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My textbook tries to prove that for Entropy of Irreversible Process > 0 by using the example of irrev expasion into a vacuum which doesn't make sense to me.

If work is = 0 then no heat is exchanged between the sys and surrounding so qsurr = 0

s(uni) = s(sys) + 0

since S(sys)=qirr/t and no heat is being exchanged then S(sys) = 0

then S(uni) SHOULD = 0 why would does my textbook put S(uni)> 0 by using the nr*ln(T2/T1) equation for S(sys) when no work was done and q was suppose to be 0? how can I prove to that S(uni) is > 0 for irreverisble process?

Thank you

If work is = 0 then no heat is exchanged between the sys and surrounding so qsurr = 0

s(uni) = s(sys) + 0

since S(sys)=qirr/t and no heat is being exchanged then S(sys) = 0

then S(uni) SHOULD = 0 why would does my textbook put S(uni)> 0 by using the nr*ln(T2/T1) equation for S(sys) when no work was done and q was suppose to be 0? how can I prove to that S(uni) is > 0 for irreverisble process?

Thank you

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