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Human Physiology an Integrated Approach

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Human Physiology an Integrated Approach Appendix Physics and Math Richard D. Hill and Daniel Biller B University of Texas Introduction Using these fundamental units of measure, we can now es- tablish standard units for physical concepts ( Tbl. B.1 ). Although This appendix discusses selected aspects of biophysics, the these are the standard units for these concepts at this time, they are study of physics as it applies to biological systems. Because liv- not the only units ever used to describe them. For instance, force ing systems are in a continual exchange of force and energy, it is can also be measured in dynes, energy can be measured in calories, necessary to define these important concepts. According to the pressure can be measured in torr or mm Hg, and power can be mea- seventeenth-century scientist Sir Isaac Newton, a body at rest sured in horsepower. However, all of these units can be converted tends to stay at rest, and a body in motion tends to continue mov- into a standard unit counterpart, and vice versa. ing in a straight line unless the body is acted upon by some force The remainder of this appendix discusses some biologically (Newton’s First Law). relevant applications of physical concepts. This discussion in- Newton further defined force as an influence, measurable in cludes topics such as bioelectrical principles, osmotic principles, both intensity and direction, that operates on a body in such a and behaviors of gases and liquids relevant to living organisms. manner as to produce an alteration of its state of rest or motion. Put another way, force gives energy to a quantity, or mass, thereby Bioelectrical Principles enabling it to do work. In general, a driving force multiplied by a quantity yields energy, or work. For example: Living systems are composed of different molecules, many of which exist in a charged state. Cells are filled with charged par- = force * distance work ticles such as proteins and organic acids, and ions are in continual Energy exists in two general forms: kinetic energy and potential flux across the cell membrane. Therefore, electrical forces are im- energy. Kinetic energy { kinein, to move} is the energy possessed portant to life. by a mass in motion. Potential energy is energy possessed by a When molecules gain or lose electrons, they develop posi- mass because of its position. Kinetic energy ( KE ) is equal to one- tive or negative charges. A basic principle of electricity is that op- half the mass (m ) of a body in motion multiplied by the square of posite charges attract and like charges repel. A force must act on the velocity (v ) of the body: a charged particle (a mass) to bring about changes in its position. KE = 1∕2 mv2 Potential energy (PE ) is equal to the mass (m ) of a body multiplied by acceleration due to gravity ( g ) times the height ( h ) Standard Units for Table B-1 of the body above the earth’s surface: Physical Concepts PE = mgh where g = 10 m s2 > Mathematical Both kinetic and potential energy are measured in joules. Measured Standard (SI*) Derivation/ Concept Unit Definition Force Newton (N) 1 N = 1 kg # m s2 Basic Units of Measurement > For physical concepts to be useful in scientific endeavors, they Energy/Work/ Joule (J) 1 J = 1 N # m must be measurable and should be expressed in standard units Heat of measurement. Some fundamental units of measure include the following: Power Watt (W) 1 W = 1 J s > Length ( l ): Length is measured in meters (m). = # Time ( t ): Time is measured in seconds (s). Electrical Coulomb (C) 1 C 1 A s Mass ( m ): Mass is measured in kilograms (kg), and is defined as charge the weight of a body in a gravitational field. Potential Volt (V) 1 V = 1 J C Temperature ( T ): Absolute temperature is measured on the > Kelvin (K) scale, Resistance Ohm (⍀) 1 Æ = 1 V A where K = degrees Celsius (ЊC) + 273.15 > and ЊC = degrees Fahrenheit - 32 1.8 Capacitance Farad (F) 1 F = 1 C V 1 2> > Electric current ( I ): Electric current is measured in amperes (A). Pressure Pascal (Pa) 1 Pa = 1 N m2 Amount of substance ( n ): The amount of a substance is mea- > sured in moles (mol). * SI = Système International d’Unités 944 Appendix B Physics and Math Therefore, there must be a force acting on charged particles Faraday constant (F) is an expression of the electrical charge car- to cause attraction or repulsion, and this electrical force can be ried by one mole of electrons and is equal to 96,485 coulombs/ measured. mole. Electrical force increases as the strength (number) of charges The amount of current that flows depends on the nature of increases, and it decreases as the distance between the charges in- the material between the charges. If a material hinders electron creases ( Fig. B.1 ). This observation has been called Coulomb’s flow, then it is said to offer resistance (R), measured in ohms. law , and