If the air temperature is the same as the temperature of your skin (about 30 degrees Celcius), 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 71.0 kg person’s body produces energy at a rate of about 501 W due to metabolism, 82.0 percent of which is converted to heat. [Recall that the normal internal body temperature is 98.6 degrees Farenheit and the specific heat capacity of the body is 3480 J/(kg*degrees C)]. By how much would the body temperature of the bicyclist increase in an hour if he were unable to get rid of the excess heat?

Compute the energy deposited in the body as heat in that time interval, and divide it by the heat capacity of the body.

The heat deposited is
(0.82)(501 W)(3600 s) = __ Joules

The heat capacity is (71.0 kg)(3480 J/kg C)= __ J/C

226200

To calculate the increase in body temperature of the bicyclist, we need to find the amount of heat energy produced by the body in 1 hour and then determine how much it would increase the body temperature.

1. Find the heat generated by the body in 1 hour:
Energy produced by metabolism = 501 W
Heat produced = 82.0% of energy produced by metabolism

Heat produced in 1 hour = Heat produced x Time
Heat produced in 1 hour = (82.0/100) x 501 W x 60 minutes x 60 seconds

2. Convert the heat produced to joules:
1 Watt = 1 Joule/second
Heat produced in 1 hour = (82.0/100) x 501 W x 60 minutes x 60 seconds

3. Calculate the temperature increase using the specific heat capacity of the body:
Specific heat capacity of the body = 3480 J/(kg*degrees C)
Mass of the person = 71.0 kg

Temperature increase = Heat produced / (Mass x Specific heat capacity)

Plug in the values into the equation:

Temperature increase = [(82.0/100) x 501 W x 60 minutes x 60 seconds] / (71.0 kg x 3480 J/(kg*degrees C))

Solve the equation to find the temperature increase.

To determine the increase in body temperature, we need to calculate the amount of heat produced by the person's body in one hour and then use it to find the change in temperature using the specific heat capacity of the body.

Let's break down the calculations step by step:

Step 1: Calculate the amount of heat produced by the person's body in one hour.
Given:
- Power produced by metabolism = 501 W
- Efficiency of converting energy to heat = 82.0%

We need to calculate the amount of heat produced per hour.

Heat produced per second = Power produced by metabolism * Efficiency
Heat produced per second = 501 W * 0.82

Heat produced per hour = Heat produced per second * 3600 seconds (convert seconds to hours)
Heat produced per hour = (501 W * 0.82) * 3600 s

Step 2: Convert the heat produced into joules (J) using the conversion factor between watts and joules/second.

1 W = 1 J/s

Heat produced per hour (in joules) = Heat produced per hour (in watts) * 3600 J/s
Heat produced per hour (in joules) = (501 W * 0.82) * 3600 J

Step 3: Calculate the change in body temperature using the specific heat capacity.

Given:
- Mass of the person = 71.0 kg
- Specific heat capacity of the body = 3480 J/(kg * degrees C)

Change in temperature = Heat produced per hour (in joules) / (Mass * Specific heat capacity)

Change in temperature = [(501 W * 0.82) * 3600 J] / (71.0 kg * 3480 J/ (kg * degrees C))

Now we can perform the calculation:

Change in temperature ≈ [(501 * 0.82) * 3600] / (71.0 * 3480) degrees C

Calculating this expression will give us the approximate increase in body temperature in degrees Celsius if the excess heat cannot be dissipated.