Question

Assuming the severity of a burn increases as the amount of energy put into the skin increases, which of the following would cause the most severe burn (assume equal masses)? a) water at \(90^{\circ} \mathrm{C}\) b) copper at \(110^{\circ} \mathrm{C}\) c) steam at \(180^{\circ} \mathrm{C}\) d) aluminum at \(100^{\circ} \mathrm{C}\) e) lead at \(100^{\circ} \mathrm{C}\)

Short answer

Answer: (c) steam at \(180^{\circ} \mathrm{C}\)

Step-by-step solution

Research the specific heat capacities of the materials

We need to look up the specific heat capacities of each material in order to make a comparison. Here are the specific heat capacities of each material listed in the problem: Water: \(4.18 \ \mathrm{J / (g \cdot K)}\) Copper: \(0.385 \ \mathrm{J / (g \cdot K)}\) Steam: \(2.03 \ \mathrm{J / (g \cdot K)}\) Aluminum: \(0.897 \ \mathrm{J / (g \cdot K)}\) Lead: \(0.127 \ \mathrm{J / (g \cdot K)}\)

Decide on the temperature difference of each material to skin

Next, we need to decide on the temperature difference for each material. We will assume that the temperature of the skin is \(30^{\circ} \mathrm{C}\). The temperature difference (\(ΔT\)) for each material is: Water: \(60^{\circ} \mathrm{C}\) Copper: \(80^{\circ} \mathrm{C}\) Steam: \(150^{\circ} \mathrm{C}\) Aluminum: \(70^{\circ} \mathrm{C}\) Lead: \(70^{\circ} \mathrm{C}\)

Calculate the total energy absorbed by skin for each material

Now, we will calculate the energy absorbed by the skin for each material using the specific heat capacities and temperature differences found in steps 1 and 2: Water: \(Q = 4.18 \times 60 = 250.8 \ \mathrm{J}\) Copper: \(Q = 0.385 \times 80 = 30.8 \ \mathrm{J}\) Steam: \(Q = 2.03 \times 150 = 304.5 \ \mathrm{J}\) Aluminum: \(Q = 0.897 \times 70 = 62.79 \ \mathrm{J}\) Lead: \(Q = 0.127 \times 70 = 8.89 \ \mathrm{J}\)

Compare the energy values

We can now compare the calculated energy values to determine which material will cause the most severe burn: Water: \(250.8 \ \mathrm{J}\) Copper: \(30.8 \ \mathrm{J}\) Steam: \(304.5 \ \mathrm{J}\) Aluminum: \(62.79 \ \mathrm{J}\) Lead: \(8.89 \ \mathrm{J}\) We can conclude that, given equal masses, steam at \(180^{\circ} \mathrm{C}\) would cause the most severe burn, as the energy absorbed by the skin is the highest (\(304.5 \ \mathrm{J}\)) among all materials. Therefore, the correct answer is (c) steam at \(180^{\circ} \mathrm{C}\).

Key concepts

Specific Heat Capacity

Specific heat capacity is a property that describes how much heat energy is needed to raise the temperature of a certain mass of substance by one degree Celsius (or one Kelvin). Formally, it is expressed as joules per gram per degree Celsius \( \mathrm{J / (g \cdot ^{\circ}C)} \).

A substance with a high specific heat capacity can absorb a lot of heat without changing its temperature significantly. This is crucial when considering burn severity, as a material's specific heat capacity influences the amount of energy it can transfer to the skin. For instance, water has a high specific heat capacity \(4.18 \mathrm{J / (g \cdot K)} \), which means it can store and release a large amount of energy, potentially causing more severe burns compared to other materials with a lower specific heat capacity, such as lead \(0.127 \mathrm{J / (g \cdot K)} \).

Understanding specific heat capacity helps us to predict the outcome when different materials at various temperatures come into contact with the skin, by showing how much energy can be transferred and possibly causing burns.

Thermal Energy Transfer

Thermal energy transfer, often referred to as heat transfer, describes the flow of heat energy from a hotter object to a cooler one. There are three methods of heat transfer: conduction, convection, and radiation. In the context of burn severity, we primarily consider conduction, which is the direct transfer of heat through a medium or between objects in physical contact.

If a material at a high temperature comes into contact with skin, thermal energy will be transferred until there is no temperature difference between the two, hence the severity of a burn highly depends on the amount of energy transferred. In the exercise, materials with higher temperatures and specific heat capacities have the potential to transfer more energy to the skin. For example, steam at \(180^\circ \mathrm{C}\) can transfer substantial energy leading to severe burns, particularly because steam can also release latent heat during condensation.

Temperature Difference

Temperature difference, often symbolized as \( \Delta T \), is a critical factor in the severity of burns due to its direct impact on the amount of thermal energy transferred. It's the difference in temperature between two substances - in this case, between the skin and the material in question. The larger the temperature difference, the higher the rate of thermal energy transfer, at least initially.

In our exercise, assuming the skin has a temperature of \(30^\circ \mathrm{C}\), materials with higher initial temperatures like steam will have a larger \( \Delta T \). Hence, they can initially transfer energy more rapidly compared to materials with temperatures closer to that of the skin. The equation for heat transfer used in the step by step solution \(Q = m \cdot c \cdot \Delta T\) takes into account this temperature difference, which is why steam, despite its lower specific heat capacity than water, can cause more severe burns due to its much higher temperature relative to the skin.