Equivalence of the Clausius and the Kelvin statements Second law of thermodynamics

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derive kelvin statement clausius statement


suppose there engine violating kelvin statement: i.e., 1 drains heat , converts work in cyclic fashion without other result. pair reversed carnot engine shown figure. net , sole effect of newly created engine consisting of 2 engines mentioned transferring heat



Δ
q
=
q

(


1
η


−
1
)



{\displaystyle \delta q=q\left({\frac {1}{\eta }}-1\right)}

cooler reservoir hotter one, violates clausius statement. violation of kelvin statement implies violation of clausius statement, i.e. clausius statement implies kelvin statement. can prove in similar manner kelvin statement implies clausius statement, , hence 2 equivalent.







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