Biomedical Engineering Reference
In-Depth Information
Besides the evaporative latent heat loss associated with respiration, there is also a sensi-
ble heat loss (when T
o
>
T
i
) or heat gain (when T
o
<
T
i
) that is described by
Q
sl
¼ð
dm
a
=
dt
Þ
C
p
ð
T
o
T
i
Þ
where C
p
is the specific heat. This is the heat loss due to heating up the dry air component
of the inspired air. An example of calculating heat loss follows.
Assume that 6 liters/min of bone-dry air at 20
C is inspired (12 breaths per minute at
500 ml tidal volume per breath
6 liters per minute). Also assume that the expired air is
fully saturated with water vapor (47 mm Hg) and is at 37
C. The physical properties are
C
p
,
air
at 20
C
¼
g
C
¼
0
:
25 cal
=
l at 37
C
g
Vapor pressure of water at 37
C
¼
577 cal
=
¼
47 mm Hg
The dry air mass flow rate in grams per minute can be calculated via the ideal gas law:
273
K
293
K
ð
dm
s
=
dt
Þ¼ð
6 liters
=
min
Þð
1mol
=
22
:
4 liters
Þð
=
Þð
28
:
9g
=
mol
Þ
¼
7
:
2g
=
mol of dry air
The amount of water vapor in the expired air is
ð
dm
w
=
dt
Þ¼ð
7
:
2
=
28
:
9
Þð
47
=
760
47
Þð
18
Þ¼
0
:
295 g
=
min
Note that the true ratio of the partial pressure of water vapor in the lungs is not 47/760 but
rather 47/760 - 47, since the water vapor is attached to the dry gas, which is the remainder
of the partial pressure (713). The molecular weight of water is 18. It is necessary to compute
the moles of water vapor when multiplying by the partial pressure ratio, since the partial
pressures are related to the moles rather than the mass. Multiplying by the molecular
weight returns the calculation back to units of mass.
The latent heat loss is
Q
el
¼
0
:
295
ð
577
Þ¼
170 cal
=
min
The sensible heat loss is
Q
sl
¼
7
:
2
ð
0
:
25
Þð
37
20
Þ¼
30
:
4 cal
=
min
Note that the latent heat loss is far more significant than the sensible heat loss. The total
heat loss of approximately 200 cal/min equals 12.0 kcal/hr, which is 17 percent of the basal
metabolic rate of the body—an appreciable quantity. During exertion, one's respiration
increases, which provides even greater heat loss by this mode. The overall rise in the meta-
bolic heat production rate is also greater, such that an additional heat loss mode is neces-
sary, such as sweating. Evaporation of sweat from the body produces the same latent
heat loss as was evident via respiration. However, if one sweats profusely, such that sweat
rolls off the body, then dehydration may occur, which can be quite dangerous.
An interesting note is that the panting of dogs is the primary mechanism of heat rejec-
tion, since dogs cannot sweat. By interchanging air with the dead space on a rapid basis,
rather than via deep breathing, the dogs avoid hyperventilation yet produce heating of
inspired air as well as humidification. Thus, there is latent and sensible heat loss. Many
dogs have thick coats that provide insulation against heat gain or loss via conduction. Thus,
