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When we talk about changing a substance from a solid to a liquid, like ice turning into water, there's a special type of heat involved. This is called the latent heat of fusion. It is the hidden energy required to change the state of a substance without changing its temperature.
For water, the latent heat of fusion is quite high, specifically 334,000 J/kg. This means for each kilogram of ice at 0°C, 334,000 joules of heat are needed to turn it into liquid water at the same temperature.
This energy breaks the bonds holding the ice structure, allowing the molecules to move freely and form a liquid. It's crucial for accurately calculating how much energy we need during processes involving melting or freezing. Hence, in any problems related to melting, remember to use the latent heat of fusion formula:

• \(Q = mL_f\) where \(m\) is the mass and \(L_f\) is the latent heat of fusion.

Entropy is a measure of disorder or randomness in a system. For the melting ice problem, calculating the change in entropy involves considering the heat added to the system and the temperature at which it occurs.
When ice at 0°C melts, it absorbs heat while remaining at a constant temperature. The change in entropy (ΔS) can be calculated using the formula:

• \( ∆S = \frac{Q}{T} \)

where \(Q\) is the heat absorbed and \(T\) is the temperature in Kelvin. In the example, ice absorbed 116,900 J of heat at 0°C, or 273.15 K.
Replacing these values gives us:

• \( ∆S = \frac{116,900 \, ext{J}}{273.15 \, ext{K}} \approx 428.1 \, ext{J/K} \)

This positive change indicates an increase in entropy, as liquid water is more disordered than solid ice.

Thermodynamic processes describe how systems exchange energy as heat and work. The transfer of heat can lead to changes in entropy, as we saw with our ice melting example.
Let's summarize various key ideas about these processes:

• **Isothermal process:** Occurs at a constant temperature. In our problem, the ice melts at 0°C.
• **Isobaric process:** Happens when the pressure stays constant.
• **Adiabatic process:** Involves no heat exchange with the environment. Here, energy stays within the system, purely altering internal temperature or pressure.
• **Isochoric process:** The volume remains constant.

While these terms define various types of thermodynamic processes, they highlight the universal importance of heat, temperature, and energy exchange in determining how substances behave under different conditions.
In our original exercise, the melting of ice represents an isothermal process, showcasing how energy is required to cause phase changes even without temperature variation.