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The latent heat of vaporization is a fundamental concept in thermodynamics. It refers to the amount of energy required to turn a liquid into a vapor without changing its temperature. In this case, it is the energy needed for the water to evaporate from the weight lifter's body during exercise.
The formula for calculating this energy is straightforward:

• \(Q = mL\)
• where \(Q\) is the energy, \(m\) is the mass of the substance (in kg), and \(L\) is the latent heat of vaporization (in J/kg).

In the exercise, the weight lifter loses 0.150 kg of water. Using the given latent heat of vaporization, \(2.42 \times 10^6 \text{ J/kg}\), the energy required for evaporation is found to be \(3.63 \times 10^5 \text{ J}\).
Understanding this concept helps us appreciate the significant energy transfer that occurs even in a common process like sweating during exercise.

Internal energy is an important concept in thermodynamics, as it represents the total energy contained within a system. It includes all forms of energy, such as kinetic and potential energy at the molecular level.
When the weight lifter exercises, they work to lift weights and lose energy through the evaporation of sweat. The change in internal energy (\( \Delta U \)) can be calculated by combining both these energy components:

• The energy lost due to evaporation (\( 3.63 \times 10^5 \text{ J} \)
• The work done lifting weights (\( 1.40 \times 10^5 \text{ J}\)

Using the formula:

• \( \Delta U = Q + W \)
• where \(Q\) is the energy lost through evaporation and \(W\) is the work done.

The total change in internal energy is found to be \(5.03 \times 10^5 \text{ J}\).
This illustrates how physical activities affect the body's energy balance.

Nutritional calories are a crucial unit of measurement in understanding energy balance, especially when it comes to diet and exercise. In physics, energy is usually measured in joules, but the food industry uses nutritional calories to express energy values.
One nutritional Calorie is equivalent to 4186 joules, which helps to quantify the energy intake from food to replace the energy spent.
In this exercise, after calculating the total energy loss of the weight lifter as \(5.03 \times 10^5 \text{ J}\), it's essential to convert it into nutritional Calories to understand how much energy needs to be replenished through food.

• The conversion is done using the formula:\( \text{Calories} = \frac{\text{Energy in J}}{4186} \)

Resultantly, the weight lifter needs to consume approximately 120.2 nutritional Calories to replace the lost energy.
This conversion is crucial for anyone looking to balance their energy expenditure with energy intake.