Which takes more heat: melting a gram of ice already at \(0^{\circ} \mathrm{C},\) or bringing the melted water to the boiling point?

Heat transfer is a fundamental concept in physics and engineering, referring to the movement of thermal energy from one place to another and from one substance to another. It happens as a result of a temperature difference and is essential in understanding how energy is redistributed in physical systems.

In the context of our exercise, heat transfer plays a crucial role in both melting ice and heating the resultant water to its boiling point. External heat must be transferred to the ice for it to absorb enough energy to overcome its molecular structure and transform into a liquid. Similarly, heat must be transferred into the water to raise its temperature to the boiling point.

There are three modes of heat transfer: conduction, which occurs through direct contact; convection, which involves fluid movement; and radiation, which happens through electromagnetic waves. In the scenarios described in the textbook exercise, conduction would be the primary mode of heat transfer, as the heat would likely be conducted from a warmer surface to the ice or water.

Specific heat capacity, often simply called specific heat, is a property of a material that indicates how much heat energy is required to raise the temperature of a unit mass of the material by one degree Celsius (or one kelvin). The higher a material's specific heat, the more energy it takes to change its temperature.

In our exercise, water's specific heat capacity is a critical factor in determining how much energy is needed to heat it from 0 to 100 degrees Celsius. With a high specific heat capacity of 4.18 joules per gram per degree Celsius (J/g°C), water requires a significant amount of energy to change its temperature, reflecting its ability to absorb and store heat. This is why heating the melted water to boiling requires more energy than melting the ice, despite both beginning at 0°C.

Practical Implications

Understanding specific heat capacity is crucial in many fields, such as cooking, where it affects how quickly ingredients change temperature, or in climate science, as it influences how bodies of water can moderate local climates by absorbing and releasing large amounts of heat.

Thermodynamics is a branch of physics that deals with the relationships between heat, work, energy, and temperature. It encompasses a set of laws that govern energy conversion and transfer. The exercise we are examining is rooted in the principles of thermodynamics, primarily the first law, which states that energy cannot be created or destroyed, only transformed.

During the phase change from solid ice to liquid water, energy is neither lost nor gained by the universe; it's simply repurposed, from organizing the molecular structure of ice to boosting the kinetic energy of the water molecules. When heating water, the energy supplied increases the internal energy of the water, which manifests as a higher temperature.

Thermodynamics helps us understand why different amounts of heat are involved in melting ice versus boiling water. Although no temperature change occurs during the melting, energy is still consumed in breaking the bonds, which is a different kind of energy transformation compared to heating water, where the temperature does rise.

A phase change is a transition of matter from one state to another, such as from solid to liquid (melting), liquid to gas (boiling), or the reverse transitions (freezing and condensation). During a phase change, the temperature of the substance remains constant while the substance undergoes a physical transformation.

In the melting of ice, a specific type of phase change, the latent heat of fusion is the amount of heat energy per mass unit required for the substance to change from solid to liquid without changing its temperature. This energy is used to overcome the molecular forces keeping the solid structure intact.

Energy Consumption During Phase Change

The process of bringing water to its boiling point involves heating the liquid until its molecules have enough energy to break free into a gaseous state, which requires overcoming the latent heat of vaporization. Although it's not part of the initial exercise, it's worth noting that boiling would take even more energy per gram than both melting and heating to 100°C combined, because the latent heat of vaporization is higher than the latent heat of fusion for water.