Problem 52 - University Physics with Modern Physics

Question

Steam Burns Versus Water Burns. What is the amount of heat input to your skin when it receives the heat released (a) by 25.0 g of steam initially at \(100.0^{\circ} \mathrm{C},\) when it is cooled to skin temperature \(\left(34.0^{\circ} \mathrm{C}\right) ?\) (b) By 25.0 \(\mathrm{g}\) of water initially at \(100.0^{\circ} \mathrm{C},\) when it is cooled to \(34.0^{\circ} \mathrm{C} ?(\mathrm{c})\) What does this tell you about the relative severity of steam and hot water burns?

Step-by-Step Solution

Answer

Steam transfers 63407.5 J, while water transfers 6907.5 J. Steam burns are more severe.

Step 1: Understanding the Problem

We need to calculate the amount of heat released by 25.0 g of steam and 25.0 g of water as they both cool down to 34.0°C. For steam, we must account for both the heat released as it condenses and cools. For water, we only consider cooling.

Step 2: Calculate Heat Released by Steam Condensation and Cooling

First, calculate the heat released by the phase change and cooling of steam. The total heat will be the sum of the heat of condensation and the cooling of the resulting water.- **Condensation:** The heat released by the steam as it condenses into water is calculated using the formula \( q_\text{condensation} = m \cdot L_v \), where \( m \) is mass and \( L_v = 2260 \text{ J/g} \) is the latent heat of vaporization.- **Cooling of Water:** The heat released by the cooling of water from 100°C to 34°C is given by \( q_\text{water cooling} = m \cdot c \cdot \Delta T \), where \( c = 4.186 \text{ J/(g·°C)} \) is the specific heat and \( \Delta T = 66 \text{ °C} \).Calculation:- \( q_\text{condensation} = 25.0 \text{ g} \times 2260 \text{ J/g} = 56500 \text{ J} \)- \( q_\text{water cooling} = 25.0 \text{ g} \times 4.186 \text{ J/(g·°C)} \times 66 \text{°C} = 6907.5 \text{ J} \)- **Total Heat from Steam:** \( 56500 \text{ J} + 6907.5 \text{ J} = 63407.5 \text{ J} \)

Step 3: Calculate Heat Released by Water Cooling

For water, only the cooling needs to be considered, as there is no phase change. Use the formula for the heat released by cooling:- **Cooling of Water:** \( q_\text{cool water} = m \cdot c \cdot \Delta T \), where \( \Delta T \) is the temperature change from 100°C to 34°C.Calculation:- \( q_\text{cool water} = 25.0 \text{ g} \times 4.186 \text{ J/(g·°C)} \times 66 \text{ °C} = 6907.5 \text{ J} \)

Step 4: Compare the Heat from Steam and Water

By comparing the heat quantities calculated: - Heat from steam (including condensation): 63407.5 J - Heat from water (just cooling): 6907.5 J The steam transfers much more heat to the skin, making steam burns potentially more severe than water burns of the same initial temperature and mass.

Key Concepts

Latent Heat of Vaporization

When something changes from a liquid to a gas, it absorbs a large amount of energy. This energy is known as the "latent heat of vaporization." This concept is crucial in understanding why steam burns can be so harmful.

Latent heat of vaporization is the heat required to change one gram of a liquid into a gas at a constant temperature. For water, this value is particularly high at approximately 2260 J/g.

• When steam, which is water vapor, comes into contact with skin, it releases this stored energy.
• Even when steam just cools down, it releases a huge amount of energy during condensation, leading to severe burns.

Without factoring in latent heat, you cannot accurately estimate the heat released during steam burns.

Specific Heat Capacity

Specific heat capacity is a measure of how much heat energy is needed to raise the temperature of one gram of a substance by one degree Celsius. Understanding specific heat capacity can help make sense of why certain substances feel hot or cold when they transfer heat.

Water has a specific heat capacity of 4.186 J/(g·°C), which is quite high. This means water changes temperature much more slowly compared to substances with lower specific heat values.

• When water cools down from a high temperature, it releases heat gradually due to its high specific heat capacity.
• This gradual release of heat can still contribute significantly to burns, but is minor when compared to the latent heat released upon steam condensation.

Specific heat capacity helps understand the slow temperature change and heating ability of water.

Phase Change

A phase change is when a substance changes from one state of matter to another, such as solid to liquid, or liquid to gas. During a phase change, you might notice that the temperature of the substance doesn’t change, even though heat is being added or removed.

When steam condenses into water, it's undergoing a phase change from gas to liquid, releasing latent heat in the process.

• This is why steam burns are more severe than hot water burns; during a phase change, a lot of energy is transferred as heat to your skin.
• Heat from phase changes can cause rapid temperature changes, leading to more intense burns.

Phase changes are pivotal in understanding heat transfer and the severity of burns caused by steaming substances.

Thermal Energy

Thermal energy is the total kinetic energy of the particles in a substance due to their motion. The faster particles move, the higher the temperature and thermal energy.

When steam or water transfers its thermal energy to your skin, it causes burns. More thermal energy transfer results in more severe burns.

• Thermal energy from steam not only comes from its temperature but also from the latent heat released during condensation.
• In water, only the kinetic energy from its temperature contributes to the burn.

In essence, understanding how thermal energy plays a role in heat transfer allows one to predict the effects of such burns, distinguishing the serious nature of steam burns from those of hot water.