Problem 48. Your body must dissipate energy from metabolism at a rate of about 1
ID: 1659293 • Letter: P
Question
Problem 48. Your body must dissipate energy from metabolism at a rate of about 100 W by various mecha- nisms to keep the body from overheating. Suppose these mechanisms stopped working (perhaps you are wrapped in a very good thermal blanket, so no heat can flow from or to your body). At what rate will your body temperature in crease? How long will it take for your body temperature to increase by 5 °C? Assume you have a mass of 70 kg, and the specific heat of your body tissue is the same as of water 4 200 J K- kg 1Explanation / Answer
given that dQ/dt = 100 W
then but dQ = m*S*dT
m is the mass of the body
S is the specific heat capacity of the body
dT is the change in temperature
(m*S*dT)/dt = 100
(70*4200*dT)/dt = 100
dT/dt = 100/(70*4200) = 3.4*10^-4 deg C/sec
time taken to increase temerature by 5 deg C is t
(70*4200*5)/dt = 100
dt = (70*4200*5)/100 = 14700 sec = 14700/60 = 245 mins = 4.1 hours