Biophysics: Transformation of Energy and Thermodynamics in the Human Body

Transformation of Energy in the Human Living Body

Heat and Transfer of Heat

Heat is a fundamental form of energy in biological systems, transferred from regions of higher temperature to regions of lower temperature. In the human body, heat can be transformed into work and is essential for maintaining physiological functions.

• Definition of Heat: Energy transferred from a hotter body to a colder body.

• Heat as Energy: Heat may be transformed into work, making it a form of energy.

Kinetic Theory

The kinetic theory explains the behavior of matter based on the motion of its constituent particles. This theory is crucial for understanding thermal properties and energy transfer in biological systems.

• Atoms and Molecules: Matter is composed of atoms and molecules in continuous chaotic motion.

• States of Matter:

  • Gas: Atoms/molecules move randomly and collide with each other and the container walls.

  • Solid: Atoms are bound together and vibrate randomly around average positions.

  • Liquid: Intermediate behavior between solids and gases.

• Kinetic Energy: Moving particles possess kinetic energy.

• Internal Energy: The sum of kinetic energies of all particles; also called thermal motion.

• Temperature: Quantitative measure of hotness; proportional to the internal energy of matter.

Equations:

• Average kinetic energy of a molecule gas: $\frac{1}{2}mv^2 = \frac{3}{2}kT$ where $k = 1.38 \times 10^{-23} \text{J/mol·K}$

• Relationship between pressure, volume, and temperature: $PV = NkT$ where $N$ is the total number of gas molecules.

Specific Heat and Latent Heat

Specific heat and latent heat are important for understanding how substances absorb and release energy.

• Specific Heat: Quantity of heat required to raise the temperature of 1 g of a substance by 1 degree.

• Latent Heat: Energy required to convert a solid to a liquid or a liquid to a gas.

• Units: $J/gK$, $cal/gK$ (1 cal = 4.184 J)

Substance	Specific heat (cal/g°C)
Water	1.0
Ice	0.490
Average for human body	0.83
Aluminum	0.214
Protein	0.4

Transfer of Heat

Heat can be transferred by four main mechanisms: conduction, convection, radiation, and diffusion.

• Conduction: Transfer of heat through a solid material.

• Convection: Transfer of heat in fluids (liquids and gases) via movement of the fluid itself.

• Radiation: Transfer of energy by electromagnetic waves.

• Diffusion: Movement of particles from regions of high concentration to low concentration.

Conduction

Conduction is the process by which heat is transferred through a material without the movement of the material itself.

• Equation: $H_c = \frac{K_c A}{L}(T_1 - T_2)$ where $A$ is the area perpendicular to heat flux, $L$ is the length, $T_1 - T_2$ is the temperature difference, and $K_c$ is the thermal conductivity coefficient.

Convection

Convection occurs in fluids, where heated molecules move away from the heat source, causing energy transfer.

• Equation: $H_c' = K_c' A (T_1 - T_2)$ where $A$ is the area exposed to convective currents, $T_1 - T_2$ is the temperature difference, and $K_c'$ is the convection coefficient.

Radiation

Thermal radiation is the emission of electromagnetic waves due to the vibration of charged particles within matter.

• Equation: $H_r = K_r A_r \epsilon (T_s - T_r)$ where $A_r$ is the radiative surface area, $T_s$ and $T_r$ are skin and radiative surface temperatures, $K_r$ is the radiation coefficient, and $\epsilon$ is emissivity.

Diffusion

Diffusion is the process by which molecules move from regions of high concentration to regions of low concentration.

• Equation for average distance after N collisions: $S = L \sqrt{N}$

• Total distance traveled: $Total\,distance = N L = \frac{S^2}{L}$

• Time required: $t = \frac{S^2}{L v}$

• Example (in water): For $L = 10^{-8}$ cm, $v = 10^4$ cm/s, time to diffuse 1 cm: $t = \frac{1^2}{10^{-8} \times 10^4} = 10^4 s = 2.8 h$

Diffusion through Membranes

In biological systems, diffusion through membranes is essential for the transport of oxygen, nutrients, and waste products. The rate depends on pore size and the properties of the diffusing molecules.

Diffusion and Contact Lenses

Oxygen diffuses to the cornea from the tear fluid. Contact lenses can impede this process, especially during sleep, leading to reduced oxygen supply and loss of corneal transparency.

Thermodynamics

First Law of Thermodynamics

The first law of thermodynamics states that energy, including heat, is conserved. Energy can be converted from one form to another, but the total amount remains constant.

• Energy Conservation: $\Delta E = Q - W$ (where $Q$ is heat added, $W$ is work done by the system)

• Application in Living Systems: For constant internal temperature and weight, energy intake must equal work done plus heat lost.

Energy Balance in Living Systems

Animals maintain energy balance by consuming food (chemical energy), performing work, and rejecting excess heat through various cooling mechanisms.

• Internal Thermal Energy ($E_t$) and Chemical Energy ($E_c$) are stored in the body.

