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A sample of 100 g water is slowly heated...

A sample of 100 g water is slowly heated from `27^(o)C` to `87^(o)C`. Calculate the change in the entropy of the water. specific heat capacity of water =4200 j/kg k .

Text Solution

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The heat supplied to increase the temperature of the sample from `T to T+^DeltaT,is `
`DeltaQ=ms DeltaT`.
where `m=100 g=0.1 kg and C=4200 J kg^(-1) K^(-1)`.
the changr in entropy as the tempreture rises from`T_(1) to T_(2) is`,
`S_(2)-S_(1)=int_T_(1)^T^(2) ms (dT)/(T)`
`=ms In(T_(2)/T_(1)`
Putting `T_(1)=27^(0)C=300 K and T_(2)=87^(0)C=360 K`,
`S_(2)-S_(1)=(0.1 kg)(4200 J kg^(-1) K^(-1)) in (360)/(300)`
`=76.6 JK^(-1)`.
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