Temperature, Pressure, and KMT

Definitions and Their Relationships

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)

Hot Molecules(fast!!!)

Cold Molecules(slow!!!)

Molecules in Motion and Temperature

Temperature isthe

AVERAGE of ALL themolecules

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.

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 = D oC)

Formula: o C + 273 = K

Kelvin

O Celsius

0 100 200 273 300 373 400

-273 -173 -73 0 23 100 123

Absolute Zero Water Freezes Water Boils

Room Temperature

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

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

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.

Kinetic Molecular Theory• Kinetic Molecular Theory (KMT)  premises:a) Gas molecules have no attraction for each other. ( Not true at low

temperatures, quasi-liquid properties can begin even before condensation) 

b) 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.)

c) Gas molecules collide against each other and the walls of the container with perfect elasticity. No energy is lost as they move

d) Gas molecules move in perfectly straight lines at high speed. (Gravity has no effect; they don't arc like a ball thrown.)

e) 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

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).

Fraction%

Velocity of Molecules (meters/sec)

It compares how many molecules

(percent out of some population) move with a certain speed .

0 100 200 300 400 500 600

Notice the scale : molecules move really fast !!!!Some molecules move slowly

Most, the greatest fraction, moveat moderate speeds

A few move at very great speeds

AverageThe average speed

is related to the temperature

The distribution of molecular speeds at hot and cold

temperatures

Fraction%

Velocity of Molecules (meters/sec)

0 100 200 300 400 500 600

Average

Cold Molecules will have a certain range of speeds

Average

A group of hot molecules willhave a higher average speed(and so higher temperature.)

For example, the range of speeds in a cup of cold water versus a cup of hot water

What are the differences?

Fraction%

Velocity of Molecules (meters/sec)

0 100 200 300 400 500 600

1. Hot water has a higher average than cold water2. Cold water has more slow molecules3. Hot water has more very fast molecules (but cold water

still has a few fast ones.)4. The temperature is higher in the hot water.

Cold WaterAverage Hot Water

Average

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.