The entropy change associated with the conversion of 1 kg of ice at 273 K to water vapours at 383 K is :
(Specific heat of water liquid and water vapour are `4.2kJK^(-1)kg^(-1)` and `2.0kJK^(-1)kg^(-1)` , heat of liquid fusion and vapourisation of water are `334kJ kg^(-1)` and `2491kJ kg^(-1)`, respectively ). (`log 273=2.436,log373=2.572, log 383=2.583`)

Options

A. `9.26 kJ kg^(-1) K^(-1)`
B. `2.64 kJ kg^(-1) K^(-1)`
C. `7.90 kJ kg^(-1) K^(-1)`
D. `8.49 kJ kg^(-1) R^(-1)`

Answer

A

Explanation

Overall process
`underset(273 K)(H_(2)O)(ice) overset(a) to underset(273 K)(H_(2)O)(l) overset(b) to underset(373 K)(H_(2)O(l) overset ( c) to underset(373 K)(H_(2)O)(g) overset(d) to underset(338 K)(H_(2)O)(g)`
`DeltaS_(a) = (DeltaH_("fusion"))/273 = 334/273 = 1.22`
`DeltaS_(b) = 4.2 ln (373/273) = 1.31`
`DeltaS_( c) = 2ln (383/373) = 0.05`
`DeltaS_("total") = DeltaS_(a) + DeltaS_( c) + DeltaS_(d) = 1.22 + 1.31 + 6.67 + 0.05 = 9.26 kJ kg^(-1) K^(-1)`