12.3 Second Law of Thermodynamics: Entropy
3 min read•june 24, 2024
measures disorder in systems, while the states that total entropy always increases. These concepts explain why certain processes occur spontaneously, like heat flowing from hot to cold objects.
The Second Law has wide-ranging applications, from predicting energy transformations to determining process feasibility. It helps us understand why some changes happen naturally, while others require external energy input to overcome entropy increases.
Entropy and the Second Law of Thermodynamics
Entropy and Second Law
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- Entropy () measures disorder or randomness in a system
- Higher entropy indicates greater disorder or randomness (gas molecules spread out in a room)
- Lower entropy indicates greater order or predictability (neatly stacked books)
- Second Law of Thermodynamics states total entropy of an always increases over time
- In any , entropy of the universe increases (ice melting, salt dissolving in water)
- Entropy can remain constant in reversible processes, but never decreases
- Entropy determines direction of spontaneous processes
- Processes that increase entropy are more likely to occur spontaneously (heat flowing from hot to cold object)
- Processes that decrease entropy are not spontaneous and require external energy input (separating mixed salt and pepper)
- The Second Law provides a fundamental explanation for the , indicating why certain processes are irreversible
Applications of Second Law
- Energy transformations always involve an increase in total entropy of system and surroundings
- from hot object to cold object increases entropy (coffee cooling to room temperature)
- Mixing of two substances increases entropy due to increased randomness (cream mixing with coffee)
- Spontaneous processes occur naturally without external intervention
- Examples include heat flow from hot to cold, gas expansion, and (perfume spreading through a room)
- Non-spontaneous processes require external energy input to overcome entropy increase (separating a mixture of gases)
- Second Law helps predict direction and feasibility of thermodynamic processes
- Processes that increase entropy are more likely to occur spontaneously (rusting of iron)
- Processes that decrease entropy are less likely to occur without external energy input (converting waste heat into useful work)
Entropy changes in systems
- Change in entropy () for a system can be calculated using formula:
- is heat transferred to or from system (in )
- is absolute temperature of system (in )
- For reversible processes, change in entropy can be calculated by integrating over process
- ( of an ideal gas)
- For irreversible processes, change in entropy is always greater than
- states for irreversible processes (heat transfer through a finite temperature difference)
- Changes in entropy can also be calculated using
- relates entropy to number of ():
- is ( ) (relates microscopic properties to macroscopic thermodynamic quantities)
Thermodynamic Cycles and Efficiency
- Heat engines convert thermal energy into mechanical work
- The is an ideal thermodynamic cycle that achieves maximum theoretical efficiency
- concepts, such as Gibbs free energy, help determine the spontaneity and maximum work output of thermodynamic processes
Key Terms to Review (26)
Arrow of Time: The arrow of time refers to the unidirectional nature of time, where events progress from the past to the future in an irreversible manner. This concept is closely tied to the Second Law of Thermodynamics and the increase of entropy in closed systems over time.
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 statistical mechanics.
Boltzmann's Equation: Boltzmann's equation is a fundamental relationship in statistical mechanics that describes the distribution of particles in a system at equilibrium. It connects the microscopic properties of individual particles to the macroscopic thermodynamic properties of a system, providing a bridge between the two realms.
Carnot Cycle: The Carnot cycle is an idealized thermodynamic cycle that describes the maximum possible efficiency of a heat engine operating between two thermal reservoirs at different temperatures. It is named after the French physicist Sadi Carnot, who first proposed the concept in 1824.
Clausius Inequality: The Clausius inequality is a fundamental principle in thermodynamics that establishes a relationship between the change in entropy of a system and the amount of heat exchanged with its surroundings. It is a mathematical expression of the Second Law of Thermodynamics and is closely related to the concept of entropy.
Diffusion: Diffusion is the process by which particles or molecules move from an area of high concentration to an area of low concentration, driven by the natural tendency to equalize concentrations. This movement occurs without the need for external forces, as it is a spontaneous process driven by the random motion of the particles.
Energy Transformation: Energy transformation is the process by which energy changes from one form to another. It is a fundamental concept in physics that describes how various types of energy, such as mechanical, thermal, electrical, or chemical energy, can be converted and utilized in different ways.
