Question

In very cold weather, a significant mechanism for heat loss by the human body is energy expended in warming the air taken into the lungs with each breath. A) On a cold winter day when the temperature is -19.0 C, what is the amount of heat needed to warm to internal body temperature (37 C ) the 0.470 J (Kg *K) of air exchanged with each breath? Assume that the specific heat capacity of air is 1020 and that 1.0 L of air has a mass of 1.3 g . B) How much heat is lost per hour if the respiration rate is 21.0 breaths per minute?

Answer 1

Answer:

A) $Q_a=74256\ J$

B) $Q=93562560\ J$

Explanation:

Given:

• temperature of air, $T_a=-19+273=254\ K$

• temperature of lungs, $T_l=37+273=310\ K$

• specific Heat exchanged from the lungs , $c_l=0.47\ J.kg^{-1}.K^{-1}$

• specific heat of air, $c_a=1020\ J.kg^{-1}.K^{-1}$

• mass of 1 L air, $m'=1.3\ kg$

• breath rate, $b=21\ breath.min^{-1}$

A)

Now,

amount of heat needed to warm the air of lungs to the body temperature:

$Q_a=m'.c_a.\Delta T$

$Q_a=1.3\times1020\times (310-254)$

$Q_a=74256\ J$

B)

Amount of heat lost per hour:

No. of breaths per hour:

$B=b.60$

$B=21\times 60$

$B=1260$

Now the total loss of energy in 1 hr.:

$Q=Q_a.B$

$Q=74256\times 1260$

$Q=93562560\ J$