Work and energy

Energy, work and power of the body Chapter 2:

For basal conditions there are about:
25% of body s energy used by skeletal muscles and heart,
19% used by the brain,
10% used by the kidneys,
27% used by liver, spleen.
The body uses food energy to operate its various organs, maintain constant body temperature and do external work, small percentage 5% of food energy excreted in the feces and urine, any energy left over is stored as body fat.

Conservation of energy in the human body

A thermodynamic system exchange energy with its surroundings by mean of heat and work. When heat is added to the system and work is done by it, both Q, W are positive, when heat is transferred out of the system and work is done on it Q,W are both negative.
The energy of human body is controlled by the first law of thermodynamics for a closed system.



?U: changed in the stored energy
?Q: heat lost or gained
?W: work done by the body.
Its important to determine the rates for the energy changes in a small time ?t:



Where ?U/?t: Catabolic rate
?Q/?t: Heat loss or absorption rate
?W/?t: Mechanical power


Basal Metabolic Rate (BMR):
The amount of energy needed to perform a minimal body function (breathing, pumping blood through the arteries under resting conditions). BMR depends on thyroid function. A person of an overactive thyroid has a higher BMR than with normal thyroid function.
Since the energy used for metabolism becomes heat and dissipated from the skin so it related to surface area or the mass of the body.



104

103

102

101

101 102 103

This figure shows a plot of BMR for various animals of different weights.
BMR depends on the temperature of the body, if a patient has a temp. 39° C or 2 above normal, BMR is about 20 % greater than normal.
Work and Power
Chemical energy stored in the body is converted into external mechanical work as well as in life-preserving functions.
Power P=?W/?t = F?x/?t = F V
When a man is climbing a hill or walking up stair we calculate the work done by multiplying a person s weight (m g) by vertical distance (h).
When a man walking at a constant speed on a level surface the force act in the direction perpendicular to his motion, thus external work done by him appears to be zero. However, his muscles are done as internal work which appear as heat and causes a rise in muscle temp.



The Heat losses from the body
Human body core temperature is constantly around 37.1 ± 1.0 C. The hypothalamus of the brain contains the body thermostat to keep the temp. close to the normal value. The mechanism of heat losses are:

If the core temp. rises, the hypothalamus initiates sweating and vasodilatation which increases skin temp. If the skin temp. drops, the thermo-receptors on the skin inform hypothalamus and it initiate shivering, which causes an increase in the core temp.

The difference between energy radiated by the body and the energy absorbed from surrounding can be calculated by:



Hr energy loss or gain
Ar surface area of emitting radiation
e emissivity of surface
TS skin temp.
Tw surrounding temp.
Kr constant= 5 kcal/m2hr.°C

The heat loss due to convection Hc is:


KC const. depend on the movement of air
AC surface area
Ta air temp.
Example: When the wind const. =2.3 Kcal/m3 hr.C, Ta=25 °C, TS=34°C, AC=1.2m2 what is the heat loses by convection?
When the air is moving, the constant Kc increase, according to the equation:




Where V is the wind speed in m/sec.


40

30

20

10 wind speed
2 3 10 15 20
Home works
1. Calculate the convective heat loss per hour for a person standing in a 5 m/Sec wind. Assume TS=33°, Ta=10°, AC=1.2 m2. If wind speed 2.23 m/Sec find the still air temperature that would produce the same heat loss. Hint kc=27. 8

2. A 70 kg hiker climbed a mountain 1000 m high, he reached the peak in 3 hours, calculate the external work done and power generated?
3. Someone with body surface area of 0.9m2, Ts=32C receive radiation from the sun at the rate of 30 kcal/hr the temperature of the surrounding is 30 C, Find the net energy gained by radiation?