Question

Assume the weight of an average adult is 70. kg, and that 420. kJ of heat are evolved per mole of oxygen consumed as a result of the oxidation of foodstuffs, knowing that the number of moles of O2 inhaled per minutes are 0.02 mol/min. Suppose an adult body were encased in a thermally insulating barrier. If as a result of this barrier all the heat evolved by metabolism of foodstuffs were retained by the body, what would the temperature of the body reach after 3 hours? Assume the specific heat capacity of the body is 4.18 J /g K.

Answer 1

SOLUTION:

CONCEPT: First calculate the total heat evolved, in next step calculate the rise in temperature.

Time = 3 hr = 3 X 60 = 180 min

Oxygen inhaled in 1 min = 0.02mol

Therefore oxygen inhaled in 180 min = 0.02 X 180 = 3.6 mol

When one mole of O2 is inhaled 420KJ

Therefore energy released when 3.6 mol of O2 is inhaled = 3.6 X 420 = 1512KJ = 1512 X 10³J

Then Increase in Temperature can be had as:

Q = m X C X ΔT ====1)

Q = heat supplied , m = mass of adult, C = heat capacity of the body = 4.18J/gK = 4.18 X 10³ J/Kg K

ΔT = change in temperature = T2 - T1

T1 = initial temperature = 37^oC = 310K, T2 = ?

Using values in eqn 1)

1512 X 10³J = 70 Kg X 4.18 X 10³ J/Kg  K X (T2 - 310)

(T2 - 310) = 1512 X 10³J /  70 Kg X 4.18 X 10³ J/Kg K = 5.17

T2 = 310 + 5.17 = 315.17K

In degree celcius T2 = 315.17 - 273 = 42.17^oC