Question

An ice cube at \(0.0^{\circ} \mathrm{C}\) is slowly melting. What is the change in the ice cube's entropy for each \(1.00 \mathrm{g}\) of ice that melts?

Short answer

Answer: The change in entropy for every 1.00 g of ice that melts from 0.0°C is approximately 1.22 J/K.

Step-by-step solution

Determine the heat of fusion of ice

The heat of fusion is the amount of heat required to change a substance from the solid phase to the liquid phase without changing its temperature. For ice, the heat of fusion is equal to \(333.55 \mathrm{J/g}\).

Calculate the heat needed for melting 1 gram of ice

For every \(1.00 \mathrm{g}\) of ice that melts, we can determine the total heat needed for the process by multiplying the heat of fusion by the mass of ice. $$Q = m \times L = (1.00 \thinspace \mathrm{g}) \times (333.55 \thinspace \mathrm{J/g}) = 333.55 \thinspace \mathrm{J}$$

Calculate the change in entropy

To calculate the change in entropy, we will use the formula: $$\Delta S = \frac{Q}{T}$$ where \(\Delta S\) is the change in entropy, \(Q\) is the heat added to the system, and \(T\) is the temperature. Remember to use temperature in Kelvin. First, convert the temperature to Kelvin: $$T_{\text{K}} = T_{\text{C}} + 273.15 = 0.0^{\circ} \mathrm{C} + 273.15 \thinspace\mathrm{K} = 273.15 \thinspace\mathrm{K}$$ Now, calculate the change in entropy: $$\Delta S = \frac{333.55 \thinspace \mathrm{J}}{273.15 \thinspace \mathrm{K}} \approx 1.22 \thinspace \mathrm{J/K}$$ So, for every \(1.00 \mathrm{g}\) of ice that melts, the change in the ice cube's entropy is approximately \(1.22 \thinspace \mathrm{J/K}\).