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Conservation of Energy

A very important principle of Physics is ‘Conservation of Energy’. This is that energy cannot be created or destroyed, only transformed.

Consequences: the Second Law of Thermodynamics and Entropy.

Entropy

In any closed system (a system which has no loss or gain of energy from its surroundings), the total amount of energy will always be the same.

The Second Law of Thermodynamics assures us that in any transformation of energy from one form to another there cannot be 100% efficiency. For example, a car engine only uses 15% of the chemical energy of its fuel to move the car (kinetic energy). The remaining 85% of the energy results in 'useless' heat and noise. (see Carnot Heat Engine)

The concept of entropy derives from these principles: if energy cannot be transformed with 100% efficiency, the energy of a system must move from a more concentrated form to a state of greater dispersal. For example, a hot cup of tea in a room will cool while it heats the air and table it is on. It is not possible to reverse the direction of energy transfer without introducing more energy from outside (boiling a kettle).

Carnot heat engine
The Carnot heat engine explains why all energy conversions are inefficient

Efficiency

An important principle of thermodynamics states that no conversion is perfect – there will always be some loss to another form of energy. The amount of energy available to the animal’s body is much less than the total amount of energy from the sun to make the glucose in the plant. A ball does not bounce back to the same height as before, because some of the energy is ‘lost’ to heat and sound. The total amount of energy is always the same, but not all of the energy can be converted to a single form. The percentage that can be converted is known as efficiency.

$$η = {(output)}/{(input)} $$

This loss of 'usable' energy is called degradation of energy.

Efficiency is a technical term for the conversion of one energy from one form to another. Energy is never lost (Second Law of Thermodynamics), so if a fuel is burnt entirely, 100% has been converted to other energy forms. However, much of the new energy may be 'unusable', such as sound. If heat is the objective of the conversion, as it is in a boiler and turbine power generator, the efficiency would be a measure of how much electrical power results from the burning of an amount of fuel.

Burning oil in a power plant has the purpose of heating water, which is converted to steam, which drives a turbine, which generates electricity. Burning petrol in a car considers efficiency of conversion to be the kinetic energy of motion, and heat is 'unusable', so is lost to the purpose of the conversion.

Efficiency in power Generation

Energy sourceEnergy typeCurrent rangeTheoretical max.
Windkinetic30-50%59%
Photovoltaicradiative15-20%90%
Hydropowergravitational80-90%90%
Fuel cellchemical70-80%85%
Gas turbinechemical30-40%40%
Combined cycle*chemical and thermal40-60%60%
World TotalAll types39% gross33% net

* Two stage production: gas turbine then steam turbine

Photosynthesis and Respiration

Photosynthesis
Photosynthesis is a process by which solar radiation energy is converted and stored as chemical energy.

All of nature works by transformation of energy. When a plant grows it converts sunlight into glucose through photosynthesis. Glucose stores energy in a chemical form. When an animal eats a plant it gains this chemical energy and stores it in its own body as carbohydrate. When it needs this energy for its body to survive and move, its cells convert the carbohydrate to a form its muscles can use through a process called respiration. In respiration, the chemical energy of carbohydrate is converted to movement and heat.

Bouncing Ball

Ball bouncing
A ball bouncing experiences several energy transformations.

When a ball falls to the floor, it converts gravitational potential energy to kinetic energy. When it hits the floor, it converts kinetic energy to elastic potential energy, as well as some heat and noise. When it bounces away from the floor, this elastic potential energy is reconverted to kinetic energy. As the ball rises it loses kinetic energy and gains gravitational potential energy. Then the whole process repeats.

Example: conservation of energy in freefall

A body in freefall experiences a transformation of its gravitational potential energy to kinetic energy.

The total energy of the body is assumed to remain with the body: i.e. energy transformation is assumed to be 100% for the purposes of the exercise. In reality, there would be losses to the environment, primarily to the air as heat and noise due to air resistance.

The initial energy is entirely potential: $E_i = E_p$.

At the end of the fall (ground), the relative potential energy is zero. This means that the final energy at just above the ground is entirely kinetic: $E_f = E_k$ (= $E_i$).

At any point in between the energy is partially potential and partially kinetic: $E_t = E_p + E_k$.

Therefore, at any height h, and velocity v, the total energy of the body is: $E_t = E-p + E_k = mgh + ½mv^2$, and $E_t = E_i = E_f$.

Content © Andrew Bone. All rights reserved. Created : September 23, 2013 Last updated :December 15, 2015

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