Gavin Howe
The law of conservation of energy states that energy can neither be created nor destroyed. However, it can be transformed from one form to another. For example, in a torch, the chemical energy of the batteries is converted into electrical energy, which is then converted into light and heat energy. While the law of conservation of energy is widely accepted, some scholars claim that it is not well-defined and may not hold in certain cases, such as in an expanding universe or in quantum mechanics.
| Characteristics | Values |
|---|---|
| Energy can be created | False |
| Energy can be destroyed | False |
| Energy can be converted from one form to another | True |
| Total energy of a system remains constant | True |
| Total energy of a system can change if energy is added from the outside | True |
What You'll Learn
The expansion of the universe
The law of conservation of energy states that energy can neither be created nor destroyed. However, this law is not always upheld. The expansion of the universe, for example, contradicts this principle.
In an expanding universe, the total energy does not necessarily increase. If the global energy is conserved but the expansion does not stop, the universe will eventually reach a state of heat death. However, in an accelerating, expanding universe, the total energy must increase. This is because the expansion is tied to a constant in Einstein's equations, and as the volume of space increases, so does the acceleration.
The origin of this so-called dark energy is still a mystery. String theorists attribute it to the energy of the ground state of all the quantum fields in the universe, but the best calculations are off by 120 orders of magnitude.
The concept of total energy is not well-defined in general relativity. Energy is conserved locally at each point in spacetime, but the metric is not time-translation symmetric. Energy conservation in general relativity is purely local, expressed as the conservation of the stress-energy tensor.
Photons travelling through empty space are redshifted due to the expansion of the universe, and as the wavelength of light increases, its energy decreases. This energy is simply lost.
The universe's expansion also affects the energy of moving particles, slowing them down, and dark energy, which gains energy as the universe expands.
The total energy of the universe cannot be considered in such a way that it would be found to be conserved. However, within the universe, energy is locally conserved everywhere.
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Non-elastic collisions
Inelastic collisions occur when multiple masses collide and a significant amount of kinetic energy is lost in the collision. This lost kinetic energy is converted into other forms of energy, such as potential energy, thermal energy, or mechanical vibration. Inelastic collisions can also occur when masses collide and stick together, deforming upon impact.
In an inelastic collision, the objects after impact will stick together and move with a common velocity. The maximum amount of kinetic energy is lost in completely inelastic collisions, where the objects become one after the collision. An example of a completely inelastic collision is a bullet that comes to a complete stop when fired into a block of wood.
The law of conservation of energy states that energy is always conserved in an isolated system. This means that the total amount of energy in an isolated system remains the same, and energy is only converted between different forms. However, in inelastic collisions, kinetic energy is not conserved, and some of it is lost to heat and mechanical vibration. This loss of energy is challenging to calculate mathematically, making it difficult to balance the energy before and after the collision.
While the total momentum of the system is always conserved in collisions, as long as no external forces are acting on the system, inelastic collisions do not conserve kinetic energy. This means that the total kinetic energy before the collision differs from the total kinetic energy afterward.
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Perpetual motion
The law of conservation of energy states that energy can neither be created nor destroyed in an isolated system. However, it can be transformed from one form to another. For example, chemical energy is converted to kinetic energy when a stick of dynamite explodes.
The first law of thermodynamics, also known as the law of conservation of energy, states that energy cannot be created or destroyed, only transformed from one form to another. A perpetual motion machine of the first kind would have to produce work without any energy input, violating this law.
The second law of thermodynamics states that an isolated system will move towards a state of disorder, and that the more energy is transformed, the more is wasted. A perpetual motion machine would have to have energy that was never wasted and never moved towards a disordered state, which is impossible.
Despite the laws of physics suggesting that perpetual motion machines are impossible, people have continued to attempt to create them, often with the goal of achieving ''over-unity' performance, where the machine puts out more useful work than its energy input. Some of the earliest attempts include a wheel created by Indian author Bhaskara in the 12th century, a 16th-century windmill, 17th-century siphons, and several water mills.
Most perpetual motion attempts have been driven by scientific inquiry, but others have been designed to deceive and make money. One of the most famous hoaxes was created by Charles Redheffer in 1812. He charged people to view his machine, which he claimed could keep moving forever without ever being touched. The machine was eventually debunked by engineers, who discovered that it was powered by an old man sitting on a chair, turning a crank with one hand and eating a crust of bread with the other.
