医学物理学第九周周三物理のchapter6a3

1、Chapter 6 The surface phenomenon of liquidApplications to life scienceSphere (球体), spherical (球形的)，boundary, borderCurvature radius (曲率半径)metal frame (金属架)，convex (凸起的), concave (凹入的)contact angle (接触角), lotus leaf ()Capillary （毛细管）, capillarity (毛细管现象)embolism (栓塞), cohesion 聚合力force of adherence 附

2、着力, transfuse (输血)vein (静脉), syringe (注射器)Macro-objects (宏观物体), microstructure (微观结构)gravitational and repulsive (引力的与斥力的)isotropic (各向同性的), anisotropic Boundary (边界的)，border , edge Pellicle (薄膜) film, tensional pellicle Alveolus , alveoli /lvilai/ n 肺泡6.1 The micro-structure of matterMacro-objects

3、consist of a great number of molecules or atoms. These particles also have physical quantities such as size, mass, velocity and energy. The molecules or atoms in macro objects are permanently and irregularly in motion. Such a motion which contains a large number of molecules or atoms is called therm

4、al motion. States of substances: Gas, liquid and solid Liquid and solid are called condensed matter as they are hardly compressible. Interaction between molecules: gravitational forcerepulsive force What is the relation between them? In what distance does the gravitation dominate the system and in w

5、hat distance the repulsive force controls the system?r0r0rrFEp00The gravitational and repulsive force among molecules is totally called Molecular Force. According to experiments, the molecular force can be expressed asGravitational & elastic potential where C1, C2, m and n are constants. As m and n

6、are quite big and m n , the molecular force is a short-distance force. r0 10-10 m. When r r0(r is between 10-10 10-8 m), molecules have gravitation. r0r0rrFEp00The above formula is semi-experienced one and the four parameters in this formula are determined by experiments. The positive term express r

7、epulsion with m between 915, and the negative term denotes gravitation with n between 47. r0r0rrFEp00Potential Energy and its Force Gravitational potential energyElastic potential energy6.2 Thermal properties of matterIdeal gas law The pressure of gas can be changed in several ways. (1). One way to

8、increase the pressure of a gas confined in a fixed volume is to increase the number of gas molecules in the volume. (pumping air into bicycle tires or balls)(2). To change the gas pressure need to change its temperature. (tires at summer).(3) A third way to change the gas pressure is to change the v

9、olume containing the gas; decreasing the volume causes an increase in pressure. For low density gases, there is a simple, universal relationship between gas pressure P, volume V, Kelvin temperature T and other constants, which gives as follows: Equation of state for ideal gasesWhere R = 8.314 Jmol K

10、-1, it is the universal gas constant or mole gas constant. is the mass of one mole molecules (its no. is NA called Avogadro constant = 6.02 1023) and M is the mass of gas in container with unit of kg, V is the volume of the container with units of m3, P is the pressure with units of N m-2. (dimensio

11、ns of PV?)2. The model of the ideal gas(1). The size of molecules can be ignored comparing with the average distance between two molecules,(2). The interaction forces between molecules and the wall of container could be ignored except the right-time of collision,(3). All collisions are elastic,(4).

12、Ignoring the gravity suffered by moleculesExample 6.1 The temperature of an ideal gas after compression.An ideal gas has a volume of 1.0 liter (L), a pressure of 1.0 atm, and a temperature of 27C. The pressure is raised to 2.0 atm, compressing the volume of the gas to 0.6L. Find the final temperatur

13、e of the gas. Solve: write the equations of the initial state and the final state:Substituting the corresponding values into above equations, we have 3. The pressure formula of ideal gasesWhere is the average translational kinetic energy (平均平动能), n is the number of molecules per unit volume, m is th

14、e mass of one molecule and v is the speed of molecule. 4. The energy formula of ideal gasesAs is Avogadro constant.is Boltzmann constant.This equation shows that the temperature of an ideal gas is a measure of the average kinetic energy of its molecules. It is valid to any systems, including liquids

15、 and solids.5. The laws of ideal gases(1). Avogadro lawThis law means that at the same temperature and the same pressure or the same ratio of pressure to temperature, the number of molecules contained in the same volume is the same. And also the pressure is relative to the temperature. (2). Doltan l

16、awSuppose that there are many kinds of molecules in one container and the number of molecules per unit volume are n1, n2, respectively, The average translational kinetic energy are the same for all kinds of molecules as they have the same temperature and this means that Where P1, P2, P3 are the pres

17、sures respectively for that kind of molecules to be present alone in the container. This is called Doltans law of partial pressures. Example 6-2: there is a vacuum tube, at 0C temperature, its degree of vacuum is 1.3310-3 Pa, find the number of molecules per unit volume in the tube and its total ave

18、rage translational kinetic energy. Solve: note that (just hint): And (2)P92(3) Boltzmanns energy distribution lawIn the gravitational field, molecules not only have kinetic energies, but also potential energies. The number of molecules per unit volume is followed by Boltzmanns energy distribution la

19、w: Where n is the number of molecules per unit volume and n0 is the number for Ep =0.As the pressure is proportional to the number of molecules per unit volume (at the iso-temperature layer) and Ep = mgh, we haveTherefore: Where P0 is air pressure at the sea level, P is the pressure at a height of h

20、. Taken by Robert Anderson, 20056.3 Surface tension (张力) and surface energy1. Surface tensionThe surface of a liquid acts as a tensional film. It proves that the surface of liquid has tension. It is called surface tension.How is the surface tension formed?How about its energies? Do the molecules in

21、the surface have the same energy as molecules in the liquid?r0r0rrFEp00repulsive gravitational Only if a molecule is in the sphere of radius of 10-9 m, it can be gravitated by the center of molecule. This sphere is called molecular action sphere. We draw a thin layer on the surface of a liquid. The

22、thickness of the layer is equal to the radius of the molecular action sphere and the layer is called surface layer.At least 10 molecules in the surface layerThe molecules in the surface layer and those in the liquid experience different applied forces. In liquid, the molecules are gravitated by thei

23、r neighbor molecules in all directions and the total force for each molecule is zero, while the molecules in the surface layer have different gravitations in different directions. The direction of total force acting on the molecules in the surface layer is perpendicular to the surface layer, pointing to the inside of the liquid. Generally speaking, the total force points to the inner liquid. Due to the total forces, the surface is in tension. This is the so-called surface tension.A