Find the increase in entropy of 1.00 kg of ice originally at 0º C that is melted to form water at 0º C .

Strategy As before, the change in entropy can be calculated from the definition of ΔS once we find the energy Q needed to melt the ice.

Question

Find the increase in entropy of 1.00 kg of ice originally at 0º C that is melted to form water at 0º C .

Strategy As before, the change in entropy can be calculated from the definition of ΔS once we find the energy Q needed to melt the ice.

Accepted Answer

The change in entropy is defined as:

[latex]\Delta S=\frac{Q}{T}[/latex]. (15.61)

Here Q is the heat transfer necessary to melt 1.00 kg of ice and is given by

[latex]Q=m L_{ f }[/latex], (15.62)

where m is the mass and [latex]L_{ f }[/latex] is the latent heat of fusion. [latex]L_{ f }=334 kJ / kg[/latex] for water, so that

[latex]Q=(1.00 kg )(334 kJ / kg )=3.34 imes 10^{5} J[/latex]. (15.63)

Now the change in entropy is positive, since heat transfer occurs into the ice to cause the phase change; thus,

[latex]\Delta S=\frac{Q}{T}=\frac{3.34 imes 10^{5} J }{T}[/latex]. (15.64)

T is the melting temperature of ice. That is, T = 0ºC=273 K . So the change in entropy is

[latex]\Delta S=\frac{3.34 imes 10^{5} J }{273 K }[/latex] (15.65)

[latex]=1.22 imes 10^{3} J / K[/latex].

Discussion
This is a significant increase in entropy accompanying an increase in disorder.

Question 15.8: Find the increase in entropy of 1.00 kg of ice originally at...