Question

Suppose an adult is encased in a thermally insulating barrier so that all the heat evolved by metabolism of foodstuffs is retained by the body. what is her temperature increase after 2.5 hours? assume the heat capacity of the body is 4.18 j g–1k–1 and that the heat produced by metabolism is 9.4 kj kg–1hr–1.

Answer 1

Given:
Q = 9.4 kJ/(kg-h), the heat production rate
c = 4.18 J/(g-K), the heat capacity
t = 2.5 h, amount of time

Note that
c = 4.18 J/(g-K) = 4180 J/(kg-K) = 4.18 kJ/kg-K)

Consider 1 kg of mass.
Then
Qt = cΔT
where ΔT is the increase in temperature (°K)
(1 kg)*(9.4 kJ/(kg-h))*(2.5 h) = (1 kg)*(4.18 kJ/(kg-K))*(ΔT K)
23.5 = 4.18 ΔT
ΔT = 23.5/4.18 = 5.622 K = 5.622 °C

Answer: 5.62 K (or 5.62 °C)