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Entropy is a fundamental concept in thermodynamics that refers to the measure of disorder or randomness in a system. When you think about melting ice, you're essentially thinking about a change in entropy. At 0°C, ice transforms into water as it absorbs heat, making the molecules within the substance increase their disorder.
This transformation from a solid to a liquid markedly increases entropy because the water molecules in liquid form have more freedom of movement.

• Entropy (\( \Delta S \)) quantifies this change.
• It is given by the formula: \( \Delta S = \frac{Q}{T} \), where \( Q \) is the heat added and \( T \) is the absolute temperature in Kelvin.

Considering the transformation of \( 0.350 \, \mathrm{kg} \) of ice at 0°C, the change in entropy of the water was calculated using the formula \( \Delta S = \frac{117 \, \mathrm{kJ}}{273.15 \, \mathrm{K}} = 0.428 \, \mathrm{kJ/K} \). This value showcases how energy and randomness increase upon melting.

The latent heat of fusion is the amount of heat required to convert a solid into a liquid at its melting point without changing its temperature. This is an important concept in determining how much energy is needed to melt ice, as it allows us to calculate the heat absorbed by the substance.The latent heat of fusion for ice is \( 334 \, \mathrm{kJ/kg} \). This means that every kilogram of ice requires \( 334 \, \mathrm{kJ} \) of energy to change its phase from solid to liquid without any temperature change. In our exercise:

• The mass of ice is \( 0.350 \, \mathrm{kg} \).
• The heat required can be calculated with the formula \( Q = m \times L_f \), which gives us \( Q = 0.350 \, \mathrm{kg} \times 334 \, \mathrm{kJ/kg} = 117 \, \mathrm{kJ} \).

This latent heat ensures that the ice will melt completely without raising its temperature, highlighting the energy stored in the process of melting.

Heat transfer is the process of energy flowing from a warmer object to a cooler one. In our scenario, heat is transferred from a massive object at 25°C to the ice at 0°C, causing the ice to melt.Three key modes of heat transfer are conduction, convection, and radiation:

• Conduction is the transfer of heat through a solid material, like the warmth moving from the surface of our heat source to the ice.
• Convection involves the movement of fluid (liquid or gas) transferring heat.
• Radiation transfers heat in the form of electromagnetic waves, such as light or infrared light.

In this case, conduction likely plays the most significant role, as heat flows from the heat source into the ice.
The entropy change for the heat source is calculated as:\( \Delta S_{source} = -\frac{Q}{T_{source}} \), where \( Q = 117 \, \mathrm{kJ} \) and \( T_{source} = 298.15 \, \mathrm{K} \). This results in an entropy change of \( -0.392 \, \mathrm{kJ/K} \), indicating heat lost by the source.