91Ó°ÊÓ

When a substance changes from one state of matter to another—like from a solid to a liquid—the energy involved in this phase transition is called the latent heat of fusion. This is often simply termed as the heat of fusion and is unique for each substance. For instance, to convert water to ice or ice to water, energy must either be absorbed or released by water molecules.

In our exercise problem, the heat of fusion comes into play when steam at 100 degrees Celsius condenses into water without changing the temperature. It's this hidden energy, which does not affect the temperature, that contributes significantly to the thermal energy transferred. The formula to calculate this energy is given by \(Q = mL_f\), where \(m\) is the mass of the substance undergoing the phase change, and \(L_f\) is the latent heat of fusion. For water at its boiling point, \(L_f\) is 2260 J/g; thus steam releasing latent heat can cause severe burns, more so than water at the same temperature.

The specific heat capacity, denoted as \(c\), is a property that describes how much heat energy (in joules) is needed to raise the temperature of one gram of a substance by one degree Celsius. This concept helps us understand how different materials react to heat. For example, metals typically have a low specific heat capacity, which means they heat up and cool down quickly.

In the context of our exercise, the specific heat capacity of water is used in the formula \(Q = mc\Delta T\) to calculate the heat lost as steam and hot water cool down to skin temperature. This formula quantifies the thermal energy (\(Q\)) exchanged during a temperature change (\(\Delta T\)) by accounting for the material's mass (\(m\)) and its ability to store heat (\(c\)). Water has a relatively high specific heat capacity of 4.186 J/g°C, which means it can hold a significant amount of heat. This characteristic of water is essential for understanding the heat exchange process with the skin in the given scenarios.

Thermal energy in heat exchange refers to the transfer of heat between objects or systems resulting from a temperature difference. In essence, heat flows from a higher temperature object to a lower temperature one until thermal equilibrium is reached. The amount of thermal energy transferred is influenced by the properties of the substances involved, such as their mass, specific heat capacity, and phase changes.

In our exercise, thermal energy transfer occurs when steam and hot water are cooled to the skin's temperature. The presence of steam entails two parts of heat transfer: the release of latent heat during the phase change from steam to water, and the subsequent cooling of the resultant water. Conversely, the hot water's cooling involves only the specific heat exchange with no latent heat, as it's already in the liquid phase. We can quantify the thermal energy transferred with the formula \(Q = mc\Delta T\) for the cooling process and \(Q = mL_f\) for the phase change, elucidating the more substantial impact steam has due to the additional latent heat release. This can explain why steam burns can be much more severe compared to hot water burns.