Science Web Assignment for Unit 47
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We haven't actually looked at Watts' engine, and it's worth doing, just so that you understand how heat-to-motion conversion works. Study this animation of a double-action steam engine, then look at the diagram and image of Watt's actual engine.
Two important rules grew out of Carnot and Clausius' work, and these became the basis of the new area of thermodynamics: heat and force. As we have seen, the law of the conservation of energy was established by Clausius, and became known as "the first law of thermodynamics". But there was a more fundamental principle behind the conservation of energy. This is the tendency of energy to dissipate into all parts of a system, to flow from hotter areas to colder areas, until all parts of a system are in thermal equilibrium. When equilibrium is reached, heat flow ceases, and temperatures stop changing, although individual particles colliding with one another can still exchange energy on an individual basis. The rule that at systems tend toward equilibrium became known as the "zeroth" law of thermodynamics.
The first law of thermodynamics states that energy in a system is always conserved. Another way to state this is that the total amount of energy in a system cannot change: energy cannot be created or destroyed.
We need to look at the conditions under which this happens. A system is some collection of objects in space, with a recognized boarder. We can arbitrarily designate a system as whatever we happen to be studying at the time: the contents of a thermos bottle, a container of gas particles, a car on a street, the earth, or the entire universe. The ability of energy or matter to cross the boundaries of the system define the kind of system we have.
One form of the conservation of energy states that heat flow is equal to the total amount of energy in a system minus the work done on the system by its surroundings, or by the system on its surroundings. We can apply this idea to the steam engine this way:
The piston is a system. Heat enters the system, and the gases inside the piston expand, pushing the piston cap up. This compresses the volume outside the piston -- that is, the piston does work on its environment. As the piston cools and heat flows out of the system, the cap drops and the volume inside the piston contracts. The environment is doing work on the system of the piston. The amount of work done depends on the heat flow into and out of the piston. The "efficiency" of the engine depends on the ratio of much heat we put in to how much heat we get out. The greater this difference, the more heat energy goes into work energy.
The efficiency ε is the work done, or the amount of heat flow, divided by the original heat energy in a kinetic system:
The greater the heat flow compared to the original amount of heat in the system, the more efficient the engine is.
Because of the relationship between heat and temperature, we can also write this relationship as
where the exhaust at a temperature Tcold carries heat away from the engine which is operating at temperature Thot. We can figure out the energy efficiency of an engine by measuring its internal temperature and its exhaust temperature.
Notice that since Tcold and Thot are measured in Kelvin or absolute temperatures, they are always positive. Also, since Tcold is less than Thot, the fraction Tcold/Thot is always positive and less than one, so the value of 1 - Tcold/Thot is always less than one. The theoretical maximum efficiency of the engine is 1 (100%): even if it is operating perfectly, we can never get more energy out of the engine that we put into it. Since we know that some energy will be lost at each step where energy is converted from one form to another, Tcold will be less tan Thot, and ε will always be less than 100%. Perpetual motion machines (a machine which, once started, can run forever without further energy input) are not possible.
We've talked about rates in other circumstances: a rate is the change in some quantity with respect to time. In the field of energy, the rate of energy expenditure over time is power. If we measure energy in joules (named after James Joule) then power is measured in joules/second, or watts, named after James Watt. The rate at which a light bulb consumes energy is given in watts: a 45 watt light bulb uses 45 joules per second to operate.
One of the prime concerns of the industrial revolution was increasing the efficience of engines. Ideally, all heat energy should be converted to work. In practice, about 25% of the heat energy can be converted to useful work; the rest is lost to the environment as heat, sound, and wear on the parts. From Carnot's work, we can use several different measurements to show the ratio of energy leaving an engine to the energy entering the engine. The closer this value is to 1, the more efficient the engine is. A power plant running coal can convert about 36% of the coal energy to heat or electrical energy; a nuclear power plant is about 30% efficient, and a geothermal plant is only 16% efficient.
Study the diagram and heat flow through an engine that uses steam heat to turn a turbine that can then generate electric.
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