If the air temperature is the same as the temperature of your skin (about 30.0 C), your body cannot get rid of heat by transferring it to the air. In that case, it gets rid of the heat by evaporating water (sweat). During bicycling, a typical 70.0 kg person's body produces energy at a rate of about 500 W due to metabolism, 80.0 % of which is converted to heat.
How many kilograms of water must the person's body evaporate in an hour to get rid of this heat? The heat of vaporization of water at body temperature is 2.42*10^6 J/kg.
m=??kg
The evaporated water must, of course, be replenished, or the person will dehydrate. How many 750 mL bottles of water must the bicyclist drink per hour to replenish the lost water? (Recall that the mass of a liter of water is 1.00 kg.)
=?? bottles per hour
Our teacher hasn't gone over a problem this complex, and the book isn't any help for something this hard either...I'm extremely lost!
Convert 500 watts to joules/sec.
That is 500 J/sec. The problem states about 80% is converted to heat so 500 J/sec x 0.8 = ?? heat produced in 1 sec.
How many J is that per hour.
500 J/sec x (60 sec/min) x (60 min/hour) = ?? J/hour.
Then q = mass H2O in kg x heat of vap of water at 30o C. You have q and you have heat of vap of water, solve for mass H2O in kg.
Then convert to # bottles of water to replenish.
Post your work if you get stuck.
It isn't that hard if you think it through one step at a time.
80% of 500 W converted to heat is 400 W (Joules per sec) In one hour, that is 1 hr x 400 J/s x3600 s/hr= 1.44*10^6 J to be removed
Each kg of water evaporated removes
2.42*10^6 J . So.. divide 1.44*10^6 J by 2.42 J/kg to get the number of kg of sweat to be evaporated. Each kg is one liter. For the number of bottles of water, divide the # of kg by 0.75 kg/bottle.
Well, don't worry! I'm here to help you out with a touch of humor. Let's break down the problem step by step.
First, we need to find out how many kilograms of water the person's body must evaporate in an hour to get rid of the heat. We are given that 80% of the energy produced is converted to heat, which is 500 W. So, we can calculate the heat produced per hour by multiplying the power by the time: 500 W * 3600 s = 1,800,000 J.
Now, we know the heat of vaporization of water at body temperature is 2.42 * 10^6 J/kg. To find the mass of water evaporated, we divide the total heat produced by the heat of vaporization: 1,800,000 J / (2.42 * 10^6 J/kg) ≈ 0.744 kg.
Therefore, the person's body needs to evaporate about 0.744 kg of water in an hour to get rid of the heat.
Now, let's move on to the second part of the problem. We need to determine how many 750 mL bottles of water the bicyclist needs to drink per hour to replenish the lost water.
We found that the person's body evaporates 0.744 kg of water in an hour. Since the mass of one liter of water is 1.00 kg, we can convert 0.744 kg to liters: 0.744 kg * (1 L / 1.00 kg) ≈ 0.744 L.
Since one bottle contains 750 mL, we need to convert 0.744 L to milliliters: 0.744 L * (1000 mL / 1 L) = 744 mL.
So, the bicyclist needs to drink approximately 744 mL of water per hour to replenish the lost water. Since one bottle contains 750 mL, they will need just one bottle per hour.
I hope this helps! Remember, staying hydrated is no joking matter!
No worries, I'll walk you through the problem step by step. Let's start with calculating the amount of water that needs to be evaporated by the person's body.
Step 1: Calculate the amount of heat produced by the person's body in one hour.
Given:
Power output (P) = 500 W
Conversion efficiency (ε) = 80% = 0.8
The amount of heat produced by the body in one hour can be calculated using the formula:
Heat produced = Power output * Conversion efficiency * Time
Since the time is given in hours, we have:
Heat produced = 500 W * 0.8 * 1 hour
Step 2: Convert the heat produced to the quantity of water evaporated.
Given:
Heat of vaporization of water (Hv) = 2.42 x 10^6 J/kg
The quantity of water evaporated can be calculated using the formula:
Quantity of water evaporated = Heat produced / Heat of vaporization of water
Step 3: Calculate the mass of water evaporated.
Now, we need to convert the quantity of water evaporated into kilograms (kg) instead of Joules (J).
Given:
1 liter of water = 1.00 kg
So, to convert liters to kilograms, we can assume that 1 liter of water weighs 1.00 kg, since the density of water is close to 1 kg/L.
Now, you have the mass of water evaporated. Let's move on to calculating the number of bottles of water the bicyclist needs to drink to replenish the lost water.
Step 4: Calculate the number of 750 mL bottles of water needed.
Given:
Volume of one bottle (V) = 750 mL = 0.75 L
The number of bottles of water needed can be calculated using the formula:
Number of bottles = Mass of water evaporated / Volume of one bottle
Now, you have the number of bottles the bicyclist needs to drink per hour to replenish the lost water.
Just plug in the values and do the calculations, and you'll get your answer.
To solve this problem, we can use the concepts of energy and heat transfer.
First, let's calculate the amount of heat produced by the person's body in 1 hour. We know that the person's body produces energy at a rate of 500 W (watts) due to metabolism, and 80% of this is converted to heat.
So, the amount of heat produced per hour can be calculated as follows:
Heat produced = (Energy produced) x (Conversion efficiency)
= (500 W) x (0.80)
= 400 J/s x 3600 s
= 1.44 x 10^6 J
Now, let's calculate the mass of water that needs to evaporate to get rid of this heat. We'll use the heat of vaporization of water at body temperature, which is given as 2.42 x 10^6 J/kg.
Mass of water evaporated = (Heat produced) / (Heat of vaporization)
= (1.44 x 10^6 J) / (2.42 x 10^6 J/kg)
= 0.595 kg
Therefore, the person's body needs to evaporate approximately 0.595 kg of water in an hour to get rid of the heat.
Next, let's calculate the number of 750 mL bottles of water the bicyclist needs to drink per hour to replenish the lost water. Since the mass of a liter of water is 1.00 kg, the mass of 750 mL of water is 0.750 kg.
Number of bottles = (Mass of evaporated water) / (Mass of water in one bottle)
= (0.595 kg) / (0.750 kg)
= 0.793 bottles
Since we can't have fractional bottles, the bicyclist would need to drink approximately 1 bottle of water per hour to replenish the lost water.
To summarize:
- The person's body needs to evaporate approximately 0.595 kg of water in an hour to get rid of the heat.
- The bicyclist would need to drink approximately 1 bottle of water per hour to replenish the lost water.