A person eats a container of yogurt. The Nutritional Facts label states that it contains 195 Calories (1 Calorie = 4186 J). What mass of perspiration would one have to lose to get rid of this energy? At body temperature, the latent heat of vaporizaiton of water is 2.42 106 J/kg.
To calculate the mass of perspiration one would have to lose to get rid of the energy from the yogurt, we first need to convert the energy from calories to joules.
Given, 1 Calorie = 4186 J
So, the energy content of the yogurt in joules can be calculated as follows:
Energy content = 195 Calories × 4186 J/Calorie
Now, let's calculate the energy content of the yogurt in joules:
Energy content = 195 × 4186 J = 814,170 J
Next, we need to calculate the mass of perspiration that would carry away the same amount of energy. We can use the formula:
Energy released = mass of perspiration × latent heat of vaporization
In this formula, the latent heat of vaporization of water is given as 2.42 × 10^6 J/kg.
So, the mass of perspiration can be calculated as:
mass of perspiration = Energy released / latent heat of vaporization
mass of perspiration = 814,170 J / (2.42 × 10^6 J/kg)
Now, let's calculate the mass of perspiration:
mass of perspiration ≈ 0.336 kg or 336 grams
Therefore, to get rid of the energy from the yogurt, a person would have to lose approximately 0.336 kg or 336 grams of perspiration.