(a) What is the entropy change of a 12.0gice cube that melts completely in a bucket of water whose temperature is just above the freezing point water?(b) What is the entropy change of a 5.00gspoonful of water that evaporates completely on a hot plate whose temperature is slightly above the boiling point of water?

1. Mass of the ice cube, m = 12.0 g
2. Mass of the spoonful of water, M = 5.00 g

Entropy change is a phenomenon that quantifies how disorder or randomness has changed in a thermodynamic system. We can use the formula for change in entropy in terms of heat energy. Then this heat energy can be written in terms of latent heat. Inserting respective masses, we can find the entropy change of ice and water.

Formulae:

The entropy change for an isothermal expansion, $∆S=\frac{Q}{T}$ (i)

The heat released by the body due to latent heat, Q = mL (ii)

Freezing point of water is T = 273K and latent heat of fusion of water, $L_f=333J/g$.

Change in the entropy of the ice cube for a reversible isothermal process using equations (i) and (ii) can be given as follows:

$$\begin{gathered} ∆S=\frac{m{L}_f}{T} \\ =\frac{12g\times 333J/g}{273K} \\ =14.637J/K \\ \approx 14.6J/K \end{gathered}$$

Hence, the value of the entropy change of the ice cube is 14.6 J/K

Boiling point of water is T = 373K and latent heat of vaporization of water, $L_v=2256J/g$.

Similarly, using equations (i) and (ii), the entropy change of water is given as follows:

$$\begin{gathered} ∆S=\frac{m{L}_v}{T} \\ =\frac{5g\times 2256J/g}{373K} \\ =30.24J/k \\ \approx 30.2J/K \end{gathered}$$

Hence, the value of entropy change of water is 30.2 J/K