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Section 2: Kinetic and Potential Energy
The precursor to the modern concept of energy was the idea of vis viva (Latin for "living force"), which was proposed in the 17th century by Gottfried Wilhelm Leibniz (1646–1716), the German mathematician and philosopher who developed the differential and integral calculus. Scholars differed on the question of how to measure the vis viva possessed by an object, but agreed that it depended on an object's mass and velocity. The definition of vis viva is very similar to the modern definition of kinetic energy, which is one of two ways in which an object—for example, a molecule, a rock, or a rider on a bicycle—can possess energy. Kinetic energy is the energy of moving objects. The heavier the object is and the faster it moves, the more kinetic energy it has. An object's kinetic energy is represented by the formula:
Kinetic Energy = $1/2$mv2
where m represents the object's mass and v represents its velocity (or speed).
Figure 7-2. Pumped-Storage Hydropower
Pumping water to a storage pool above a power plant when electricity demand is low increases its potential energy, which can be used to generate electricity later by releasing the water and letting it flow down through turbines.
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Objects can also possess potential energy. An object has potential energy because of its position in relation to other objects. When an object rises against the force of gravity, it gains potential energy; when it falls, it loses potential energy. The object stores this energy as it rises and releases it as it returns to Earth.
One familiar technology that taps potential energy is hydropower, which uses the energy of water flowing from a high point to a low point to generate electricity. Hydropower stations contain turbines that are positioned in the path of falling water—typically embedded in a dam. As water flows over the dam and through the turbines, it spins the machines' blades, powering generators that produce electricity. Potential energy (water at a high elevation) is converted into kinetic energy (falling water), which in turn generates electric power.
Some hydropower stations use a system called "pumped storage" to match their generating time to peak electricity demand phases. When demand is low (typically at night), the stations pump water uphill to storage ponds, increasing its potential energy. Then, when demand rises, the water is released and flows back through the turbine, generating power. (Figure 7-2)
As we learned in Unit 2, when a substance goes through a phase change, its particles gain or lose kinetic energy. For ice to change to water or for water to change to steam, the water molecules must gain enough energy to overcome the intermolecular forces that hold them together. For boiling, this energy is called the "heat of vaporization"; for melting, it is referred to as the "heat of fusion."
Figure 7-3. Heating Curve for Water
In this heating curve, water starts out in the solid phase (ice) at -20°C. As the water is heated, its temperature rises. Once it reaches the melting point, continued heating no longer increases the temperature. Over the length of the melting plateau, the additional heat goes into breaking molecules free from their crystal structure. Only when melting is complete will the temperature rise again.
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Although it may seem counterintuitive, water's temperature does not change while it is undergoing a phase change such as melting or boiling. This is because during the phase change, all of the energy added to the system (i.e., to the pot of water) is used to break the bonds between water molecules. In other words, it is providing potential energy. If we continue to add heat after all of the bonds have been broken and the water has turned to steam, it will flow into the system as kinetic energy that raises the temperature of the steam. We can see the relationship between the water's temperature and the amount of heat added to it in a diagram of water's heating curve. (Figure 7-3)