On a winter camping trip in the Adirondack Mountains, you and your friends stumb
ID: 1623932 • Letter: O
Question
On a winter camping trip in the Adirondack Mountains, you and your friends stumble across a denning black bear that weighs 350 kg. Just for fun, you measure the bear's body temperature and find that it is 5°C. Before you disturb the bear further, you decide to calculate how long it would take the bear to warm up to normal body temperature, which is 37°C. Luckily, one of your studious friends has brought their physiology textbook for some light campfire reading and finds out that denning bears have a rate of heat production equal to 1930 Joules/sec (or WATTS) and this heat is available for heat storage. Fortunate for all of you, your forward-thinking friend has also brought a copy of the Heat Budget Equations from class, an essential tool for thermal physiology! Using that rate of heat production and the specific heat capacity of tissue, calculate how long it will take the bear to warm up from 5to 37°C.Explanation / Answer
heat capacity of the tissue C = 3.473 J/C deg /gm
rate of heat production = 1930 J/s
intial temp of the bear T1= 5 deg C
final temp T2 = 37 degC
mass of the bear = 350 kg
heat required to raise the temp Q = (37 -5) 350.0e+3*3.473 = 3.89e+7 J
time to reach the temp t = 3.89e+7 /1930 = 20,154 s