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Heat Engines

Heat Engines - identity as σ in = Q in τ in We want some...

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Heat Engines We need to think of entropy in a new way, though it is yet the same fundamentally as before. Entropy cannot build up indefinitely in a system. If it is introduced accompanying some heat input, it must eventually be released from the system. This restriction does not affect the conversion of work into work, however. A plant that converts the rush of a river into electricity does not have to worry about entropy. Similarly, conversion of work into heat does not lead to a buildup of entropy. Conversion of heat to work, however, the basic process of a heat engine, must be done carefully to avoid buildup of entropy. In fact, heat cannot be completely converted into work. Some heat must also be outputted as heat, to carry the entropy back out of the system. We can rewrite part of the thermodynamic
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Unformatted text preview: identity as: σ in = Q in / τ in . We want some of the input heat Q in to be converted into work, so we know that Q out will be less than Q in . We want all of the entropy to be extracted, however, and so we want σ in = σ out . The only way to accomplish such a feat is to have τ in > τ out . For this reason, we replace all of the "in" subscripts by "h", standing for "high temperature", and the "out" subscripts by "l", to indicate "low temperature". Carnot Efficiency The work that we actually get out in a heat engine is the difference between the input and output heat W = Q h- Q l = Q h . Ideally, we would want W = Q h , for in that case the system would be completely efficient. For that reason, we define the Carnot efficiency, η C , to be the ratio of the work to the input heat: η C âÉá...
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