Problem 52 - University Physics with Modern Physics

Question

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

Step-by-Step Solution

Answer

Steam burns are more severe as they release more heat due to phase change.

Step 1: Understanding the Concept

The problem involves calculating the heat released by steam and water separately when they are cooled. The heat released when steam condenses and the heat consumed to cool down the resultant water have distinct processes: 1) release of latent heat during condensation, 2) cooling of water from condensation, and 3) cooling of water from original water. We will use these steps to find the total heat for steam and water.

Step 2: Calculating Heat Released by Steam Condensation

To find the heat released by 25.0 g of steam as it condenses, use the formula: \( Q = mL \), where \( m = 25.0 \) g, and \( L = 2260 \) J/g, the latent heat of vaporization. So, \( Q = 25.0 \times 2260 = 56500 \) J.

Step 3: Cooling the Condensed Water to Skin Temperature

The steam that condensed into water is now cooled from 100.0°C to 34.0°C. Use the formula \( Q = mc\Delta T \), where \( m = 25.0 \) g, \( c = 4.18 \) J/g°C, and \( \Delta T = 100.0°C - 34.0°C = 66.0°C \). Therefore, \( Q = 25.0 \times 4.18 \times 66.0 = 6897 \) J.

Step 4: Total Heat Released by Steam

Add the heat released during condensation to the heat released when the condensed water is cooled: \( 56500 \text{ J} + 6897 \text{ J} = 63397 \text{ J} \).

Step 5: Calculate Heat Released by Water

For water at 100.0°C cooling to 34.0°C, use the formula \( Q = mc\Delta T \), where \( m = 25.0 \) g, \( c = 4.18 \) J/g°C, and \( \Delta T = 66.0 \)°C. Therefore, \( Q = 25.0 \times 4.18 \times 66.0 = 6897 \) J.

Step 6: Comparison and Conclusion

Compare the heat absorbed by the skin in both cases: Steam releases \( 63397 \text{ J} \) while water releases \( 6897 \text{ J} \). The amount of heat from steam is significantly greater due to the additional heat from the phase transition from steam to water.

Key Concepts

Phase Transitions

A phase transition occurs when a substance changes from one state of matter to another, like solid to liquid or liquid to gas. In this exercise, we're dealing with the transition from steam (gas) to water (liquid).
The key element in phase transitions is that they involve the absorption or release of energy, called latent heat.
When steam condenses into water, it releases a large amount of energy, known as latent heat of vaporization. This phase transition from steam to water significantly increases the amount of heat transferred to the skin.

• Steam to water transition releases energy.
• This process involves latent heat.

The immense energy release during phase transitions makes steam burns more severe than burns from hot water.

Heat Transfer

Heat transfer refers to the movement of thermal energy from one object to another and is a critical concept in understanding burns.
In our problem, heat is transferred from steam or hot water to the skin, causing potential burns.
There are three modes of heat transfer: conduction, convection, and radiation. However, here, we focus on the conduction occurring when steam or water comes in contact with the skin.
Heat transfer is calculated using the formula: \[ Q = mc\Delta T \]where \( Q \) is the heat transferred, \( m \) is the mass, \( c \) is the specific heat capacity, and \( \Delta T \) is the change in temperature.

• Heat flows from the hotter steam or water to cooler skin.
• Heat transfer can cause damage like burns.

Understanding how heat is transferred can help in explaining why steam burns cause more damage.

Latent Heat

Latent heat is the heat absorbed or released during a phase transition without changing the temperature.
In the context of steam, the latent heat of vaporization is a key factor. When steam condenses to water, it releases latent heat, which is a large amount of energy.
The formula to calculate this energy release is: \[ Q = mL \]where \( Q \) is the amount of heat, \( m \) is the mass, and \( L \) is the latent heat of vaporization.

• The latent heat of vaporization for water is very high at \( 2260 \text{ J/g} \).
• This additional heat from phase change is what makes steam burns more severe.

Understanding latent heat is crucial to explaining why a small amount of steam can cause significant burns.

Specific Heat Capacity

Specific heat capacity is the amount of heat required to change the temperature of a unit mass of a substance by one degree Celsius.
For water, the specific heat capacity is \( 4.18 \text{ J/g°C} \).
In our scenario, once steam condenses to water, the resultant water further cools, releasing more heat during this process as per the formula:\[ Q = mc\Delta T \]where \( m \) is the mass, \( c \) is the specific heat capacity, and \( \Delta T \) is the temperature change.

• The specific heat explains how much energy is needed to cool down the water after steam condensation.
• This process adds to the total heat imparted to the skin, making burns worse.

Specific heat capacity helps understand the energy transferred during cooling after a phase transition.