Clausius's theorem | Wikipedia audio article
Channel: wikipedia tts
Date: 2018-12-30

This is an audio version of the Wikipedia Article:
https://en.wikipedia.org/wiki/Clausius_theorem


00:02:19 1 History
00:07:14 2 Proof
00:19:48 3 See also



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SUMMARY
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The Clausius theorem (1855) states that a system exchanging heat with external reservoirs and undergoing a cyclic process, is one that ultimately returns a system to its original state,

  
    
      
        
          
            
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    {\displaystyle \oint {\frac {\delta Q}{T_{surr}}}\leq 0,}
  where 
  
    
      
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    {\displaystyle \delta Q}
   is the infinitesimal amount of heat absorbed by the system from the reservoir and 
  
    
      
        
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    {\displaystyle T_{surr}}
   is the temperature of the external reservoir (surroundings) at a particular instant in time. In the special case of a reversible process, the equality holds. The reversible case is used to introduce the entropy state function. This is because in a cyclic process the variation of a state function is zero. In words, the Clausius statement states that it is impossible to construct a device whose sole effect is the transfer of heat from a cool reservoir to a hot reservoir. Equivalently, heat spontaneously flows from a hot body to a cooler one, not the other way around. The generalized "inequality of Clausius"

  
    
      
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    {\displaystyle dS{\frac {\delta Q}{T_{surr}}}}
  for an infinitesimal change in entropy S applies not only to cyclic processes, but to any process that occurs in a closed system.