Temperature, Pressure, and KMT

1. Temperature, Pressure, and KMT Definitions and Their Relationships

2. Temperature • Remember that all molecules move. Even solid molecules will be vibrating in place. • Definition • The speed at which molecules are moving • It’s the average kinetic energy of a group of molecules • Kinetic Energy = ½ mass(velocity)2 • Measurement • Fahrenheit (not used in this class) • Celsius (Centigrade) (o C) • Kelvin (K) ( it is o C + 273)

3. Temperature is the AVERAGE of ALL the molecules Hot Molecules (fast!!!) Cold Molecules(slow!!!) Molecules in Motion and Temperature

4. Kelvin vs. o Celsius • Remember that temperature measures how fast, on average, molecules move. • Question: What would be the temperature of molecules that are NOT moving? • It should be zero degrees (No speed=no temperature) • It is…for the Kelvin scale. Zero Celsius just measures the temperature that water freezes. • Celsius used to be handy (and still is for most people) when they needed something that they could commonly experience. • But if you want a scale that related to how fast molecules are moving, then you need the Kelvin scale.

5. Kelvin 0 100 200 273 300 373 400 -273 -173 -73 0 23 100 123 O Celsius Absolute Zero Water Freezes Water Boils Room Temperature Converting o Celsius to Kelvin • The scales are the same, it’s just that the starting point is different. Celsius is set to zero when Kelvin is already at 273. The Celsius scale has negatives. There is no negative Kelvin. Zero Kelvin is called Absolute Zero • A change of 1 Kelvin = a change of 1 oC (D K = DoC) Formula: o C + 273 = K

6. Pressure • Pressure is the force (push) put on an area • The more the push, the more the pressure • The smaller the area, the more the pressure • Pressure = Force/Area • Pressure is, generally, only important in affecting Gases. • Solids and Liquids are not really affected

7. Pressure, continued • Measurements: There are three different units • Pascals (or kilopascals) (Pa or kPa) • Atmospheres ( as in our atmosphere) • Torr or mm Hg (millimeters mercury) • 1 atmosphere = 760 torr = 101.3 kPa

8. Kinetic Molecular Theory • This sets up some basic ideas for how molecules and compounds move. • It is useful mainly for describing the behavior of gases, but it also helps to understand liquids and solids • The basic ideas are true, but it, some of the premises are simplifications of real molecules • These simplifications don’t work for solids and liquids, and for gases that are close to becoming liquids.

9. Kinetic Molecular Theory • Kinetic Molecular Theory (KMT)  premises: • Gas molecules have no attraction for each other. ( Not true at low temperatures, quasi-liquid properties can begin even before condensation)  • Gas molecules have no volume. They are dimensionless points. (Not perfectly true at high pressures and densities, then they begin to bounce against each other instead of the walls of the container.) • Gas molecules collide against each other and the walls of the container with perfect elasticity. No energy is lost as they move • Gas molecules move in perfectly straight lines at high speed. (Gravity has no effect; they don't arc like a ball thrown.) • Gas molecules move with a range of velocities. The average kinetic energy (mass x velocity2 ) of the molecules is proportional to its absolute temperature (in Kelvin). The molecules move with a range called a Maxwell-Boltzmann distribution. Think of them as Ping-Pong balls Really, really small ping-pong balls Ping-pong balls that never, ever stop bouncing

10. Average The average speed is related to the temperature It compares how many molecules (percent out of some population) move with a certain speed . Notice the scale : molecules move really fast !!!! Maxwell-Boltzmann distribution. • This is a statistical description of how molecules move. • For example, all the molecules in a cup of water • It applies to ALL matter (solid liquid and gas). Most, the greatest fraction, move at moderate speeds Fraction% A few move at very great speeds Some molecules move slowly 0 100 200 300 400 500 600 Velocity of Molecules (meters/sec)

11. Average Average Cold Molecules will have a certain range of speeds A group of hot molecules will have a higher average speed(and so higher temperature.) Fraction% 0 100 200 300 400 500 600 Velocity of Molecules (meters/sec) The distribution of molecular speeds at hot and cold temperatures For example, the range of speeds in a cup of cold water versus a cup of hot water

12. Cold Water Average Hot Water Average Fraction% 0 100 200 300 400 500 600 Velocity of Molecules (meters/sec) What are the differences? • Hot water has a higher average than cold water • Cold water has more slow molecules • Hot water has more very fast molecules (but cold water still has a few fast ones.) • The temperature is higher in the hot water.

13. Summary • Molecules move • They do with a certain amount of speed. • When they hit, or push on objects, they exert a pressure. • A mathematical description of the movement of molecules is possible with a few simplifications. • These descriptions of temperature, pressure and the Kinetic Molecular Theory allow for a rigorous analysis of the states of matter and how they change. That is the subject of our next unit.