Question

Which causes a more severe burn: spilling \(0.50 \mathrm{~g}\) of \(100{ }^{\circ} \mathrm{C}\) water on your hand or allowing \(0.50 \mathrm{~g}\) of \(100^{\circ} \mathrm{C}\) steam to condense on your hand? Why?

Short answer

Allowing 0.50 g of 100°C steam to condense on your hand causes a more severe burn because steam must first condense, releasing the heat of vaporization, and then cool, which overall transfers more heat than just the cooling of liquid water.

Step-by-step solution

Understand the concept of heat transfer

When a substance comes into contact with the skin, it can cause a burn by transferring heat. The severity of a burn depends on the amount of heat transferred, which can be calculated using the heat transfer equations for phase changes and temperature changes. For water, this involves using specific heat capacity for temperature change, and heat of vaporization for phase change from steam to water.

Calculate heat transferred by the liquid water

To calculate the heat transferred by the liquid water cooling from 100 degrees Celsius to the average skin temperature (assumed about 37 degrees Celsius), use the equation \( Q = mc\text{\textDelta}T \). Here, \(m = 0.50 \text{ g}\), \(c = 4.18 \text{ J/g}^{\circ}\text{C} \) for water, and \(\text{\textDelta}T = 100^{\circ}\text{C} - 37^{\circ}\text{C} \). Calculate \( Q = (0.50 \text{ g})(4.18 \text{ J/g}^{\circ}\text{C})(63^{\circ}\text{C}) \).

Calculate heat transferred by the steam

For the steam to burn the skin, it must first condense into water, which involves the heat of vaporization, and then cool to skin temperature. The heat released during condensation can be found using \( Q = mL \) where \( L = 2260 \text{ J/g} \) is the heat of vaporization for water and \( m = 0.50 \text{ g} \). Then add the heat released during cooling as calculated in the previous step to find the total heat transferred.

Compare the heat transfers

By comparing the heat transferred in both scenarios, the one with the greater amount of heat will cause a more severe burn. The steam will typically transfer more heat since it includes both the heat of vaporization and the heat released during cooling to skin temperature.

Key concepts

Specific Heat Capacity

Understanding specific heat capacity is crucial when analyzing how substances interact with heat. It is defined as the amount of heat energy required to raise the temperature of one gram of a substance by one degree Celsius. If we visualize a marathon, where each runner represents a different substance, specific heat capacity would be like the amount of energy each runner needs to finish the race. Some runners (substances) might require more energy (heat) to complete the same distance (temperature change), while others need less.

For instance, when considering the severity of a burn from spilling water on your hand, we look at the specific heat capacity of water, which is quite high at about \(4.18 \text{ J/g}^{\circ}\text{C}\). This means that water can absorb a lot of heat before its temperature rises significantly, and conversely, when it cools down, water releases a substantial amount of heat, which can cause a burn.

Heat of Vaporization

The heat of vaporization is another pivotal concept in heat transfer chemistry. It represents the amount of energy needed to convert one gram of a liquid into vapor without changing the temperature. Following our marathon analogy, this would be like an additional energy boost required for a runner to jump over a hurdle. This hurdle represents the phase change, and for water to go from liquid to gas, it needs a high energy input. The heat of vaporization for water is particularly notable, at \(2260 \text{ J/g}\).

This energy plays a significant role when evaluating burns from steam. In the exercise, the steam transfers this 'extra' energy to the skin during the phase change from gas to liquid, known as condensation, and that is what makes steam burns more severe than those from boiling water. It's essential to comprehend that the release of the latent heat of vaporization can inflict more damage due to the higher energy involved in the phase transition.

Phase Change

Lastly, phase change is a fundamental concept that explains the transitions between solid, liquid, and gas states of matter. It is pivotal to grasp that during these transitions, the temperature of the substance does not change, even though heat energy is absorbed or released. The marathon analogy can illustrate this as our runners pausing to change gear without moving forward – the effort they put into changing gear is akin to the energy absorbed or released during a phase change.

That's why when steam condenses on your skin, it inflicts a serious burn. Despite the steam being at the same temperature as boiling water, the phase change from gas (steam) to liquid (water) releases extra energy. The body must absorb this energy to facilitate the phase change, resulting in a higher heat transfer and thus a more severe burn. Phase changes are not just simple temperature transitions; they are energy exchanges that have significant implications, especially in understanding heat-related injuries.