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Unformatted text preview: hermal energy
reservoirs. Likewise, an irreversible refrigerator or a heat pump has a lower
coefficient of performance (COP) than a reversible one operating between the
same temperature limits. Another important inequality that has major consequences in thermodynamics is the Clausius inequality. It was first stated by
the German physicist R. J. E. Clausius (1822–1888), one of the founders of
thermodynamics, and is expressed as
T That is, the cyclic integral of dQ/T is always less than or equal to zero. This
inequality is valid for all cycles, reversible or irreversible. The symbol (integral symbol with a circle in the middle) is used to indicate that the integration is to be performed over the entire cycle. Any heat transfer to or from a
system can be considered to consist of differential amounts of heat transfer.
Then the cyclic integral of dQ/T can be viewed as the sum of all these differential amounts of heat transfer divided by the absolute temperature at the
To demonstrate the validity of the Clausius inequality, consider a system
connected to a thermal energy reservoir at a constant absolute temperature of
TR through a rev...
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This document was uploaded on 11/28/2012.
- Spring '09