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Kinetic Theory of Gases

Brownian Motions. — The simplest and most direct evidence for the existence of molecules was first noted by an English botanist by the name of Brown. With a microscope he observed very fine particles held in suspension in water and noted that these fine particles are con­stantly in motion. The smaller the particles the more freely do they move. The motion of these particles is caused by the incessant bombardment of the molecules of the water or other liquid in which they are suspended. This bombardment of the water molecules is not the same on the different sides of the particles. Hence they are driv­en hither and thither. An approximate picture of the behavior of such small particles is obtained by projecting on a screen the shadows of finely divided glass particles that are set in motion by rapidly boiling mercury.

Perrin and others who have made careful studies of these motions have found that the distribution of these particles, their velocities, and their mean free paths are precisely what should be expected from the kinetic theory of gases. From these observations it is possible to de­termine the number of molecules in 1 cu cm of a gas under standard conditions. The fact that the number of molecules per cubic centimeter in a gas as determined in this way is in good agreement with the number derived from the methods involving the kinetic theory of gas­es shows that the motion of these particles obeys the same general laws as the motion of molecules.

Basic Assumptions. — To explain the physical properties of gases, three basic assumptions are necessary:

1. The molecules of a gas are extremely small, perfectly elastic spheres. This assumption implies that when molecules of gas collide with other molecules or with the walls of the containing vessel, the total kinetic energy of the molecules is not diminished in any way.

2. The molecules move with changing velocities through the space occupied by the gas. Between collisions, their paths are straight lines. This assumption implies that the forces acting on the molecules are neg­ligible except at collision.

3. The time occupied in a collision between two molecules or in a collision of a molecule with the wall is small compared with the time between collisions. This assumption implies that a collision is nearly instantaneous.

Specific Heats of Gases. — The specific heat of a gas depends on whether the gas is heated at constant volume or at constant pressure. These two specific heats are known as specific heat at constant pres­sure and specific heat at constant volume.

Specific Heat at Constant Volume.—When heat is supplied to a gas in which the volume is kept constant, the pressure increases, and all the energy which is supplied to the gas is used to increase the kinetic energy of the molecules. There is no external work done by the gas. When the temperature of 1 g of the gas is raised through l°C, the gas will absorb C_v units of heat, and this quantity of heat is its specific heat at constant volume.

Specific Heat at Constant Pressure. — In heating a gas 1 °C, at constant pressure the heat required to increase the speed of the molecules will be the same as it was in case the gas was heated an equal amount at constant volume. In addition to this heat, it is necessary to supply a certain amount of heat to do external work while the gas is expanding. For example, if the gas is expanding in a cylinder closed by a moving piston, the molecules after colliding with the piston will rebound with less energy than that with which they reached the piston. Additional energy must be supplied to make up this decrease. Consequently, the specific heat at constant pressure must exceed the specific heat at constant volume by an amount which is just equal to the thermal equivalent of the work which is done when unit mass of gas is heated through 1 °C at constant pressure.

The ratio of the specific heat of a gas at constant pressure C_p to the specific heat at constant volume C_v is

C_p / = 1.41 for air

–– /

k = C_v /= 1.66 for mercury vapor [2, С. 74 - 75].

2.9.9 Read the text “Properties of Gases”, translate it and choose the best ending to the sentences:

a) Study of air properties…

· is of great importance because of its components: oxygen and nitrogen;

· has the same value for gases study as that of water properties for liquids study;

b) We can find the weight of the air removed from the sphere…

· by using an air pump and the stopcock and counting the difference between two weights before and after pumping out the air;

· by using an air pump at the tem­perature of melting ice and counting the difference between two weights at different tem­peratures;

c) Due to the compressibility of gases…

· it is not so difficult to change the volume of the air-filled object;

· the volume of the air-filled object increases very little;

d) According to Boyle's law the volume of the mass of gas …

· depends on the pressure exerted on it;

· is proportional to the pressure exerted on it.

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