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Latent heat of vaporization is the amount of energy required to convert a liquid into a vapor without changing its temperature. It is a critical concept in thermodynamics because it helps us understand how energy is transferred during phase changes.
The latent heat of vaporization for water is a large value. In our example, it is given as \(2.42 \times 10^6\) J/kg, meaning this amount of energy is needed to evaporate just one kilogram of water.
In our weightlifter's case, they lose \(0.150\) kg of water, and we calculate the heat energy required to vaporize this water using the formula \(Q = mL\).
Here,

• \(m\) is the mass of the water (0.150 kg),
• and \(L\) is the latent heat of vaporization (\(2.42 \times 10^6\) J/kg).

When plugging in these values, we find that the energy used for evaporation is \(3.63 \times 10^5\) J. This process is crucial because it involves lots of energy transfer from the body, affecting how internal energy changes.

Internal energy is a thermodynamic property representing the total energy contained within a system. It encompasses both the kinetic energy of molecules moving and vibrating, and potential energy from molecular forces.
In the context of our exercise, the weight lifter's internal energy changes due to work and heat changes. Using the equation \(\Delta U = Q - W\) helps calculate this change, where:

• \(Q\) is the heat transfer (\(3.63 \times 10^5\) J) due to evaporation.
• \(W\) is the work done (\(1.40 \times 10^5\) J), which is the energy expended during lifting.

By substituting these values, we determine \(\Delta U\), the change in internal energy, as \(2.23 \times 10^5\) J.
This tells us that even though the heat was lost due to sweat evaporating, some energy was also expended as work. The difference between these two values is the change in internal energy. Understanding this energy balance is key when considering how physical activities can affect the body's energy storage.

Nutritional calories are units of energy intake, crucial for maintaining the body's energy balance. They are technically referred to as kilocalories, where 1 nutritional Calorie equals 4,186 Joules.
When a weight lifter loses energy from the body through evaporation and work, it's important to replace it with food energy. This ensures the body can function optimally and recover.
To find out how many Calories are needed to replace lost energy, we divide the change in internal energy by 4,186 J/Calorie.
For instance, with an internal energy change of \(2.23 \times 10^5\) J, the nutritional calorie requirement becomes approximately 53.3 Calories. This simple conversion helps us understand how much dietary energy is needed to balance the energy lost during physical exertion.
Keeping track of Calories helps maintain energy equilibrium and is vital for both athletes and anyone involved in regular physical activity.