The differential equation representing simple harmonic motion is
dy dt2 + wy = 0
Substitute y1 = eut, y2 = e-iwt, and y = C1yı+C22 in this equation and check that they all are indeed solutions of this equation.
Answers
Answer:
149 22.4 GAS EXCHANGE
Learning Objectives
By the end of this section, you will be able to:
Compare the composition of atmospheric air and alveolar air
Describe the mechanisms that drive gas exchange
Discuss the importance of sufficient ventilation and perfusion, and how the body adapts when they are insufficient
Discuss the process of external respiration
Describe the process of internal respiration
The purpose of the respiratory system is to perform gas exchange. Pulmonary ventilation provides air to the alveoli for this gas exchange process. At the respiratory membrane, where the alveolar and capillary walls meet, gases move across the membranes, with oxygen entering the bloodstream and carbon dioxide exiting. It is through this mechanism that blood is oxygenated and carbon dioxide, the waste product of cellular respiration, is removed from the body.
GAS EXCHANGE
In order to understand the mechanisms of gas exchange in the lung, it is important to understand the underlying principles of gases and their behavior. In addition to Boyle’s law, several other gas laws help to describe the behavior of gases.
GAS LAWS AND AIR COMPOSITION
Gas molecules exert force on the surfaces with which they are in contact; this force is called pressure. In natural systems, gases are normally present as a mixture of different types of molecules. For example, the atmosphere consists of oxygen, nitrogen, carbon dioxide, and other gaseous molecules, and this gaseous mixture exerts a certain pressure referred to as atmospheric pressure (Table 2). Partial pressure (Px) is the pressure of a single type of gas in a mixture of gases. For example, in the atmosphere, oxygen exerts a partial pressure, and nitrogen exerts another partial pressure, independent of the partial pressure of oxygen (Figure 1). Total pressure is the sum of all the partial pressures of a gaseous mixture. Dalton’s law describes the behavior of nonreactive gases in a gaseous mixture and states that a specific gas type in a mixture exerts its own pressure; thus, the total pressure exerted by a mixture of gases is the sum of the partial pressures of the gases in the mixture.
Partial Pressures of Atmospheric Gases (Table 2)
Gas Percent of total composition Partial pressure
(mm Hg)
Nitrogen (N2) 78.6 597.4
Oxygen (O2) 20.9 158.8
Water (H2O) 0.04 3.0
Carbon dioxide (CO2) 0.004 0.3
Others 0.0006 0.5
Total composition/total atmospheric pressure 100% 760.0
The left panel of this figure shows a canister of oxygen. The middle panel shows a canister of nitrogen. The right panel shows a canister containing a mixture of oxygen and nitrogen. A pressure gauge on each container shows the pressure exerted by the gas in that container.
Figure 1. Partial and Total Pressures of a Gas. Partial pressure is the force exerted by a gas. The sum of the partial pressures of all the gases in a mixture equals the total pressure.
Partial pressure is extremely important in predicting the movement of gases. Recall that gases tend to equalize their pressure in two regions that are connected. A gas will move from an area where its partial pressure is higher to an area where its partial pressure is lower. In addition, the greater the partial pressure difference between the two areas, the more rapid is the movement of gases.
SOLUBILITY OF GASES IN LIQUIDS
Henry’s law describes the behavior of gases when they come into contact with a liquid, such as blood. Henry’s law states that the concentration of gas in a liquid is directly proportional to the solubility and partial pressure of that gas. The greater the partial pressure of
The differential equation of linear S.H.M. is d²x/dt² + (k/m)x = 0 where d²x/dt² is the acceleration of the particle, x is the displacement of the particle, m is the mass of the particle and k is the force constant. ... The negative sign indicated that acceleration and displacement are in opposite direction of each other.