Chapter 22 Molecular properties of gases
Chapter 22 Molecular properties of gases
22-1 The atomic nature of matter 物质的原 质 .J. Thomson discovered electrons in 1897 Rutherford discovered the nature of atomic nucleus He was at his lab at Mcgill Univ. in 1905
J. J. Thomson discovered electrons in 1897. 22-1 The atomic nature of matter (物质的原子本质) Rutherford discovered the nature of atomic nucleus. He was at his lab at McGill Univ. in 1905
1 Brownian motion The modern trail to belief in atoms can be said to have started in 1828 the observation of Brownian motion In 1828 Robert Brown observed through his microscope that tiny grains of pollen suspended in water underwent ceaseless random motion We now call this phenomenon“ Brownian motion” See动画库\力学夹\4-01布朗运动
In 1828 Robert Brown observed through his microscope that tiny grains of pollen suspended in water underwent ceaseless random motion. We now call this phenomenon “Brownian motion”. The modern trail to belief in atoms can be said to have started in 1828: the observation of Brownian motion. 1. Brownian motion See动画库\力学夹\4-01布朗运动
2. Properties of the ideal gas O The ideal gas consists of particles, which are in random motion and obey Newtons Laws of motion. These particles are"“ atoms”or“ molecules” ()The total number of particles is "large. The rate at which momentum is delivered to any area A of the container wall is essentially constant (I)The volume occupied by molecules is a negligibly small fraction of the volume occupied by the gas
(I) The ideal gas consists of particles, which are in random motion and obey Newton’s Laws of motion. These particles are “atoms” or “molecules”. (II) The total number of particles is “large”. The rate at which momentum is delivered to any area A of the container wall is essentially constant. (III) The volume occupied by molecules is a negligibly small fraction of the volume occupied by the gas. 2. Properties of the ideal gas
(M No forces act on a molecule except during a collision M All collisions are elastic and negligible duration Total kinetic energy of the molecules is a constant, and total potential energy is negligible
(IV) No forces act on a molecule except during a collision. (V) All collisions are elastic and negligible duration. Total kinetic energy of the molecules is a constant, and total potential energy is negligible
22-2 A molecular view of pressure(压强) How to relate pressure to Fig 22-2 microscopic quantities P We will take the ideal gas as our system Consider N molecules of an ideal gas X confined within a cubical box of edge length L, as in Fig 22-2
22-2 A molecular view of pressure(压强) We will take the ideal gas as our system. Consider N molecules of an ideal gas confined within a cubical box of edge length L, as in Fig 22-2. L L y x z m L A1 → v A2 How to relate pressure to Fig 22-2 microscopic quantities? P ~ ρ, v ...?
The average impulsive force exerted by the molecule on a is 2 2L (22-4 The total force on a, by all the gas molecules is the sum of the quantities mvx /L for all the molecules Then the pressure on Alis (Fx1+F32+…) (22-5) 1mv,+m1v,2+ V;+1 L
The average impulsive force exerted by the molecule on is A1 L mv v L mv F x x x x 2 2 2 = = (22-4) The total force on by all the gas molecules is the sum of the quantities for all the molecules. Then the pressure on A1 is (22-5) A1 mvx / L 2 ( ) 1 ( ...) 1 2 2 2 3 1 2 2 2 1 2 2 1 2 = + + + + = = + + x x x x x x v v L m L m v m v L F F L P
P=a 2 If N is the total number of molecules in container the total mass is nm the density is p=Nm/E P- Ly 22-6) N The quantity in parenthesis is average value of for all the molecules in the container P=p( av 22-7)
If N is the total number of molecules in container, the total mass is Nm. the density is . (22-6) The quantity in parenthesis is average value of for all the molecules in the container. (22-7) 3 = Nm/ L 2 x v x av P (v ) 2 = [ ] 2 2 3 N v N v L mN P i xi i xi = = ( ) 2 2 2 3 1 = + + x x v v L m P v v N i x av xi ( ) ( )/ 2 2 =
P=p(vx2)(227) For any molecules v2=v +v2+vand 1 so Eq 22-7)becomes 2 o(v av (22-8) 3 1. the result is true even when we consider collisions between molecules 2. the result is correct even with consideration of the collisions between molecules and other walls in the box 3. The result is correct for boxes with any kinds of shape
For any molecules, , and so Eq(22-7) becomes (22-8) 1.The result is true even when we consider collisions between molecules. 2. The result is correct even with consideration of the collisions between molecules and other walls in the box. 3. The result is correct for boxes with any kinds of shape. 2 2 2 2 x y z v = v + v + v x a v y a v z a v a v v v v (v ) 3 1 ( ) ( ) ( ) 2 2 2 2 = = = P v av ( ) 3 1 2 = x av P (v ) 2 = (22-7)
4.The“oot-mean- square”(均方根) speed of the molecules: 3P Vp (22-9) In eq(22-8, 9), we relate a macroscopic quantity( the pressure p)to an average value of a microscopic quantity, that is to (va,or v
(22-9) In Eq(22-8,9), we relate a macroscopic quantity ( the pressure P) to an average value of a microscopic quantity, that is to or . P v v rms a v 3 ( ) 2 = = rms v av (v ) 2 4. The “root-mean-square” (均方根)speed of the molecules：