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4.10 Conservation of Energy

There are many forms of energy in the universe. At first glance the types of energy we have discussed seem very different. What could possibly relate the energy in a coiled spring to the energy in a cup of gasoline? What do the energy in a hot coal and the energy in a falling meteor have in common? First, all these types of energy are quantifiable and measurable. Second, scientists have shown that all the different forms of energy are interchangeable. Energy changes form all the time.

The idea of the transformation of energy is a basic example of how science works. One of the basic goals of science is to provide simple explanations for the diversity of the natural world. Scientists can show that kinetic energy and gravitational potential energy are not fundamentally different. Both have the ability to cause a change. Both can be measured in units of Joules. And one can be converted to the other. The transformation of energy is an important unifying principle throughout science.
 


Joule's Heat Apparatus used for measuring heat, 1845. Click here for original source URL.

In Joule's famous experiment, he started by raising a weight in his apparatus. This then stored gravitational potential energy. The falling weight caused a paddle to rotate. The gravitational energy was transformed into the kinetic energy of the moving paddle. The paddle agitated the water molecules, giving them each a bit more energy. So the kinetic energy was transformed into heat energy in the water.

Energy is transformed into many forms and can even be stored. For example, mechanical energy might be stored in the wind-up spring of a toy car or a clock, and then released in the form of motion to move the car or the hands of the clock. A battery stores electrical energy that can then be released to move the shutter of your camera. The head of a match stores chemical energy that can be released into heat. Energy can also change forms continually. A child on a swing is constantly changing gravitational potential energy into kinetic energy and back again. At the top of the swing's arc, the motion momentarily stops and all the energy is potential energy. At the lowest point in the arc, all the potential energy has been converted into kinetic energy. An elliptical orbit is similar. Kepler's second law relates the speed of a planet's orbit to its distance from the Sun. A planet has the most gravitational potential energy and the least kinetic energy when it is farthest from the Sun. It has the least gravitational potential energy and the most kinetic energy when it is closest to the Sun. The orbit is a continuous conversion of the two types of energy.
 


Impact debris from comet Shoemaker-Levy on Jupiter. Click here for original source URL.

Suppose an asteroid hurtles through space at 10 kilometers per second and crashes into a planet. Before the asteroid hits the planet, it has a certain amount of kinetic energy. It also has a significant but much smaller amount of gravitational energy due to its position above the planet. As it falls toward the planet and speeds up, it gains additional kinetic energy. After it hits the planet, its material comes to rest and thus has no kinetic energy or gravitational energy with respect to the surface. Does the energy disappear? No, it is simply transformed. The kinetic energy of the asteroid heats the impact site, makes an explosion, and blasts out small, hot fragments that fall back on the planet. (If the asteroid is large enough, there is enough energy to liquefy or vaporize significant amounts of rock.) Soon after the impact, the total system would have the same amount of energy, but the asteroid's initial energy would now be present as extra heat in the planetary material.

On Earth almost all energy originates from the Sun. Light energy from the Sun reaches the Earth, where a fraction of it is stored as chemical energy in the cells of plants. Some of that energy is retained in fossil fuels, which we then release to drive our cars and heat our homes. We take in more of that chemical energy when we eat. Our bodies break down the chemicals and store the energy in our cells. Some of that stored chemical energy is eventually released as heat to maintain the temperature of our bodies at 37° C (equal to 98.6° F, or 310 K). In this way we can see on the Earth a great chain of energy conversion that leads back to the Sun. It is an interesting exercise to take some activity in the natural world and see how many transformations separate it from the Sun's energy.

Scientists went from the idea of the convertibility of energy to an important physical law. In any closed system, the total amount of energy is constant. This is the law of conservation of energy. What do we mean by a "closed system?" We mean that if you draw a giant box around the objects you are considering, the energy contained within the box will not change. Energy can change between any of the forms we have described, but the total amount of energy is conserved. The conservation of energy is one of the most important principles in science.

This law operates in an astronomical orbit. The total energy in a closed orbit is constant. An elliptical orbit has a continual exchange between kinetic and potential energy but the sum does not change. In a circular orbit, neither kinetic nor potential energy changes. In the case of the asteroid hitting a planet, the energy of motion is converted into an equal amount of heat, which then converts into thermal energy that radiates away slowly into space. Energy does not come and go arbitrarily. Many systems appear to lose energy, but if you consider them carefully you will see that the lost energy has turned into another form. A rolling ball or a swinging pendulum each eventually come to a halt; in each case friction turns kinetic energy into heat. This is more obvious in the commonplace example of the brakes of your car. When you jam on your brakes, the kinetic energy of your car is converted to heat in your brake linings through friction. The design of the linings must take into account the conservation of energy.
 


Basic overview of energy and human life. Click here for original source URL.

We can bring the discussion down to earth with a human example. People get their energy from the food they eat. Food energy is measured in calories, which is the amount of energy needed to heat 1 kilogram of water by 1° Celsius. In our physical system of units 1 calorie = 4186 Joules. The chemical energy stored in the food you eat is used in various ways by your body, but since it keeps your temperature high, most of it is released as heat. The average adult consumes 2500 calories per day. This is 2500 × 4186 = 1.05 × 107Joules. Now we note that there are 24 × 60 × 60 = 86,400 seconds in a day. So the rate at which the human body generates heat is 1.05 × 107 / 8.64 × 104 = 121 Joules per second, or 121 Watts. Each of us radiates as much energy as a light bulb! If you consume more than 2500 calories per day, the extra energy has to go somewhere. If you exercise, the extra calories can be converted into heat and radiated away. If you don't exercise, the extra calories are stored as chemical energy in fat. The issue of exercise and diet comes down to the conservation of energy.