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.
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If mass of water lost =m and latent heat =L
then energy used to evaporate water is mL
If work done in lifting weights is W then the total energy used is mL+W
Assuming that this is the energy that needs to be replaced then the number of calories is (mL+W)/4186
If you want to post your calculations we can check these.
(a) To find the change in internal energy of the weight lifter, we need to calculate the energy used to evaporate the water and subtract it from the work done in lifting weights.
Given:
Mass of water lost (m) = 0.100 kg
Latent heat of vaporization (L) = 2.42 x 10^6 J/kg
Work done in lifting weights (W) = 1.30 x 10^5 J
The energy used to evaporate the water is given by mL, where m is the mass of water lost and L is the latent heat of vaporization.
Energy used to evaporate water = mL
= 0.100 kg * 2.42 x 10^6 J/kg
= 2.42 x 10^5 J
Change in internal energy = Work done - Energy used to evaporate water
= 1.30 x 10^5 J - 2.42 x 10^5 J
= -1.12 x 10^5 J
Therefore, the change in internal energy of the weight lifter is -1.12 x 10^5 J.
(b) To determine the minimum number of nutritional calories of food that must be consumed to replace the loss of internal energy, we need to convert the energy into nutritional calories.
Given:
Energy used to evaporate water = 2.42 x 10^5 J
To convert energy from joules to nutritional calories, we divide by the conversion factor 4186 J/1 nutritional calorie.
Number of nutritional calories = Energy used to evaporate water / 4186
= (2.42 x 10^5 J) / (4186 J/nutritional calorie)
≈ 57.97 nutritional calories
Therefore, the minimum number of nutritional calories of food that must be consumed to replace the loss of internal energy is approximately 58 nutritional calories.