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Conservation of Energy

1847

Émilie du Châtelet
Julius Robert von Mayer
James Prescott Joule
Hermann von Helmholtz

(generated image for illustration only)

A fundamental principle stating that the total energy of an isolated system remains constant over time. Energy can neither be created nor destroyed, only transformed from one form to another, such as from potential to kinetic energy. In classical mechanics, for systems with only conservative forces, the total mechanical energy \(E = T + V\) is conserved.

The law of conservation of energy is one of the most fundamental and universally applicable principles in all of science. Its development spanned centuries, evolving from early ideas about motion into a precise mathematical statement in the 19th century that unified mechanics, heat, and chemistry.

In the context of classical mechanics, the principle is most clearly seen in systems subject only to conservative forces, such as gravity or the force from an ideal spring. A force is conservative if the work it does on an object moving between two points is independent of the path taken. For such forces, a potential energy function \(V\) can be defined. The work-energy theorem states that the net work done on an object equals the change in its kinetic energy, \(W_{net} = \Delta T\). For conservative forces, this work can be expressed as the negative change in potential energy, \(W_{cons} = -\Delta V\). Combining these gives \(\Delta T = -\Delta V\), or \(\Delta T + \Delta V = \Delta(T+V) = 0\). This shows that the total mechanical energy, \(E = T + V\), is a constant of motion.

When non-conservative forces like friction are present, mechanical energy is not conserved; it is typically dissipated as heat. However, the total energy of the isolated system, including this thermal energy, is still conserved. This broader principle is the First Law of Thermodynamics.

In the 20th century, Emmy Noether’s theorem provided a deeper understanding of this law. It showed that the conservation of energy is a direct mathematical consequence of a fundamental symmetry of the universe: the fact that the laws of physics do not change over time (time-translation invariance).

Energy, Enthalpy, Kinematics, Mechanical Engineering, Physics, Renewable Energy, Thermodynamics

UNESCO Nomenclature: 2211

– Physics

Type

Physical Law

Disruption

Revolutionary

Usage

Widespread Use

Precursors

Vis viva concept (Gottfried Leibniz)
Studies on heat and work (Sadi Carnot, Émile Clapeyron)
Newtonian mechanics
Galileo’s experiments with pendulums

Applications

power generation (hydroelectric dams, thermal plants)
thermodynamics and engine design
chemical reaction analysis (enthalpy)
roller coaster design
understanding metabolic processes in biology

Patents:

Potential Innovations Ideas

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Related to: conservation of energy, kinetic energy, potential energy, work-energy theorem, thermodynamics, isolated system, noether’s theorem, conservative force.

Historical Context

Daniell cell with copper and zinc electrodes in electrochemistry laboratory setup.

Daniell Cell Operation

An improvement on the Voltaic pile, the Daniell cell consists of a copper electrode in a copper(II) sulfate solution and a zinc electrode in a zinc sulfate solution, separated by a porous barrier. This two-fluid design prevents hydrogen gas buildup (polarization) on the copper electrode, resulting in a much more stable and reliable voltage source for a longer duration.

The Photovoltaic Effect

The photovoltaic effect is the generation of voltage and electric current in a material upon exposure to light. It is a physical and chemical phenomenon. A common application is the solar cell, which uses this effect to convert sunlight directly into electricity. The effect is based on photons of light exciting electrons into a higher state of energy.

19th century laboratory with thermodynamic instruments and Mayer's relation equations.

Mayer’s Relation (thermodynamics)

Mayer's relation connects the specific heats of a perfect gas to the specific gas constant (\(R_s\)). The relation is \(c_p - c_v = R_s\). For molar specific heats (\(C_p\) and \(C_v\)), the relation is \(C_p - C_v = R\), where \(R\) is the universal gas constant. This shows that \(c_p\) is always greater than \(c_v\).

Conservation of Energy

Laboratory setup for measuring viscosity of fluids at varying temperatures in thermodynamics.

Temperature Dependence of Viscosity

For a Newtonian fluid, viscosity is a function of temperature and pressure but not shear rate. In liquids, viscosity decreases significantly as temperature increases because higher thermal energy allows molecules to overcome cohesive intermolecular forces more easily. Conversely, in gases, viscosity increases with temperature as more frequent molecular collisions at higher speeds lead to greater momentum transfer.

First Law of Thermodynamics

The First Law is a statement of the conservation of energy. It posits that the change in a closed system's internal energy (\(\Delta U\)) is equal to the heat supplied to the system (\(Q\)) minus the work done by the system on its surroundings (\(W\)). The governing equation is \(\Delta U = Q - W\). This law links heat, work, and internal energy, establishing heat as a form of energy transfer.

Chemist conducting experiments with catalysts in a vintage laboratory setting, 1850.

Catalyst on Chemical Equilibrium

A catalyst increases the rate of both the forward and reverse reactions equally by providing an alternative reaction pathway with a lower activation energy. While a catalyst allows a system to reach equilibrium much faster, it does not change the position of the equilibrium itself. The equilibrium concentrations of reactants and products, and the value of the equilibrium constant K, remain unchanged.

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Catalysis

Catalysis is the process of increasing the rate of a chemical reaction by adding a substance known as a catalyst. Catalysts are not consumed in the reaction and remain unchanged. They work by providing an alternative reaction pathway with a lower activation energy (\(E_a\)), thereby accelerating both the forward and reverse reactions without altering the overall thermodynamics (\(\Delta H\)).

Fuel Cell

A fuel cell is an electrochemical device that directly converts the chemical energy of a fuel, typically hydrogen, and an oxidizing agent, often oxygen, into electricity. Unlike a battery, it requires a continuous external supply of fuel and oxidant to operate. The core components are an anode, a cathode, and an electrolyte that separates them, facilitating ion transport.

Demonstration of Joule heating in a vintage laboratory with electric appliances.

Joule Heating and Electric Power

Joule heating, or ohmic heating, is the phenomenon where heat is produced by an electric current passing through a conductor. The rate of heat generation, or power dissipated (\(P\)), is given by Joule's first law, \(P = VI\). By combining this with Ohm's law, the power can be expressed as \(P = I^2 R\) or \(P = \frac{V^2}{R}\).

Internal Energy and Enthalpy of a Perfect Gas

For a perfect gas, the internal energy (\(U\)) and enthalpy (\(H\)) are functions of temperature only. Their changes are given by \(\Delta U = m c_v \Delta T\) and \(\Delta H = m c_p \Delta T\), where \(c_v\) and \(c_p\) are the specific heats at constant volume and pressure, respectively, and are assumed to be constant.

Researcher testing viscoelastic properties of synthetic polymer in a laboratory.

Viscoelasticity

Viscoelasticity is the property of materials that exhibit both viscous and elastic characteristics when undergoing deformation. Viscous materials, like honey, resist shear flow and strain linearly with time when a stress is applied. Elastic materials, like a rubber band, strain when stretched and quickly return to their original state once the stress is removed. Viscoelastic materials have elements of both.

Scientist measuring sublimation in a vintage laboratory, thermodynamics study.

Enthalpy of Sublimation

The enthalpy of sublimation, \(\Delta H_{\text{sub}}\), is the heat required to convert one mole of a substance from solid to gas at a given temperature and pressure. According to Hess's Law, since enthalpy is a state function, this energy change is the sum of the enthalpy of fusion (\(\Delta H_{\text{fus}}\)) and the enthalpy of vaporization (\(\Delta H_{\text{vap}}\)).