A student placed a few ice cubes in a drinking glass with water. A few minutes later she noticed that some of the ice cubes were fused together. Explain what happened.

The fascinating dance of energy between substances is embodied in the concept of heat transfer. When we look at a glass of water with ice cubes floating, what we're witnessing is an invisible exchange as heat journeys from the warmer water to the chillier ice. This movement is driven by the desire for thermal equilibrium; heat always flows from a warmer to a cooler area until both reach the same temperature.

In our icy glass, several modes of heat transfer occur: conduction, where heat moves directly through matter, like the intimate contact between ice and water; convection, which involves the movement of warm water upward and cooler water downward; and possibly radiation, although this plays a smaller role in this scenario, as it involves heat transfer through space without the need for a medium.

Imagine each ice cube as a tiny cold castle, slowly being besieged by the warm water. The walls of the castle— the surface of the ice cube—begin to succumb, melting away as the heat permeates throughout.

At first glance, melting seems simple—you heat something up and it turns from solid to liquid. But the interplay between melting and refreezing is a delicate one. As you've observed with the ice cubes in a glass, this process can lead to unexpected results like fusion.

When the ice absorbs heat from the surrounding water, it undergoes a phase change at the surface and transitions into water. This melted layer acts like a tiny bridge between cubes when they touch. However, if the thermal energy dwindles—a sudden chill, perhaps, or the lingering coldness of the un-melted ice—the bridge can solidify again. It's like a handshake between the cubes, solidifying into a firm grip!

It's essential to realize that only a small amount of heat needs to be lost for refreezing to occur. The change back can be quicker than expected because the temperature just needs to drop below the freezing point and since the surrounding ice is already cold, it helps accelerate this turn of events.

Thermal energy is the total energy of all the particles within a substance. It's at the heart of the phase changes we've been talking about. When focused on ice melting and refreezing, it's all about the transfer of this invisible power.

Thermal energy isn't just about temperature; it's also tied to the movement of particles. The warmer something is, the more energetically its particles move. In our ice cubes, the particles are slowly moving and locked in a structured lattice—that's what makes it a solid. Heat the ice, and you increase the motion of those particles, encouraging them to break free of their rigid arrangement.

Too much thermal energy, and the ice cube becomes water, with particles sliding past one another. Take some of that energy away, though, and water's particles slow down and snap back into a solid. This dynamic is what allows our ice cubes to both melt in the warmth of the room or the glass's water and refreeze upon touching a fellow chilly cube.