Even though perpetual motion machines are impossible, there are some systems that can appear to exhibit perpetual motion. For example, in 2016, new states of matter, time crystals, were discovered where the component atoms are in continual repetitive motion on a microscopic scale. However, these do not violate thermodynamic laws as they are in their quantum ground state, meaning no energy can be extracted from them.
Another example is a frictionless environment for motion, where an object is levitated using diamagnetic or electromagnetic levitation in a vacuum to eliminate air friction and friction from an axle. However, this type of system has no practical purpose as the levitated object cannot do any work, and it is also impossible to achieve a perfect vacuum.
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Non-conservative forces
The law of conservation of energy states that energy can neither be created nor destroyed, only transformed or transferred from one form to another. However, this law can be broken by non-conservative forces, which are forces for which work done depends on the path taken.
Friction
Friction is a force that opposes motion between two surfaces in contact. When an object moves against friction, some of its mechanical energy is lost as thermal energy, which cannot be fully recovered. For example, when a car comes to a stop due to friction, its kinetic energy is converted into thermal energy, reducing its overall mechanical energy.
Air Resistance or Air Drag
When an object moves through the air, it experiences air resistance or air drag, which is a force that opposes its motion. This force is path-dependent and leads to a loss of mechanical energy. The kinetic energy of the object is converted into thermal energy, causing a decrease in its overall energy.
Tension in a Cord
Tension force in a cord is another example of a non-conservative force. The work done by this force depends on the path taken, resulting in a loss of mechanical energy.
Push or Pull Force by a Person
The force exerted by a person when pushing or pulling an object is considered non-conservative because the work done depends on the path followed. This force can either add or remove mechanical energy from a system.
Normal Force in a Collision
When a baseball collides with a bat and bounces back, a normal force comes into play. In this collision, some of the kinetic energy is lost as sound and heat energy, demonstrating the non-conservative nature of normal force.
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Quantum mechanics
The law of conservation of energy states that the total energy of an isolated system remains constant over time. In quantum mechanics, this law is known to apply to the expected value, making any consistent conservation violation provably impossible. However, there is some debate on whether individual conservation-violating events could exist or be observed.
In classical mechanics, the energy of a system is simply a function of its position, momentum, angular momentum, and other characteristics. However, in quantum mechanics, the state of a system is specified by a wave function, a superposition of various possible measurement outcomes. The concept of energy in quantum mechanics is a bit different and more complex.
The average or expected energy of a quantum system can be calculated, and if the system obeys the Schrödinger equation, this average energy is conserved and does not change over time. However, there are cases where quantum systems do not obey the Schrödinger equation, such as when they are being measured. During a measurement, the wave function of a system can "collapse," resulting in a change in the average energy. This collapse is unpredictable and does not follow the Schrödinger equation.
In the Many-Worlds interpretation of quantum mechanics, the energy of the wave function of the universe is perfectly conserved. Each individual world or branch may perceive a change in average energy, but the total energy of the entire universe, including all branches, remains constant.
While energy conservation is a fundamental principle in physics, it can become tricky in certain situations, such as an expanding universe or in the context of quantum mechanics. The concept of energy conservation in quantum mechanics is subtle and has been the subject of ongoing research and discussion.
Some physicists argue that energy must be conserved in each individual experimental run, even if it is challenging to measure. Others suggest that energy conservation holds statistically, meaning that over the course of many experiments, the distribution of energies before and after the system's evolution should match.
In summary, while energy conservation is a fundamental principle, its interpretation and application in quantum mechanics can be complex and is still a subject of ongoing investigation.
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Frequently asked questions
No, the law of conservation of energy states that energy cannot be created or destroyed, only transformed from one form to another.
In a non-elastic collision, mechanical energy is not conserved. Some energy is lost within the materials involved in the collision, for example, energy may be lost through heat generation or deformation of the objects.
The law of conservation of energy has been repeatedly verified through experiments and observations. For example, the total energy in a closed system can be measured by calculating the mass of the system.
While potential energy cannot be directly observed, its effects can be observed and measured. For example, when a ball is dropped from a height, its potential energy is converted into kinetic energy, and we can measure the speed at which it hits the ground.
The expansion of the universe can change the total energy of a system. For example, photons travelling through space are redshifted due to the expansion, resulting in a loss of energy. However, this does not affect processes within a galaxy.
