A 60.0 kg runner expends 355 W of power while running a marathon. Assuming that 8.00% of the energy is delivered to the muscle tissue and that the excess energy is primarily removed from the body by sweating, determine the volume of bodily fluid (assume it is water) lost per hour. (At 37.0°C the latent heat of vaporization of water is 2.41 106 J/kg.)
I don't know what to do with this...
92% of the 355 W becomes body heat. That equals 327 W. In one hour, that is a total heat energy of 3600*327 = 1.18*10^6 J. Divide that by the latent heat of vaporization for the # of kg of sweat evaporated
To solve this problem, you can follow these steps:
Step 1: Calculate the total energy expended by the runner in one hour:
Since power is given in watts (W), and time is given in hours (h), we can use the formula: Energy (in joules) = power (in watts) × time (in seconds).
But since time is given in hours, we need to convert it to seconds by multiplying it by 3600 (1 hour = 3600 seconds).
So, the total energy expended (E) by the runner in one hour is: E = 355 W × 3600 s = 1,278,000 J.
Step 2: Calculate the energy delivered to the muscle tissue:
Since 8.00% of the energy is delivered to the muscle tissue, we can calculate it by multiplying the total energy (E) by 0.08.
So, the energy delivered to the muscle tissue (Em) is: Em = E × 0.08 = 1,278,000 J × 0.08 = 102,240 J.
Step 3: Calculate the volume of bodily fluid lost per hour:
To calculate the volume of bodily fluid lost per hour, we can use the formula: Volume (in kg) = Energy (in J) / latent heat of vaporization (in J/kg).
The latent heat of vaporization of water is given as 2.41 × 10^6 J/kg.
So, the volume of bodily fluid lost per hour (V) is: V = Em / latent heat of vaporization = 102,240 J / 2.41 × 10^6 J/kg.
Now you can calculate the volume of bodily fluid lost per hour by substituting the values in the formula and performing the calculations.
No worries! I can explain how to solve this problem step by step.
First, let's start by converting the power output from watts to energy in joules per second. Since power is given in watts and is equal to energy per unit time, we can use the equation: power = energy/time. Therefore, energy = power × time.
We are given that the runner expends 355 W of power while running a marathon. To find the energy expended during the marathon, we need to know the time it takes to complete the marathon. Since the time is not provided, we cannot proceed with this information alone. We will need more information to solve the problem.
Next, let's determine the amount of energy delivered to the muscle tissue. It is stated that 8.00% of the energy is delivered to the muscle tissue. So, we can calculate the energy delivered to the muscles by multiplying the total energy expended by 0.08 (8%) since only 8% of the energy is delivered to the muscles.
Now, let's consider the excess energy that is primarily removed from the body by sweating. Sweat is mostly composed of water, and when this water evaporates, it absorbs energy from the body. The energy absorbed during the evaporation of water is equal to the latent heat of vaporization of water. The latent heat of vaporization of water at 37.0°C is given as 2.41 × 10^6 J/kg.
To find the volume of bodily fluid lost per hour, we need to determine the amount of energy lost through sweating and divide it by the latent heat of vaporization of water.
Here are the steps to calculate the volume of bodily fluid lost per hour:
1. Determine the total energy expended during the marathon by multiplying the power output (355 W) by the time it takes to complete the marathon (not given).
2. Calculate the energy delivered to the muscle tissue by multiplying the total energy expended by 0.08.
3. Divide the energy delivered to the muscle tissue by the latent heat of vaporization of water (2.41 × 10^6 J/kg) to find the mass of water lost.
4. Convert the mass of water lost to volume by dividing by the density of water. The density of water is approximately 1000 kg/m^3.
5. Finally, divide the volume of water lost by the time it takes to complete the marathon (in hours) to find the volume of bodily fluid lost per hour.
Please note that without the information about the time it takes to complete the marathon, we cannot provide a specific numeric answer. You will need to determine the time to complete the marathon in order to calculate the volume of bodily fluid lost per hour.