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Question:

The entropy change associated with the conversion of 1 kg of ice at 273 K to water vapor at 383 K is: [Given that: Specific heat of water liquid and water vapor are 4.2 kJ/kg and 2.0 kJ/kg; latent heat of fusion and vaporization of water are 344 kJ/kg and 2491 kJ/kg, respectively.][Take: log 273 = 2.436, log 373 = 2.572, log 383 = 2.583]

2.64kJ/kgK

8.49kJ/kgK

9.26kJ/kgK

7.90kJ/kgK

Solution:

ΔS=ΔH/T
ΔS=nC ln(Tf/Ti)=ms ln(Tf/Ti)
n= no. of moles, m= mass, C=molar heat capacity, s= specific heat capacity
Phase change path
H₂O(s) → H₂O(l) → H₂O(l) → H₂O(g) → H₂O(g)
Δs₁ = ΔHfusion/273 = 334/273 = 1.22
Δs₂ = 4.2 ln(363/273) = 1.31
Δs₃ = ΔHvap/373 = 2491/373 = 6.67
Δs₄ = 2.0 ln(383/373) = 0.05
Δstotal = Δs₁ + Δs₂ + Δs₃ + Δs₄ = 9.25 kJ/kgK