Heat energy from hot water can melt ice cubes.

When you add ice to hot water, the ice melts and the hot water cools. This is based on the exchange of heat energy from the hot water to the ice. The exchange of energy causes the ice to melt. Once this happens, the cold water that was once ice will rise in temperature if it receives more energy from the hot water. The extent of this process depends on the available heat energy in the hot water.

### Thermal Equilibrium

In a mixture of ice and hot water, the hot water loses energy until the system is at thermal equilibrium. Thermal equilibrium is defined as the point where all components of the system are at the same temperature. When the hot water loses energy, it drops in temperature. At the same time, the ice increases in temperature and can melt due to the exchange of energy. These processes continue until thermal equilibrium is reached.

### Specific Heat

The specific heat of a substance is the amount of heat energy required to raise the temperature of one gram of the substance by one degree Celsius. The specific heat of ice is 2.095 joules per gram per degree Celsius. This means that it takes 2.095 joules of energy to raise the temperature of one gram of ice by one degree Celsius. The specific heat of water is 4.186 joules per gram per degree Celsius. This means that it takes 4.186 joules of energy to raise the temperature of one gram of water by one degree Celsius. Temperature is a gauge of the kinetic energy in a substance. Therefore, an increase in temperature represents an increase in kinetic energy. Correspondingly, a decrease in temperature represents a decrease in kinetic energy.

### Heat of Fusion

The heat of fusion is the amount of energy required to convert a solid to liquid without changing its temperature. The heat of fusion of water is around 334 joules per gram at standard atmospheric pressure. This means that it takes 334 joules of energy to convert one gram of ice into water. In this case, the ice must be at 0 degrees Celsius. If it is at a lower temperature, it must first be heated to 0 degrees. The heat of fusion is sometimes called the latent heat of fusion because the temperature of the system does not change. Because the temperature does not change during this process, kinetic energy does not increase. Instead, when ice melts, its crystalline structure is broken and potential energy increases.

### How Much Ice Melts?

The amount of ice that melts depends on how much heat energy is initially in the hot water. Energy must be conserved, so the ice can't absorb more energy than is already present in the water. The water transfers energy to the ice and decreases in temperature. The kinetic energy of the ice increases, and the ice warms. When the ice melts, its potential energy increases. When all of the heat energy of the liquid water has been transferred to the ice, the ice will no longer melt. If the hot water has enough energy to melt all of the ice, it will do so. However, if all of the heat energy is transferred before melting all of the ice, the system will be in thermal equilibrium at zero degrees Celsius. In this case, it will be a mixture of ice and liquid water.