Questions: An ice tray contains 500 g of liquid water at 0°C. Calculate the change in entropy of the water as it freezes slowly and completely at 0°C.

Solution Steps

We need to calculate the change in entropy (\(\Delta S\)) of 500 g of liquid water as it freezes completely at \(0^{\circ} \mathrm{C}\).

The change in entropy when a substance undergoes a phase change at a constant temperature is given by: \[ \Delta S = \frac{Q}{T} \] where \(Q\) is the heat exchanged and \(T\) is the absolute temperature in Kelvin.

The heat of fusion (\(L_f\)) for water is the amount of heat required to convert 1 gram of ice to water (or vice versa) at \(0^{\circ} \mathrm{C}\). For water, \(L_f = 334 \, \text{J/g}\).

The total heat exchanged (\(Q\)) when 500 g of water freezes is: \[ Q = m \cdot L_f = 500 \, \text{g} \times 334 \, \text{J/g} = 167000 \, \text{J} \]

The temperature \(T\) at \(0^{\circ} \mathrm{C}\) in Kelvin is: \[ T = 0 + 273.15 = 273.15 \, \text{K} \]

Using the formula for entropy change: \[ \Delta S = \frac{Q}{T} = \frac{167000 \, \text{J}}{273.15 \, \text{K}} \approx 611.2 \, \text{J/K} \]

Final Answer