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Question

Two blocks of the same metal having same mass and at temperature T1 and T2 respectively, are brought in contact with each other and allowed to attain thermal equilibrium at constant pressure. The change in entropy, S for this process is

A
2Cpln[T1+T22T1T2]
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B
Cp ln[(T1+T2)24T1T2]
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C
2Cp ln [(T1+T2)24T1T2]
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D
2Cp ln ⎢ ⎢ ⎢ ⎢(T1+T2)124T1T2⎥ ⎥ ⎥ ⎥
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Solution

The correct option is B Cp ln[(T1+T2)24T1T2]
As the two boxes are identical, So Cp will be same for both and
Tfinal=T1+T22

Entropy change in the first box will be given by
S1=Cp ln TfTisince,Ti=T1S1=Cp ln TfT1

Entropy change in the second box will be given by
S2=Cp ln TfTisince,Ti=T2S2=Cp ln TfT2

Total entropy change will be given by addition of above two.
S=S1+S2=Cp lnT2fT1T2
putting the value of Tf
S=Cp ln[(T1+T2)24T1T2]

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