • Entropy generally increases when number of moles of gas increases: ΔS>0\Delta S > 0 (decomposition of calcium carbonate: CaCO3(s)→CaO(s)+CO2(g)CaCO_3(s) \rightarrow CaO(s) + CO_2(g))
    • Entropy generally decreases when number of moles of gas decreases: ΔS<0\Delta S < 0 (synthesis of ammonia: N2(g)+3H2(g)→2NH3(g)N_2(g) + 3H_2(g) \rightarrow 2NH_3(g))
    • Entropy changes can be calculated using standard molar entropies (S∘S^\circ) of reactants and products: ΔSrxn∘=∑Sproducts∘−∑Sreactants∘\Delta S^\circ_{rxn} = \sum S^\circ_{products} - \sum S^\circ_{reactants}

Entropy and Energy

  • Heat is a form of energy transfer that directly affects entropy
  • combines the concepts of enthalpy and entropy to predict spontaneity and in chemical reactions
  • Systems tend to move towards a state of equilibrium, where the entropy is maximized within the constraints of the system

Key Terms to Review (32)

Boltzmann: Boltzmann is a physicist renowned for his foundational contributions to statistical mechanics and thermodynamics. He introduced the Boltzmann constant, which links the average kinetic energy of particles in a gas with temperature.
Boltzmann Constant: The Boltzmann constant is a fundamental physical constant that relates the average kinetic energy of particles in a gas to the absolute temperature of the gas. It is a crucial parameter in the study of thermodynamics and the behavior of systems at the molecular level.
Boltzmann Equation: The Boltzmann equation is a fundamental equation in statistical mechanics that describes the statistical distribution of particles in a system in thermal equilibrium. It is a central concept in the study of entropy and the behavior of thermodynamic systems.
Carnot: The Carnot cycle is a theoretical thermodynamic cycle that provides the maximum possible efficiency for a heat engine. It serves as an idealized model for understanding entropy in reversible processes.
Chemical thermodynamics: Chemical thermodynamics studies the interrelation of heat and work with chemical reactions or physical changes. It applies principles of thermodynamics to predict the direction and extent of chemical processes.
Clausius: Rudolf Clausius was a German physicist and mathematician who formulated the second law of thermodynamics and introduced the concept of entropy. His work laid the foundation for our understanding of energy conservation and transformation.
Configurational Entropy: Configurational entropy refers to the measure of disorder or randomness in the spatial arrangement or configuration of particles or molecules within a system. It is a crucial concept in understanding the spontaneous behavior of systems and the natural tendency towards increased disorder.
Disorder: Disorder refers to the degree of randomness or chaos within a system. In the context of thermodynamics, it is closely related to entropy, as higher disorder indicates a greater number of possible arrangements for the components of a system. The concept helps to understand how energy disperses and the tendency of systems to evolve towards states of higher disorder over time.
Entropy: Entropy is a measure of the disorder or randomness of a system. It represents the amount of energy in a system that is no longer available to do useful work and is instead dissipated as heat. Entropy is a fundamental concept in thermodynamics and is closely related to the second law of thermodynamics.
Entropy (S): Entropy (S) is a measure of the disorder or randomness in a system. It quantifies the number of possible microstates corresponding to a macroscopic state.
Equilibrium: Equilibrium is a state of balance or stability in a system, where the opposing forces or processes are in a state of dynamic balance. It is a fundamental concept that underpins various aspects of chemistry, including phase changes, chemical reactions, and thermodynamic processes.
Free Energy: Free energy is a thermodynamic concept that represents the maximum amount of work that can be extracted from a system while maintaining a constant temperature and pressure. It is a measure of the energy available to do useful work and is a crucial factor in determining the spontaneity and feasibility of chemical reactions and physical processes.
Free energy change (ΔG): Free energy change ($\Delta G$) is the difference in free energy between the products and reactants in a chemical reaction. It determines whether a process is spontaneous or non-spontaneous.
Heat: Heat is a form of energy that is transferred from a hotter object to a cooler object due to a temperature difference. It is a fundamental concept in thermodynamics that describes the flow of thermal energy and its effects on the physical properties of matter and systems.
Irreversibility: Irreversibility refers to the property of a process or system where the initial state cannot be fully recovered after the process has occurred. It is a fundamental concept in the study of entropy and the second law of thermodynamics, which governs the spontaneous direction of natural processes.
