Question

Patients with a high body temperature are often given "alcohol baths." The heat of vaporization of isopropanol (rubbing alcohol) is \(665 \mathrm{~J} / \mathrm{g}\). How much heat is removed from the skin by the evaporation of \(190 \mathrm{~g}\) (about half a cup) of isopropanol?

Short answer

126,350 J

Step-by-step solution

Understanding the Heat of Vaporization

The heat of vaporization is the amount of heat required to convert a unit mass of a liquid into a gas at constant temperature. For isopropanol, this value is given as 665 J/g.

Identify the Given Variables

We are given the following: the mass of isopropanol, \( m = 190 \) g, and the heat of vaporization, \( ext{Hvap} = 665 \) J/g.

Calculating the Total Heat Removed

The total heat removed during the vaporization can be found by multiplying the mass of the alcohol by the heat of vaporization: \[ Q = m \times ext{Hvap} = 190 \text{ g} \times 665 \text{ J/g} \].

Perform the Calculation

Multiply the two values: \( 190 \times 665 = 126,350 \). Thus, the total heat removed from the skin is 126,350 J.

Key concepts

isopropanol evaporation

Isopropanol, also known as rubbing alcohol, plays a crucial role in cooling treatments due to its evaporation properties. When it evaporates, isopropanol transitions from a liquid to a gas. This process requires energy, which is absorbed as heat from the surrounding environment, such as your skin. This is why applying isopropanol can cause a cooling sensation.
During evaporation, molecules at the surface gain enough energy to break free from the liquid state, turning into vapor. This phenomenon highlights the close relationship between evaporation and energy transfer, showcasing why isopropanol is effective in cooling applications.

• Isopropanol evaporates quickly at room temperature.
• It absorbs heat from your skin, causing cooling.
• The evaporation rate can be influenced by factors like temperature and air flow.

Understanding this fundamental process can give insights into how everyday applications, like alcohol baths, exploit evaporation to remove excess body heat.

thermal energy transfer

Thermal energy transfer involves the movement of heat from one location to another. In the case of isopropanol evaporation, thermal energy is transferred from the skin to the alcohol. This occurs because the molecules absorb surrounding heat energy during their transition from liquid to gas.
This transfer of energy can be understood through a simple principle: energy flows from a warmer area (your skin) to a cooler one (the isopropanol). As the alcohol absorbs heat, it cools the skin down, demonstrating thermal energy transfer in action.

• Heat flows naturally from warm to cold areas.
• Evaporation increases heat absorption, facilitating cooling.
• The efficiency of this process impacts how effective the cooling is.

Grasping thermal transfer provides a deeper understanding of how substances like isopropanol can be used to manage body temperature effectively.

vaporization calculation

Calculating the energy involved in vaporization is essential for understanding how much heat is absorbed or released during the process. In this problem, we're interested in finding out how much heat is removed from the skin by the evaporation of isopropanol.
To calculate this, we use the formula: \[ Q = m \times \text{Hvap} \] Where \( Q \) is the heat absorbed (or removed), \( m \) is the mass of isopropanol, and \( \text{Hvap} \) is the heat of vaporization.
With the given values: \( m = 190 \text{ g} \) and \( \text{Hvap} = 665 \text{ J/g} \), the calculation becomes: \( 190 \text{ g} \times 665 \text{ J/g} = 126,350 \text{ J} \).

• Calculate using the mass of the substance evaporating.
• Multiply by the heat of vaporization to find total heat transferred.
• The result gives the total thermal energy transferred due to vaporization.

This straightforward calculation helps illustrate the link between substance properties and their effect on energy transfer in practical situations like cooling.