Problem 39 - College Physics

Question

What is the amount of heat entering your skin when it receives the heat released (a) by \(25.0 \mathrm{~g}\) of steam initially at \(100.0^{\circ} \mathrm{C}\) that cools to \(34.0^{\circ} \mathrm{C} ?\) (b) by \(25.0 \mathrm{~g}\) of water initially at \(100.0^{\circ} \mathrm{C}\) that cools to \(34.0^{\circ} \mathrm{C} ?\) (c) What do these results tell you about the relative severity of steam and hot-water bums?

Step-by-Step Solution

Answer

Steam releases more heat due to phase change, causing more severe burns than hot water burns.

Step 1: Understanding Heat Transfer in Phase Changes

First, when steam condenses to water at the same temperature, it releases heat known as the latent heat of vaporization. Calculate this using the formula:\[ q_1 = mL_v \]where \( q_1 \) is the heat released, \( m \) is the mass, and \( L_v \) is the latent heat of vaporization for water (about 2260 J/g).

Step 2: Calculate Heat from Temperature Decrease (Steam to Water)

After the steam has condensed to water, the resulting liquid must be cooled from \(100.0^{\circ} \mathrm{C}\) to \(34.0^{\circ} \mathrm{C}\). Use the specific heat capacity equation:\[ q_2 = mc\Delta T \]where \( q_2 \) is the heat released in cooling, \( c \) is the specific heat capacity of water (4.186 J/g°C), and \( \Delta T \) is the temperature change.\[ \Delta T = 100.0 - 34.0 = 66.0 \text{ °C} \]

Step 3: Calculate Total Heat for Steam Cooling

Sum the heat released during the phase change and the heat released as the water cools:\[ \text{Total heat for steam } = q_1 + q_2 \]Plug the values into the equations from Steps 1 and 2 to obtain the answer.

Step 4: Calculate Heat Released by Water Cooling

For water initially at \(100.0^{\circ} \mathrm{C}\) cooling down to \(34.0^{\circ} \mathrm{C}\), only the specific heat capacity equation is used:\[ q = mc \Delta T \]Substitute the known values:\[ m = 25.0 \; \text{g}, \; c = 4.186 \; \text{J/g°C}, \; \Delta T = 66.0 \; \text{°C} \]

Step 5: Compare Heat Transfer Results for Severity of Burns

The total heat release for steam is significantly higher than for water due to the additional phase change heat component. This illustrates that steam can transfer more heat to your skin, making steam burns potentially more severe than burns from hot water.

Key Concepts

Heat of Vaporization

The heat of vaporization is a crucial concept when understanding heat transfer during phase changes. It is the amount of energy needed to turn a given quantity of a substance from liquid to gas at constant temperature and pressure. For water, the latent heat of vaporization is approximately 2260 J/g. This means that for every gram of water that vaporizes into steam, 2260 joules of energy are absorbed. Conversely, when steam condenses back into water, an equivalent amount of energy is released into the surrounding environment.

In exercises involving steam cooling, such as the original problem, the heat of vaporization plays a significant role. As the steam condenses, it releases a substantial amount of heat. This considerably increases the total heat transferred to the substance it contacts, in this case, skin.

• The formula to calculate this heat release is given by: \[ q_1 = mL_v \]where \( q_1 \) represents the heat released, \( m \) is the mass of the steam, and \( L_v \) is the heat of vaporization.

Specific Heat Capacity

Specific heat capacity indicates how much heat energy is needed to raise the temperature of one gram of a substance by one degree Celsius. For water, the specific heat capacity is 4.186 J/g°C, and it is used to calculate the heat transfer associated with temperature changes without phase changes. In calculations, this tool helps assess how much energy is transferred when water at one temperature cools down to another.

When determining the amount of energy released as water cools from 100°C to 34°C, the specific heat capacity equation is used:

• The formula is: \[ q_2 = mc riangle T \]where \( q_2 \) is the heat released during cooling, \( m \) is the mass, \( c \) is the specific heat capacity, and \( \triangle T \) is the change in temperature.

This calculation becomes crucial in understanding energy transfer dynamics when no phase change occurs, as in the cooling of hot water after it has already condensed from steam.

Phase Changes

Phase changes refer to the transition between different states of matter, such as from liquid to gas (vaporization) or gas to liquid (condensation). During these changes, energy is absorbed or released without changing the temperature of the substance.

In the context of heat transfer, phase changes significantly influence how much energy is transferred to or from a substance. When steam condenses back into water, it undergoes a phase change that releases latent heat, contributing to a notable energy transfer to the skin or another surface. Importantly, despite large energy movements, the temperature remains constant during the phase change.

• This unique feature highlights why steam burns can be so severe, as the large amount of energy released during condensation transfers quickly to anything in contact, like skin.

Understanding phase changes and their associated energy transfers is crucial for examining scenarios like those presented in the referenced exercise.

Steam Burns vs. Water Burns

Steam burns tend to be more severe than water burns due to the additional latent heat of vaporization involved in steam's transformation into liquid water. When steam contacts the skin, it first undergoes a phase change, converting into liquid, and during this conversion, it releases a significant amount of heat.

This additional heat release means that the skin absorbs more energy in the same amount of time when in contact with steam compared to hot water alone. For example, in the given exercise, when steam at 100°C condenses, it releases significantly more heat compared to the cooling of water at the same initial temperature but without a phase change.

• The comparative results from these observations underline that steam delivers more energy and does so at a higher rate, dramatically increasing the risk of more severe burns.

This knowledge is essential to understanding safety precautions around steam and high-temperature water to prevent severe injuries.