In one of your rigorous workout sessions, you lost 140 g of water through evaporation. Assume that the amount of work done by your body was 3.8 105 J and that the heat required to evaporate the water came from your body.
(a) Find the loss in internal energy of your body (due to evaporating water only), assuming the latent heat of vaporization is 2.42 106 J/kg.
(b) Determine the minimum number of food calories that must be consumed to replace the internal energy lost (1 food calorie = 4186 J).
help please!
heat=masswater*Heatvaporization.
To find the loss in internal energy due to the evaporation of water, you need to use the formula:
Loss in internal energy = Mass of water evaporated × Latent heat of vaporization
(a) First, let's find the mass of water evaporated. We know that you lost 140 g of water through evaporation. Therefore, the mass of water evaporated is 0.140 kg (since 1 kg = 1000 g).
Next, we can substitute the values into the formula:
Loss in internal energy = 0.140 kg × 2.42 × 10^6 J/kg
Simplifying the expression:
Loss in internal energy = 338.8 × 10^3 J
Therefore, the loss in internal energy of your body, due to evaporating water only, is 3.38 × 10^5 J.
(b) To determine the minimum number of food calories required to replace the internal energy lost, we divide the loss in internal energy by the conversion factor from joules to food calories.
Loss in internal energy (in food calories) = Loss in internal energy (in joules) / Conversion factor
Using the conversion factor: 1 food calorie = 4186 J
Loss in internal energy (in food calories) = (3.38 × 10^5 J) / 4186 J/cal
Calculating the value:
Loss in internal energy (in food calories) ≈ 80.7 cal
Therefore, the minimum number of food calories that must be consumed to replace the internal energy lost is approximately 80.7 calories.