Conservation of mass and energy
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Conservation of Mass and Energy: A Comprehensive Overview
Historical Foundations of Mass and Energy Conservation
The principles of mass and energy conservation have been fundamental to scientific understanding since the late 18th and early 19th centuries. Antoine-Laurent Lavoisier's quantitative investigations into combustion in 1772 laid the groundwork for the conservation of mass, while the recognition of energy conservation emerged around 18402. These foundational principles have since been integral to both classical and modern physics.
Mass-Energy Equivalence and Conservation
Einstein's equation (E = mc^2) revolutionized the understanding of mass and energy, demonstrating that they are different measures of a single quantity known as mass-energy. This principle asserts that mass-energy is conserved in all physical and chemical processes. In nuclear and subatomic reactions, although large quantities of energy are emitted, mass is not converted into energy; instead, any mass lost by the system is acquired by the surroundings along with the emitted energy4. This conservation principle holds true even in chemical reactions, though the mass changes are typically too small to detect directly4.
Conservation Laws in Fluid Dynamics
In fluid dynamics, reduced order models (ROMs) are used to simplify the complex Navier-Stokes equations while maintaining essential conservation properties. Research has shown that traditional methods using snapshot averages for centering trajectories can lead to incorrect energy balances. A proposed alternative, the Stokes extension, has been shown to produce more accurate energy balances both theoretically and numerically, especially over longer time intervals1. Additionally, ROMs created using Scott-Vogelius (SV) elements, which satisfy mass conservation pointwise, yield more accurate results compared to those using Taylor-Hood (TH) elements, which satisfy mass conservation weakly1.
Mass and Energy Conservation in Modern Physics
Modern physics continues to explore the implications of mass and energy conservation through the lenses of quantum mechanics and general relativity. These theories provide different interpretations of energy and matter, yet the law of conservation of energy remains a cornerstone. This law states that energy cannot be created or destroyed, only transformed from one form to another3. The study of dark energy and its consequences further highlights the ongoing challenges and complexities in understanding mass-energy conservation in the universe3.
Energy Conservation in Black Hole Dynamics
In the realm of astrophysics, the conservation of mass-energy is crucial in understanding black hole dynamics. The first law of black-hole dynamics describes how a black hole's mass-energy increases due to the energy densities of infalling matter and gravitational radiation. This law provides a framework for measuring both ingoing and outgoing gravitational radiation and offers insights into the growth and energy flux of black holes5.
Simplified Applications and Theoretical Insights
Simplified applications of mass and energy conservation are essential for understanding the thermodynamic states of multi-component systems. These applications serve as benchmarks for testing computational models and provide practical insights into the conservation laws7. Additionally, the analogy between random linear wave fields and mass particle ensembles demonstrates the applicability of conservation theorems in various physical contexts, including gravity wave spectra8.
Conclusion
The conservation of mass and energy remains a fundamental principle across all branches of physics and chemistry. From the historical foundations laid by Lavoisier and the development of mass-energy equivalence by Einstein, to modern applications in fluid dynamics, quantum mechanics, and black hole physics, these conservation laws continue to provide critical insights into the natural world. Understanding and applying these principles is essential for advancing scientific knowledge and technological innovation.
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Most relevant research papers on this topic
Energy balance and mass conservation in reduced order models of fluid flows
The Stokes extension for energy balance in reduced order models improves accuracy and precision, while the Scott-Vogelius element provides more accurate mass conservation results.
A Mathematical Overview of Mass and Energy Conservation in Modern Physics
The law of conservation of energy is a fundamental law in quantum mechanics and general relativity, and its implications and challenges in understanding dark energy are discussed.
Literature Review
PreprintE = mc2 for the Chemist: When Is Mass Conserved?
Mass-energy conservation is crucial in all physical and chemical processes, but it is not always obvious.
Energy conservation for dynamical black holes.
The energy conservation law for black holes explains their growth and regularity, providing a measure of gravitational radiation and a Gibbs-like equation for energy supply.
Highly CitedMass and energy
I must take issue with Sir Hermann Bondi and Mr C B Spurgin (Physics Bulletin February 1987 p62) over their dogmatic statements about mass and energy. My objection is most clearly to rules (ii) and (iii) in their final section, which say that energy is always conserved, and mass is always conserved, implying that there are two conservation laws.
On the non-linear energy transfer in a gravity wave spectrum Part 2. Conservation theorems; wave-particle analogy; irrevesibility
The non-linear energy transfer in gravity waves can be analogized to particle collisions, with the stationary wave spectrum being degenerate and the question of irreversibility being discussed but not fully resolved.
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