CK-12-Physics - Intermediate

http://www.ck12.org Chapter 13. Heat

13.2 Kinetic Theory of Temperature

Objectives

The student will:

• Describe the relationship between temperature and kinetic energy.

Vocabulary

• internal energy:The total kinetic and potential energy associated with the motions and relative positions of
  the molecules of an object, excluding the kinetic or potential energy of the object as a whole. An increase in
  internal energy results in a rise in temperature or a change in phase.


• Kinetic Theory:A theory concerning the thermodynamic behavior of matter, especially the relationships
  among pressure, volume, and temperature in gases. It is based on the dependence of temperature on the
  kinetic energy of the rapidly moving particles of a substance. According to the theory, energy and momentum
  are conserved in all collisions between particles, and the average behavior of the particles can be deduced by
  statistical analysis.

Introduction

James Clark Maxwell (1831-1879) determined a very important relationship between the motion of molecules and
temperature within a gas in the mid-19th century.

Kinetic Theoryrelies upon the following assumptions:

1. The number of molecules in a gas is very large and their motion is random.


2. The average distance between any two molecules is much greater than the diameter of the any molecule.


3. The molecules interact in accordance with Newton’s laws. Only thekinetic energyof the molecules is
   considered, and all the interactions between molecules are elastic.

Under these conditions, a gas is referred to as an ideal gas.

When we ask what the temperature is outside, we’re indirectly asking for a measure of the average kinetic energy
of the air molecules. Maxwell was able to show that the relationship between the average kinetic energy of a gas
and its temperature isKE=^12 m(vt)^2 =^32 kT, wherevtis the mean translational velocity of the molecules,mis their
mass,kthe Boltzmann constant, is equal to 1. 38 × 10 −^23 KJ, and the temperatureTis expressed in Kelvin.

The equation states that the average translational kinetic energy,KEof the molecules is directly proportional to the
temperatureTof the gas.