Carnot Engines, Efficiency, and The Second Law

# Carnot Engines, Efficiency, and The Second Law - Carnot...

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Carnot Engines, Efficiency, and The Second Law Chemistry 213 Fig. 1. The Carnot Cycle The Carnot engine is a useful construction for relating the mathematical ( S 0 for a spontaneous process in an isolated system) and the physical statements of the Second Law of Thermodynamics (heat spontaneously flows from hot to cold). This handout goes through the analysis of the amounts of work and heat produced in the isothermal and adiabatic parts of the Carnot cycle for an ideal gas. 1. Energy in an Ideal Gas: Joule’s Experiment In his study of the thermal properties of gases, Joule considerer the isothermal expansion of dilute gases using the apparatus depicted below: Winter Term 2001-2002

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Second Law of Thermodynamics -2- Chemistry CHEM 213W P=0 Thermometer P=0 / Fig. 2. Joule’s Experiment The bulb on the right was evacuated initially and heat was allowed to exchange with the heat bath, whose temperature was measured. For sufficiently dilute gases, Joule found that the tem- perature of the bath didn’t change. This has some important consequences. For this process, P op = 0, and hence, W = 0. Moreover, since the temperature of the bath remained constant, no heat was absorbed by the system, and thus E = 0. What does this say about the functional form of the energy of an ideal gas? We know that we can write the energy of a one-component system as E ( N , V , T ) = N E ( T , N / V ), where density was chosen instead of pressure as an independent variable (as can always be done if the equation of state is known). In Joule’s experiment T and N were held fixed but V, and
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