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    | • | The entropy of
    the universe increases in a 
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    |  | 
   
    |  | spontaneous
    process and is equal to zero in 
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    |  | 
   
    |  | a system at
    equilibrium. 
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    |  | 
   
    | • | Not always easy
    to calculate the entropy 
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    |  | 
   
    |  | change of the
    universe. 
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    |  | 
   
    | • | Define a new
    quantity, G,  Gibbs
    free 
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    |  | 
   
    |  | energy. G refers
    to the system we are 
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    |  | 
   
    |  | studying. 
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