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`DeltaS = 2.303 xx C_(P) xx “log” (T_(2))/(T_(1))` [where `m` in `kg` and `C_(P)` in `J kg^(-1)]`
Entropy change for heating water from `27^(@)C` to `100^(@)C`.
`DeltaS = 2.303 xx (1000)/(18) xx (4180 xx 18)/(1000) “log”(373)/(300) = 910.55J`
Entropy change for heating `1 kg H_(2)O` to `1 kg` steam at `100^(@)C`.
`DeltaS = (DeltaH_(V))/(T) = (23 xx 10^(5))/(373) = 6166.21J`
Entropy change for heating `1 kg` steam from `373 to 473K, m` in `kg`.
`DeltaS = int_(373)^(473)(nC_(P).dT)/(T)=m int_(373)^(473)((1670+0.49T)dT)/(T)`
`=m int_(373)^(473) (1670 dT)/(R) +m int_(373)^(473) 0.49 dT`
`= m xx 1670 xx 2.3030 [log T]_(373)^(473) + m xx 0.49[T]_(373)^(473)`
`= 1 xx 1670 xx2.303 xx “log” (473)/(373) +1 xx 0.49 xx 100`
`= 396.73 +49 = 445.73J`
`:.` Total entropy change `= 910.55 +6166.21 +445.73`
`= 7522.50 J`
Entropy change for heatgin 1 kg of water from `27^(@)C` to `100^(@)C`
`Delta S = 2.303 n C_(p) log. ( T_(2))/( T_(1))`
`= 2.303xx ( 1000)/( 18) “moles”xx ( 4180xx18)/( 1000) J mol^(-1) xx log. ( 373K)/( 300K) `
`= 910.55J`
Entropy change for heating 1 kg of water at `100^(@)C` to 1 kg of steam at `100^(@)C`
`Delta S = ( DeltaH_(v))/( T) = ( 23 xx 10^(5)J)/( 373 ) = 6166.21J`
Entropy change for heating 1kg steam from `100^(@)C ( 373K) ` to `200^(@)(473K) `
`DeltaS=int_(373)^(473)(nC_(p) dT)/(T) = int_373^473((1670 +0.49T))/(T) = dT`
`=int_(373)^(473)((1670)/(T)+0.49)dT`
`=[1670ln T + 0.49 T]_(373)^(473)`
`= 1670 xx 2.303 ( log473- log 373) + 0.49 ( 473- 373)`
`=1670 xx 2.303 ( 0. 1032 ) + 49`
`= 396.91 +49 =445. 9 J`
`:. `Total entropychange `= 910.55 + 6166.21 +45.9 J = 7522.6 J`