Joules per Kelvin: Joules per Kelvin (J/K) is a unit that measures the amount of energy required to raise the temperature of a system by one Kelvin. It is a fundamental unit in the study of thermodynamics and is closely related to the concept of entropy.
K: K is a variable used to represent various constants and parameters in the context of chemical processes and principles. It is a versatile term that appears in multiple areas of chemistry, including the study of gas behavior, reaction kinetics, chemical equilibrium, and thermodynamics.
Ludwig Boltzmann: Ludwig Boltzmann was an Austrian physicist who made significant contributions to the field of statistical mechanics, particularly in the understanding of entropy and the second law of thermodynamics. His work laid the foundation for the modern understanding of the behavior of gases and the relationship between microscopic and macroscopic properties of systems.
Microstate: A microstate is a specific detailed microscopic configuration of a thermodynamic system that corresponds to one particular way the system can be arranged. Each microstate represents a unique arrangement of particles and energy levels in the system.
Microstates: Microstates refer to the individual quantum states or configurations that a system can occupy at the microscopic level. In the context of entropy, microstates represent the various ways in which the energy of a system can be distributed among its constituent particles or components.
Nonspontaneous process: A nonspontaneous process is a chemical or physical change that requires external energy to proceed. These processes have a positive change in Gibbs free energy ($\Delta G > 0$).
Reversible process: A reversible process is a theoretical concept in which a system undergoes changes in such a way that the system and its surroundings can be restored to their original states without any net change. This process occurs infinitely slowly, ensuring that the system remains in thermodynamic equilibrium at all times.
Rudolf Clausius: Rudolf Clausius was a German physicist who made significant contributions to the field of thermodynamics. He is best known for his work on the concept of entropy, which he introduced and developed in the context of the second law of thermodynamics.
Second law of thermodynamics: The second law of thermodynamics states that the total entropy of an isolated system can never decrease over time. It implies that natural processes increase the overall disorder or randomness of a system.
Second Law of Thermodynamics: The second law of thermodynamics states that the total entropy of an isolated system not in equilibrium will tend to increase over time, approaching a maximum value at equilibrium. It is a fundamental principle that describes the direction of spontaneous processes in the universe.
Spontaneous Process: A spontaneous process is a natural, self-driven change that occurs in a system without the need for external intervention. It is a fundamental concept in thermodynamics that describes the natural tendency of a system to evolve towards a more stable or lower energy state over time.
Standard entropy change (ΔS°): Standard entropy change ($\Delta S^\circ$) is the change in entropy for a reaction under standard conditions, typically 1 bar pressure and 298.15 K (25°C). It provides insight into the disorder or randomness added to the system during a reaction.
Statistical Mechanics: Statistical mechanics is a branch of physics that applies the principles of probability and statistics to the study of the behavior of large systems of particles, such as gases, liquids, and solids. It provides a fundamental understanding of how the microscopic properties of individual particles give rise to the macroscopic properties of a system.
Thermal Entropy: Thermal entropy is a measure of the disorder or randomness of a system's energy at the atomic and molecular level. It quantifies the amount of energy within a system that is not available for useful work, but instead is dispersed as heat. Thermal entropy is a fundamental concept in thermodynamics that helps explain the spontaneous direction of natural processes.
Thermodynamics: Thermodynamics is the branch of physics that deals with the relationships between heat, work, temperature, and energy. It describes the fundamental physical laws governing the transformation of energy and the flow of heat, which are essential to understanding the behavior of chemical systems and processes.
W: W is a thermodynamic quantity that represents the work done by or on a system during a process. It is a fundamental concept in the study of entropy, as it is closely related to the changes in a system's internal energy and the flow of energy in and out of the system.
ΔS: ΔS, or change in entropy, is a fundamental concept in thermodynamics that describes the measure of disorder or randomness in a system. It is a key factor in understanding the spontaneity and direction of natural processes, as well as the efficiency of energy conversions.
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16.3 The Second and Third Laws of Thermodynamics