Question

A typical human has a mass of 70 kg and produces about 2000 kcal of metabolic heat per day. Find the rate of heat production in watts and in calories per hour. If none of the metabolic heat were lost, and assuming that the specific heat of the human body is 1.0 cal/g·°C, find the rate at which the body temperature would rise (°C per hour).

Answer 1

m = 70 kg

Q = 2000 kcal per day

a) rate of heat production in Watts (J/s)

Q = total heat / time

1 kcal = 4.184 kJ = 4184 J

total heat = 2000 kcal = 2000*4.184 = 8368 kJ = 8368000 J

time in seconds = 1 day = 24 hours = 24*3600 = 86400 seconds

then

Q = 8368000 /86400 = 96.851 J/s or 96.851 Watts

b) in Cal per hour

1 kcal = 1000 calories

then

1 day = 24 h so

2000/24 = 83.33 kcalories per hour

83.33*1000 calories per hour

Q = 83330 cal/h

c) rate if T increased

Assume C = 1 cal /gC

°C per hour

Q = m*Cp*dT (basis 1 hour)

m = 70 kg = 70000 g

Cp = 1 cal/gC = 4.184 J/gC

96.851 J/s * 3600 s/h = 70000*4.184*dT

96.851 *3600/(70000*4.184*) = dT

dT = 1.190465 °C per hour