91Ó°ÊÓ

When substances change from one state of matter to another, such as from liquid to gas or gas to solid, it's called a phase change. These processes occur at specific temperatures, known as melting points, freezing points, or boiling points. Notably, in our exercise, ethyl alcohol transitions from a gaseous state at its boiling point of \(78.0^{\circ} \mathrm{C}\) to a solid state at \(-114^{\circ} \mathrm{C}\).

Phase changes require or release energy, described as latent heat. For instance:

• **Heat of Vaporization** - Energy needed to convert a liquid to a gas. In ethyl alcohol, this is \(879 \mathrm{~kJ} / \mathrm{kg}\), which is significant during the condensation phase.
• **Heat of Fusion** - Energy required to change a solid to a liquid, or vice versa. For our exercise, ethyl alcohol's heat of fusion is \(109 \mathrm{~kJ} / \mathrm{kg}\), essential when freezing the liquid alcohol into solid form.

Understanding these phase changes helps calculate the total energy needed to alter the state of a given mass, like the 0.510 kg of ethyl alcohol in our problem.

Heat transfer refers to the movement of thermal energy from one place to another. In the context of our exercise, heat is transferred out of the ethyl alcohol to change its state and temperature. The process includes several stages:

• During **condensation**, energy is removed to transition from gas to liquid.
• While **cooling** the liquid ethyl alcohol down to its freezing point, more energy must be taken out.
• Finally, during **freezing**, additional energy is released as the liquid turns into a solid.

Each stage of this transformation relies on the principles of heat transfer, ensuring energy is properly calculated for the phase changes. These calculations use constants like the heat of vaporization and heat of fusion, which determine how much energy is needed or released as the alcohol changes state. Proper heat transfer calculations are crucial in thermodynamics, helping to design processes and systems like refrigerators, engines, and even climate control systems.

Specific heat is an important concept in thermodynamics. It represents the amount of heat energy required to raise the temperature of one kilogram of a substance by one Kelvin. For ethyl alcohol in our exercise, the specific heat is \(2.43 \mathrm{~kJ/kg} \cdot \mathrm{K}\). This value helps in calculating how much energy must be removed to cool the liquid alcohol from its boiling point to its freezing point.

To determine the energy requirement for cooling, we use the formula:
\[ Q = m \times c \times \Delta T \]
Where:

• **Q** is the energy transferred,
• **m** is the mass of the substance (0.510 kg in this case),
• **c** is the specific heat,
• **\(\Delta T \)** is the change in temperature (from \(78^{\circ}\text{C} \) to \(-114^{\circ}\text{C}\), which is a total of \(192^{\circ}\text{C}\)).

This formula explains how specific heat is used to quantify energy transfer needed for temperature changes, excluding any phase change. It ensures accurate calculations in cooling and heating processes across various scientific and engineering applications.