Calculate the entropy change (in J / K ) when 10 gm of ice at 0 ∘ C is added to 50 gm of water at 4 0 ∘ C in an isolated system. The latent heat of fusion of ice at 0 ∘ C is 334.4 J / gm and specific

Question

Calculate the entropy change (in J / K ) when 10 gm of ice at 0 ∘ C is added to 50 gm of water at 4 0 ∘ C in an isolated system. The latent heat of fusion of ice at 0 ∘ C is 334.4 J / gm and specific heat capacity of water is 4.18 J / gm − K . ( ln 273 = 5.61 , ln 283 = 5.65 , ln 293 = 5.68 , ln 303 = 5.71 , ln 313 = 5.75 )

TestHub · Accepted Answer

Concepts: Heat exchange, phase change (fusion), specific heat, entropy change ( $Δ S = \frac{q}{T}$ or $m c ln \frac{T _{f}}{T _{i}}$ ).

Solution:

Final temperature is $10. 1^{\circ} C$ (283.1 K). $Δ S_{t o t a l} = Δ S_{i ce \to w a t er} + Δ S_{w a t er (i ce)} + Δ S_{w a t er (ini t ia l)}$ .

$Δ S_{t o t a l} = 0.54 J/K$ .

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