The next morning you ignore your alarm clock until you realize you will not reach the bus unless you run as fast as you can to the bus station in 15min. Carrying your school books during the run results in a total energy use of 1200W. You start sweating, which is the way your body keeps you cool.
a. Assume a typical efficiency how much would your body temperature rise during the 15min if you had no way of getting rid of your excess thermal energy?
b. Assume that the only way that your body cools itself is evaporation of sweat. To keep your body temperature the same, how much water do you have to evaporate during the 15 min of running? How much water do you need to drink not to get dehydrated? The heat of vaporization of sweat from skin is slightly higher than the value for water. Use the value given in your textbook.
What type of formulas can I use and what steps do i need to take
total energy use of 1200W. <<<?????
To answer these questions, you will need to use formulas related to energy and heat transfer. Here are the formulas and steps you can take to solve both parts:
a. Formula for calculating temperature rise:
Temperature rise = Energy / (mass * specific heat capacity)
1. First, convert the power used from watts to joules by multiplying it by the time in seconds:
Energy = 1200W * 900s (15 minutes = 900 seconds)
Energy = 1,080,000 Joules
2. Determine the mass of your body. Assume an average human body mass of 70 kilograms.
3. Look up the specific heat capacity of a typical human body. Assume a value of 3500 J/kg°C.
4. Plug in the values into the formula:
Temperature rise = 1,080,000 J / (70 kg * 3500 J/kg°C)
b. Formula for calculating water evaporation:
Water evaporation = Energy / (heat of vaporization)
1. Look up the heat of vaporization of sweat from your textbook. Assume a value of 2450 J/g.
2. Convert the heat of vaporization to joules by multiplying it by 1000:
Heat of vaporization = 2450 J/g * 1000 g/kg
Heat of vaporization = 2,450,000 J/kg
3. Plug in the values into the formula:
Water evaporation = 1,080,000 J / 2,450,000 J/kg
To calculate the amount of water you need to drink, you will need to consider the amount of water lost through sweat during the run. The specific amount of sweat varies from person to person, but on average, humans lose about 0.5 to 1 liter of sweat per hour of exercise. You can estimate the amount of water you need to drink to replace the lost water based on this average. Keep in mind that individual hydration needs may differ, so it's always best to listen to your body's signals and drink water when you feel thirsty.
To summarize, to answer part a, use the temperature rise formula with the given energy, body mass, and specific heat capacity. For part b, use the water evaporation formula with the given energy and heat of vaporization. Additionally, consider the average amount of sweat lost during exercise to estimate the water intake required to stay hydrated.