• Imbalance between intake and output energy changes the sum $E_t + E_c$.

Second Law of Thermodynamics

The second law of thermodynamics states that spontaneous changes in a system proceed from arrangements of lesser probability to greater probability, i.e., towards increased entropy.

• Entropy: Measure of disorder; systems evolve towards higher entropy.

Difference Between Heat and Other Forms of Energy

Heat and work are both forms of energy, but differ in their nature and conversion efficiency.

• Work: Ordered motion of particles.

• Heat: Random motion of particles.

• Complete conversion of heat to work is impossible due to the random nature of heat (Second Law).

• Maximum ratio of work: $\frac{Work}{Heat_{input}} = 1 - \frac{T_2}{T_1}$ where $T_1$ is the higher temperature, $T_2$ is the lower temperature.

Energy Required by People

Metabolic Rate

All living systems require energy to function. The metabolic rate is the rate at which energy is consumed per unit surface area of the body.

• Basal Metabolic Rate: Energy consumption at rest.

• Equation for surface area: $Area = 0.202 \times M^{0.425} \times H^{0.725}$ where $M$ is mass in kg, $H$ is height in m.

• For a 70-kg man of height 1.55 m, surface area ≈ 1.70 $m^2$.

• Metabolic rate at rest: $40 \text{Cal}/m^2\cdot hr \times 1.70 m^2 = 68 \text{Cal}/hr \approx 70 \text{Cal}/hr$

Activity	Metabolic rate (Cal/m2/hr)
Sleeping	35
Lying awake	40
Sitting upright	50
Standing	60
Walking (3 mph)	140
Moderate physical work	150
Bicycling	250
Running	600
Showering	250

Basal Metabolic Rate and Body Size

Basal metabolic rate is proportional to body mass to the 3/4 power ($M^{3/4}$).

Energy from Foods

Energy is obtained from the oxidation of glucose and other nutrients.

• Glucose Oxidation: $C_6H_{12}O_6 + 6O_2 \rightarrow 6CO_2 + 6H_2O + Energy$ A gram of glucose releases 3.81 Cal of energy.

Activity	Energy expenditure (Cal/day)
8 hr sleeping (35 Cal/m2/hr)	280
8 hr moderate physical labor (150 Cal/m2/hr)	1200
4 hr reading, writing, TV watching (50 Cal/m2/hr)	340
1 hr heavy exercise (300 Cal/m2/hr)	300
3 hr dressing, eating (100 Cal/m2/hr)	300
Total expenditure	2120

Food	Total weight (g)	Protein (g)	Carbohydrate (g)	Fat (g)	Total energy (Cal)
Whole milk, 1 quart	950	32	48	32	650
Egg, 1	55	6	1	5	80
Hamburger, 1	85	21	0	22	290
Carrot, 1 cup	130	1	12	0	50
Apple, medium	130	1	22	0	100
Bread, 1 slice	33	1	7	1	75

Regulation of Body Temperature

Homeostasis of Body Temperature

Humans and other animals must maintain their body temperature at a nearly constant level (37°C). Deviations can cause protein damage or heart stoppage.

• High Temperature: > 44–45°C damages protein structures.

• Low Temperature: < 28°C can cause heart stoppage.

Heat Production and Loss

During physical activity, most energy consumed is converted to heat, which must be transferred from the body to the environment.

• 20% of energy is external work; 80% is converted to heat inside the body.

• Heat is conducted to the skin and then lost to the environment.

Heat Transfer Mechanisms in the Body

• Conduction: Through tissues; limited capacity.

• Circulatory System: Transports heat from the interior to the skin.

• Convection, Radiation, and Evaporation: Remove heat from the skin surface.

Equation for conductive heat flow: $H = \frac{K_c A \Delta T}{L}$ Example: For $K_c = 18$, $A = 1.5$, $\Delta T = 2$, $L = 3$, $H = 18 \text{Cal}/hr$

Control of Skin Temperature

For effective heat loss, skin temperature must be lower than internal body temperature. Heat is removed by convection, radiation, and evaporation.

• Convection: $H_c' = K_c' A_c (T_s - T_a)$

• Radiation: $H_r = K_r A_r \epsilon (T_s - T_r)$

• Evaporation: Major cooling mechanism in warm climates.

Radiative Heating by the Sun

Solar radiation contributes to body heating. The intensity at the top of the atmosphere is about 1150 Cal/m2/hr. Skin color and clothing affect absorption.

• Dark skin absorbs ~80%, light skin ~60% of solar radiation.

• Light-colored clothing decreases radiative heating by ~40%.

Evaporation

Evaporation of sweat is a major cooling mechanism, especially when convection and radiation are insufficient.

Resistance to Cold

The body increases heat outflow in cold conditions, influenced by temperature, wind velocity, and humidity. Wind increases heat loss; the body responds by decreasing heat outflow and increasing heat production.

• A mild wind at 30 cm/sec is equivalent to a temperature drop of more than 5°C.