91Ó°ÊÓ

The First Law of Thermodynamics, also known as the Law of Energy Conservation, is a fundamental principle in thermodynamics. It states that energy cannot be created or destroyed, only transformed from one form to another. This concept is critical in understanding changes in a system's internal energy. The formula we use for this is:

• \( \Delta Q = \Delta U + \Delta W \)

where:

• \( \Delta Q \) represents the heat added to the system
• \( \Delta U \) is the change in internal energy
• \( \Delta W \) is the work done by the system

In the context of melting ice in this exercise, the ice absorbs heat (\( \Delta Q \)) without performing work (since \( \Delta W = 0 \)). Thus, the First Law simplifies to \( \Delta Q = \Delta U \). The heat absorbed in this situation is used solely to change the state of the ice from solid to liquid, resulting in a change in internal energy.

The latent heat of fusion is the amount of energy required to change a substance from a solid to a liquid without changing its temperature. This concept is crucial for understanding phase changes, such as when ice melts to become water. For ice, the latent heat of fusion is given as 80 cal/g, a specific heat amount needed to overcome the intermolecular forces holding the ice together.

When solving problems related to heat and phase changes, we use the formula:

• \( \Delta Q = m L_f \)

where:

• \( m \) is the mass of the substance
• \( L_f \) is the latent heat of fusion

In our exercise, we calculated the heat needed to convert 5.0 g of ice to water at the same temperature by multiplying the mass by the latent heat of fusion, resulting in 400 cal. This calculation does not account for any temperature change since the process occurs at a constant \( 0^{\circ} \text{C} \).

The concept of internal energy change is central to thermodynamics. Internal energy refers to the total energy contained within a system, stemming from molecular motion and interactions. When energy in the form of heat is added to the system, as in our exercise where ice turns into water, the internal energy changes.

To find the internal energy change (\( \Delta U \)), we utilize the relationship with heat and work from the First Law of Thermodynamics. Since no work is done by the system in this scenario, the entire amount of heat absorbed (\( \Delta Q = 400 \text{ cal} \)) translates directly into increased internal energy.

We further converted this energy from calories to joules using the conversion factor:

• \( 1 \text{ cal} = 4.184 \text{ J} \)

Thus, the internal energy increase was calculated to be approximately 1.7 kJ. Understanding this conversion is important for expressing energy in more universally accepted units.