Physics CChapter 21

From serway book

Prepared by Anas A. Alkanoa

M.Sc.( master degree) in Theoretical Physics, Electromagnetic Waves (Optical Science) ,

Islamic University of Gaza (Gaza, Palestine).

Chapter FiveThe Kinetic Theory of Gases

20.1 Molecular Model of an Ideal Gas20.2 Molar Specific Heat of an Ideal Gas20.3 Adiabatic Processes for an Ideal Gas

20.1 Molecular Model of an Ideal Gaswe make the following assumptions:

1) The number of molecules in the gas is large, and the average separation between them is large compared with their dimensions.2) The molecules obey Newton’s laws of motion, but as a whole they move randomly.3) The molecules interact only by short-range forces during elastic collisions.

4) The molecules make elastic collisions with the walls.

5) The gas under consideration is a pure substance; that is, all molecules are identical.

For our first application of kinetic theory, let us derive an expression for the pressure of N molecules of an ideal gas in a container of volume V in terms of microscopic quantities. The container is a cube with edges of length d Figure.

A molecule of mass m makes an elastic collision with the wall of the container. Its x component of momentum is reversed, while its y component remains unchanged. In this construction, we assume that the molecule moves in the xy plane.

Remark: The subscript i here refers to the ith molecule, not to an initial value.

This result indicates that the pressure of a gas is proportional to the number of molecules per unit volume and to the average translational kinetic energy of the molecules

20.2 Molar Specific Heat of an Ideal Gas

Because T is the same for each path, the change in internal energy Eint is the same for all paths.

the heat Q is different for each path because W (the negative of the area under the curves) is different for each path.

where Cv is the molar specific heat at constant volume and Cp is the molar specific heat at constant pressure.