Entropy: Entropy is a measure of the disorder or randomness in a system. It represents the amount of energy in a system that is not available for useful work and is instead dissipated as heat. Entropy is a fundamental concept in the Second Law of Thermodynamics, which describes the natural tendency of systems to move towards a state of greater disorder over time.
Free Energy: Free energy is a thermodynamic quantity that represents the maximum amount of work that can be extracted from a system at a constant temperature and pressure. It is a measure of the useful energy available in a system, taking into account both the energy and the entropy of the system.
Heat Engine: A heat engine is a device that converts the energy from heat into mechanical work. It operates by taking in thermal energy from a high-temperature source, converting a portion of that energy into mechanical work, and then exhausting the remaining energy to a low-temperature sink.
Heat Reservoir: A heat reservoir is an idealized concept in thermodynamics that represents a system with an infinitely large thermal capacity. It can be thought of as a source or sink of heat that can exchange energy with other systems without undergoing any significant change in its own temperature or internal energy.
Heat Transfer: Heat transfer is the movement of thermal energy from a region of higher temperature to a region of lower temperature. It is a fundamental concept in thermodynamics that describes the mechanisms by which heat energy is exchanged between different systems or within a single system.
Irreversible Process: An irreversible process is a thermodynamic process that cannot be reversed and returned to its initial state without leaving some permanent change in the surroundings. It is a one-way process that results in an increase in the entropy of the universe.
Isolated System: An isolated system is a physical system that does not exchange any matter with its surroundings, though it may exchange energy. It is a self-contained system that is completely separated from the external environment, allowing for the study of its internal processes and transformations without external influences.
Isothermal Expansion: Isothermal expansion is a thermodynamic process in which a system, such as a gas, expands while maintaining a constant temperature. This means that the system exchanges heat with its surroundings in order to keep the temperature constant during the expansion.
J/K: J/K is a common abbreviation used in informal written communication, typically in online or digital contexts, to indicate that the preceding statement or remark was not meant to be taken seriously or literally. It is a way of signaling that the statement was intended as a joke or sarcasm.
Joules: Joules are the standard unit of energy in the International System of Units (SI). They measure the amount of work done or energy transferred in various physical and chemical processes, including those related to phase changes and thermodynamics.
Kelvin: Kelvin is the base unit of temperature in the International System of Units (SI), named after the renowned physicist Lord Kelvin. It is a fundamental physical quantity that is essential in understanding and describing various phenomena related to temperature, thermal energy, and thermodynamics.
Microstates: Microstates refer to the distinct microscopic configurations or arrangements of particles within a macroscopic system. They represent the different possible ways the individual components of a system can be distributed while maintaining the system's overall macroscopic properties. Microstates are a fundamental concept in the context of the Second Law of Thermodynamics and the understanding of entropy.
Reversible Process: A reversible process is a thermodynamic process that can be reversed without leaving any trace on the surroundings. In other words, it is a process that can be undone, allowing the system and the surroundings to return to their initial states without any net change. Reversible processes are idealized models used in thermodynamics to understand the fundamental limits of energy conversion and the behavior of physical systems.
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 natural direction of processes and the limits of energy conversion in physical systems.
Spontaneous Process: A spontaneous process is a natural, self-driven change that occurs in a system without the need for external intervention or the input of work. It is a fundamental concept in the Second Law of Thermodynamics and is closely related to the idea of entropy and the direction of natural processes.
Statistical Mechanics: Statistical mechanics is a branch of physics that applies the principles of probability and statistics to the study of the macroscopic behavior of systems composed of a large number of particles. It provides a framework for understanding the relationship between the microscopic properties of individual atoms and molecules and the macroscopic properties of materials and thermodynamic systems.
Thermal Equilibrium: Thermal equilibrium is a state in which two or more objects or systems have reached the same temperature, and no net transfer of thermal energy occurs between them. This concept is fundamental in understanding the behavior of heat, temperature, and the laws of thermodynamics.
Thermodynamic Process: A thermodynamic process is a series of changes that a thermodynamic system undergoes as it transitions from one state to another. It involves the exchange of energy, such as heat or work, between the system and its surroundings, and is governed by the laws of thermodynamics.
ΔS: ΔS, or change in entropy, is a fundamental concept in the Second Law of Thermodynamics that describes the measure of disorder or randomness in a system. It is a crucial quantity in understanding the spontaneous and irreversible nature of natural processes.