can be written: Current is inversely proportional to resistance, such that current decreases as resistance increases. If a material offers high resis- F = q q ed2 1 2> tance to electron flow, then that material is called an insulator. If where q1 a n d q2 are the electrical charges (coulombs), d is the dis- resistance is low, and current flows relatively freely, then the ma- tance between the charges (meters), e is the dielectric constant, terial is called a conductor. Current, voltage, and resistance are and F is the force of attraction or repulsion, depending on the related by Ohm’s law, which states: type of charge on the particles. V = IR When opposite charges are separated, a force acts over a distance to draw them together. As the charges move together, w h e r e V = potential difference in volts work is being done by the charged particles and energy is being I = current in amperes released. Conversely, to separate the united charges, energy must R = resistance in ohms be added and work done. If charges are separated and kept apart, In biological systems, pure water is not a good conductor, but wa- they have the potential to do work. This electrical potential is ter containing dissolved NaCl is a good conductor because ions called voltage. Voltage is measured in volts (V). provide charges to carry the current. In biological membranes, If electrical charges are separated and there is a potential dif- the lipids have few or no charged groups, so they offer high resis- ference between them, then the force between the charges allows tance to current flow across them. Thus, different cells can have electrons to flow. Electron flow is called an electric current. The different electrical properties depending on their membrane lipid composition and the permeability of their membranes to ions. ELECTRICAL FORCE Osmotic Principles Freezing point, vapor pressure, boiling point, and osmotic pres- If you separate two opposite charges, there will be an electric force between them. sure are properties of solutions collectively called colligative + properties. These properties depend on the number of solute particles present in a solution. Osmotic pressure is the force If you increase the number of charges that are separated, the that drives the diffusion of water across a membrane. Because force increases. there are no solutes in pure water, it has no osmotic pressure. + However, if one adds a solute like NaCl, the greater the concen- + + tration ( c ) of a solute dissolved in water, the greater the osmotic pressure. The osmotic pressure ( p ) varies directly with the con- If you increase the distance between the charges, the force decreases. centration of solute (number of particles ( n ) per volume ( V )): + p = n V RT 1 > 2 p = cRT If charges are d where R is the ideal gas constant 8.3145 joules K # mol a n d T + 1 > 2 separated by some is the absolute temperature in Kelvin. Osmotic pressure can be distance d, they have the potential to do work. measured by determining the mechanical pressure that must be This electrical potential is applied to a solution so that osmosis ceases. called voltage. Water balance in the body is under the control of osmotic pressure gradients (concentration gradients). Most cell mem- If separated charges are allowed to move together, they do work branes allow water to pass freely, primarily through open chan- and energy is released. The + Work = force X distance nels. To control the movement of water, the body either removes amount of work done depends these channels from the membrane or control solute movement on the number of particles and that creates concentration gradients. the distance between them. To separate the charged Relevant Behaviors of Gases and Liquids particles, energy must be put into the The respiratory and circulatory systems of the human body obey system and work + the physical laws that govern the behavior of gases and liquids. is done. This section discusses some of the important laws that govern Fig. B-1 these behaviors and how our body systems utilize these laws. 945 Appendix B Physics and Math Gases This equation is read as “pH is equal to the negative log of the The ideal gas law states: hydrogen ion concentration.” But what is a logarithm? A logarithm is the exponent to which you would have to PV = nRT raise the base (10) to get the number in which you are interested. For example, to get the number 100, you would have to square the w h e r e P = pressure of gases in the system base (10): V = volume of the system n = number of moles in gas 102 = 100 T = temperature The base 10 was raised to the second power; therefore, the log of R = ideal gas constant (8.3145 J/K mol) 100 is 2: If n and T are kept constant for all pressures and volumes in a sys- = tem of gases, then any two pressures and volumes in that system log 100 2 are related by Boyle’s Law, Some other simple examples include: = P1V1 P2V2 1 01 = 10 The log of 10 is 1.
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