Scope, Sequence, and Coordination

A Framework for High School Science Education

Based on the National Science Education Standards

Gas Pressure, Volume and Temperature

Heat, Internal Energy, and the Kinetic-Theory

NSES Generalization (p. 180)

Heat consists of random motion and the vibrations of atoms, molecules, and ions. The higher the temperature, the greater the atomic or molecular motion.

Further Description:

This NSES generalization confuses heat and internal energy and neglects internal potential energy as part of that energy of vibration. Heat is energy transferred to or from a system. That heat can result in changes in the internal energy of the system along with work done by the system. This latter statement is called the first law of thermodynamics. The heat energy (really internal energy) of a substance consists not only of the random translational and rotational motion and vibration of its atoms, molecules, and ions, but also of the internal stored potential energy associated with those atoms, molecules or ions.

This generalization is an assertion of the kinetic molecular theory. Any theory must have a set of observations and empirical laws to explain. In the case of the kinetic theory, most of that empirical basis comes from observed relationships among variables like temperature, pressure, volume, and numbers of particles for gases, and for the specific heats of gases and solids (considering vibrational modes for solids). It also comes from the experiments of Mayer and Joule that established heat as a form of energy equivalent to mechancial energy.

When a simple model of a gas is created, and Newton’s laws of motion applied to particles within that model, the result indicates that the product of pressure and volume of a gas is proportional to the average translational kinetic energy of its particles. Since the empirical gas law shows that the product of pressure and volume is proportional to absolute temperature, we can conclude logically that the absolute temperature must be proportional to the average kinetic energy of particles in the gas. This is an excellent example of how a theory is created to account for certain empirical laws and observations, and how that theory leads to new information.

In this case, the theory leads to the conclusion that temperature is a measure of the average translational kinetic energy of molecules of any gas. The rotational and vibrational kinetic energies, and potential energies associated with vibration, are connected to the internal energy of that gas, but not to its temperature. Thus, oxygen gas during its phase transition from gas to liquid does not have a temperature change. This topic provides excellent examples of the history of science, coupled with the best of inquiry, leading to distinctions between empirical knowledge and the theories and models used to explain that empirical knowledge.

Concepts Needed:

Grade 9

Celsius temperature, heat, calorie

Grade 10

Pressure, volume, absolute temperature

Grade 11

Pascals, atom, molecule, mean free path, rms speed, specific heat at constant volume

Grade 12

Moles, Maxwell-Boltzmann distribution, Boltzmann=s constant, momentum, impulse

Empirical Laws or Observed Relationships:

Charles= law, Boyle=s law, Gay-Lussac=s law, specific heats of solids and gases (at constant volume)

Theories or Models:

An ideal gas as a model, kinetic-molecular theory (through an application of Newton=s law to an ideal gas), the equipartition of energy theorem

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Micro-Unit Description:

Gas Pressure, Volume and Temperature
This is a good opportunity to build an empirical base for subsequent theoretical work. At this level some kinetic theory can be developed descriptively and qualitatively, leading students to understand how gases exert pressures, how temperature increases change the volume or pressure of a gas under various constraints, etc. The concept of atoms and of molecules can be developed as they relate to vibrations and random motion.

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