In exercising, a weight lifter loses 0.100 kg of water through evaporation, the heat required to evaporate the water coming from the weight lifter's body. The work done in lifting weights is 1.30 x 10^5 J.
(a) Assuming that the latent heat of vaporization of perspiration is 2.42 x 10^6 J/kg, find the change in the internal energy of the weight lifter.
(b) Determine the minimum number of nutritional calories of food (1 nutritional calorie = 4186 J) that must be consumed to replace the loss of internal energy.
To answer this question, we need to use the concept of energy conservation. We can assume that all the work done by the weight lifter is converted into internal energy and evaporation of water.
(a) The change in the internal energy of the weight lifter can be calculated by considering the work done and the heat absorbed due to evaporation.
The work done by the weight lifter is given as 1.30 x 10^5 J.
The heat required to evaporate the water can be calculated using the formula:
Heat = Mass * Latent heat of vaporization
Here, the mass of water evaporated is given as 0.100 kg, and the latent heat of vaporization is given as 2.42 x 10^6 J/kg.
Therefore, the heat absorbed due to evaporation is:
Heat = 0.100 kg * 2.42 x 10^6 J/kg
Now, we can calculate the change in the internal energy as:
Change in internal energy = Work done + Heat absorbed
Change in internal energy = 1.30 x 10^5 J + (0.100 kg * 2.42 x 10^6 J/kg)
(b) To determine the minimum number of nutritional calories of food required to replace the loss of internal energy, we need to convert the change in internal energy from joules to nutritional calories. 1 nutritional calorie is equal to 4186 J.
The change in internal energy in joules is calculated in part (a). We can convert it to nutritional calories as:
Change in internal energy (in nutritional calories) = Change in internal energy (in joules) / 4186 J/nutritional calorie
Now, we have the minimum number of nutritional calories required to replace the loss of internal energy.