Problem 53 - Chemistry: An Atoms-Focused Approach

Question

During a strenuous workout, an athlete generates \(233 \mathrm{kJ}\) of thermal energy. What mass of water would have to evaporate from the athlete's skin to dissipate this energy?

Step-by-Step Solution

Answer

Answer: Approximately \(0.103\; \mathrm{kg}\) of water needs to evaporate from the athlete's skin.

Step 1: Identify the given information

The problem provides us with the thermal energy generated by the athlete during the workout, which is \(233 \mathrm{kJ}\).

Step 2: Convert the energy to Joules

To make our calculations more consistent, let's convert the energy from kilojoules to joules. We know that 1 kJ equals 1000 J. So, \(233 \mathrm{kJ}\) is equal to \(233,000 \mathrm{J}\).

Step 3: Find the latent heat of vaporization for water

The latent heat of vaporization (L) is the amount of energy required to change 1 kg of a substance from its liquid to its vapor state without changing its temperature. For water, the latent heat of vaporization is approximately \(2.26 \times 10^6 \mathrm{J/kg}\).

Step 4: Set up the equation for energy

Now, we'll set up the equation for the energy required to evaporate a specific mass of water: \(Q = mL\) Here, Q is the energy required (which is \(233,000\; \mathrm{J}\)), m is the mass of water we need to find, and L is the latent heat of vaporization for water (\(2.26 \times 10^6 \mathrm{J/kg}\)).

Step 5: Solve for the mass of water

Now, we'll solve the equation for the mass of water (m): \(m = \frac{Q}{L}\) Plugging in the values: \(m = \frac{233,000\; \mathrm{J}}{2.26 \times 10^6\; \mathrm{J/kg}}\) \(m \approx 0.103\; \mathrm{kg}\) So, approximately \(0.103\; \mathrm{kg}\) of water would need to evaporate from the athlete's skin to dissipate the energy generated during the workout.

Key Concepts

Thermal Energy

Thermal energy is a type of energy that results from the movement of particles within a substance. It is closely related to temperature, as increased particle motion elevates temperature. During physical activities, our bodies convert stored energy into thermal energy. This increase in thermal energy reflects as a rise in body temperature.

In our exercise example, the athlete generates thermal energy during a workout. This energy buildup can lead to overheating, so the body uses sweat evaporation to cool down. Understanding thermal energy's role helps us appreciate how the body regulates itself to maintain a stable internal environment when engaging in physical exertion.

Latent Heat of Vaporization

The latent heat of vaporization is a crucial concept in thermodynamics, representing the energy required to turn a liquid into a gas without changing its temperature. Water has a high latent heat of vaporization, meaning it requires significant energy to transition from liquid to vapor. This property of water is why sweating is an effective way to cool the body.

In our scenario, to calculate how much water needs to evaporate from the athlete's skin to dissipate 233 kJ of thermal energy, we use the latent heat of vaporization for water, which is approximately \(2.26 \times 10^6 \text{ J/kg}\). By applying this value in calculations, we determine the cooling effect achieved through sweat evaporation, thus maintaining temperature balance for the athlete.

Energy Conversion

Energy conversion is the process of changing energy from one form to another. In thermodynamics, understanding these conversions is key to managing energy efficiently. During exercise, chemical energy stored in the body converts to mechanical energy for movement and to thermal energy as a result of biochemical reactions.

In the provided workout scenario, the athlete's body turns chemical energy into thermal energy. The body then uses sweat to convert this thermal energy into latent heat, allowing it to transfer into the environment through evaporation, effectively cooling the body. Recognizing the stages of energy conversion, from chemical processes to eventual heat dispersion, offers insights into body mechanisms and the role of thermodynamics in everyday life.