Question

Many species cool themselves by sweating, because as the sweat evaporates, heat is given up to the surroundings. A human exercising strenuously has an evaporative heat loss rate of about \(650 \mathrm{W}\). If a person exercises strenuously for 30.0 min, how much water must he drink to replenish his fluid loss? The heat of vaporization of water is \(2430 \mathrm{J} / \mathrm{g}\) at normal skin temperature.

Short answer

Answer: The person must drink approximately 481.48 g (or 0.481 L) of water to replenish the fluid loss.

Step-by-step solution

Calculate the total heat lost

To find the total heat lost, we'll use the formula: Total Heat Lost = Evaporative Heat Loss Rate × Time We are given Evaporative Heat Loss Rate = 650 W and Time = 30 min (which needs to be converted to seconds). So, Time in seconds = 30 × 60 = 1800 s. Now, we can calculate the total heat lost: Total Heat Lost = 650 W × 1800 s = 1170000 J (Joules)

Calculate the amount of water needed

Now that we have the total heat lost, we can use the heat of vaporization to find out the amount of water needed. We are given the heat of vaporization of water as 2430 J/g. So, we'll use the formula: Amount of Water = Total Heat Lost / Heat of Vaporization of Water Amount of Water = 1170000 J / (2430 J/g) = 481.481481 g To replenish the fluid loss, the person must drink approximately 481.48 g (or 0.481 L) of water.