Kinematics and Dynamics of Point Particles and Extended Objects

2. Kinematics and Dynamics ofPoint Particles and Extended Objects We have completed this discussion for point particles. How do you treat extended systems of particles?

3. Extended systems Rigid - even though extended, all particles move as a unit Non Rigid streamline - even though particles are not connected they seem to move as a unit Non Rigid random - cannot be described by looking at single particle motions. Just impossible!

4. Extended non-rigid systems gases and liquids • Listing individual speeds, forces, and positions is impossible for even small parts of real systems. • Consider the “standard” volume of air at “standard” room temperature. There are about 1024 particles in such a system which occupies about a cubic meter. How long would it take for a fast computer to one calculation on each particle?

5. Description of extended non-rigid bodies • What parameters are used to describe such systems? • Pressure • Volume • Temperature • “Average” energy

6. “Initial” description of extended non-rigid systems • Empirical relationship between pressure volume and temperature with no reference to particle kinematics. • P·V = N·k·T - Ideal Gas Law • N= # of molecules • k= constant • Heat - amount of caloric entering or leaving a body - 1 calorie = heat necessary to raise the temperature of 1 gm of water 1 degree C.

7. Connection between Temperature and the microscopic nature of matter • Temperature and molecular motion are related! • Specifically: • average kinetic energy per particle is related to temperature if one looks microscopically at pressure and momentum of individual particles. • <(1/2)·m·v2> = (3/2)P·V/N = (3/2)·k·T • How is the “average” measured if you can’t measure all the particles in a sample?

8. Heat • In the microscopic view, heat is simply the total energy content of a sample - Q is the symbol for heat. • Q = (3/2)·N·k·T • where N is the total number of particles in the system • the joule and calorie are related • 1 cal = 4.184 joules

9. Solid Liquid Gas requires 330 joules/gm added to ice to get liquid water requires 2260 joules/gm added to liquid to get steam(gas) note! The numbers are different for every substance States of Matter

10. Specific Heat Capacity - c • If different substances take up the same amount of “heat” they all should reach the same temperature. • They don’t! Can you think of some examples? • A description of this is • c = (1/ m)·Q/ T • c is a measured number for each substance in order to categorize the substance. • m is the mass of the substance

11. Examples of Specific Heat Capacity • Water - 1 cal/gm·K • Copper - .1cal/gm·K • Why are they different? How can you put energy into a system and not change the temperature? • We must look to the microscopic description of matter and carefully analyze the temperature measurement process.

12. Specific Heat Capacity Explained • From the detailed microscopic investigation of matter we find: • the act of measuring temperature changes temperature • specific heat capacity can be predicted if one knows the number of ways a system can move. (or can absorb energy)

13. conduction convection radiation Energy imparted by direct contact - collision energetic particles move from one place to another light-this is like convection but no medium needed. Light is different! Heat Transfer