《物理双语教学课件》Chapter 12 The Kinetic Theory of Gases 理想气体定律

Chapter 12 The Kinetic Theory of Gases

Classical thermodynamics has nothing to say about atoms or molecules. Its laws are concerned only with such macroscopic variables as pressure, volume, and temperature. However, we know that gas is made up of atoms or molecules (groups of atoms bound together). The pressure exerted by a gas must surely be related to steady drumbeat of its molecules on the walls of its container. The ability of a gas to take on the volume of its container must surely be due to the freedom of motion of its molecules. And the temperature and internal energy of a gas must surely be related to the kinetic energy of these molecules. Perhaps we can learn something about gases by approaching the subject from this direction. We call this molecular approach the kinetic theory of gases.

12.1 Ideal Gases

1、Our goal in this chapter is to explain the macroscopic properties of a gas, such as its pressure and its temperature, in terms of the behavior of the molecules that make it up.

2、The experiments show that, at low enough densities, all real gases tend to obey the relation )

pV , in

nRT

gas

(law

ideal

which p is the absolute pressure, A N N n /= is the number of

moles of gas present, and

R , the gas constant , has the same value for all gases, namely, K mol J R ⋅=/31.8. The temperature T must be expressed in kelvins. Above equation is called the ideal gas law . Provided the gas density is reasonably low, it holds for any type of gas, or a mixture of different types, with n being the total number of moles present.

3、 Work done by an ideal gas at constant temperature :

(1). Suppose that a sample of n moles of an ideal gas, confined to a piston-cylinder arrangement, is allowed to expand from an initial volume i V to a final volume f V .

(2). Suppose further that the temperature T of the gas is held constant throughout the process. Such a process is called an isothermal expansion (and the reverse is called an isothermal compression ).

4、Let us calculate the work done by an ideal gas during an isothermal expansion, we have

⎰⎰==f i f i V V V V dV V nRT pdV W i f

V V nRT ln =. Recall that the symbol ln specifies a natural

logarithm, that is, a logarithm to base e .

12.2 Pressure, Temperature, RMS Speed, and Translational Kinetic Energy

1、 Let n moles of an ideal gas

being confined in a cubical box of

volume V , as in the figure.

2、 A typical gas molecule, of mass m and velocity v, is about to collide with the shaded wall. We assume that any collision of a molecule with a wall is elastic , so the change in the particle’s momentum is along the x axis and its magnitude is x x x x mv mv mv p 2)()(-=--=∆. Hence the momentum x p ∆ delivered to the wall by the molecule during the collision is x mv 2+.

3、 The average rate at which momentum is delivered to the shaded wall by this single molecule is L

mv v L mv t p x x x x 2/22==∆∆. 4、 F rom Newton’s second law, the rate at which momentum is delivered to the wall is the force acting on that wall. To find the total force, we must add up the contributions of all molecules that strike the wall, allowing for the possibility that they all have different speeds. Dividing the total force x F by the area of the wall then gives the pressure

p on that wall. Thus