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Lecture 8 The Gas Laws. Kinetic Theory of Matter. Chapter 4.7  4.16. Outline. Ideal Gas Kinetic Theory of Matter Changes of State Entropy. Boyle’s law relates gaseous volume and pressure under constant temperature. Boyle’s Law. Gas is the simplest state of matter to study.

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Lecture 8 the gas laws kinetic theory of matter
Lecture 8The Gas Laws. Kinetic Theory of Matter.

Chapter 4.7  4.16

Outline

  • Ideal Gas

  • Kinetic Theory of Matter

  • Changes of State

  • Entropy


Boyle s law

Boyle’s law relates gaseous volume and pressure under constant temperature

Boyle’s Law

Gas is the simplest state of matter to study

p1 initial pressure, p2 final pressure

V1 initial volume, V2  final volume

p1 V2

--- = ----

p2 V1

or

p1V1 = p2V2


Charles law
Charles’ Law

Changes in volume are related to the gas temperature under a constant pressure

Cooling a volume of gas steadily from 0oC at a constant pressure decreases its volume by ~1/273 for every degree

The same rule applies to pressure if volume is constant

Conclusion:

at 273oC

the pressure is 0 if the volume was constant

or

the volume is 0 if the pressure was constant


Absolute zero temperature
Absolute Zero Temperature

It is impossible to achieve such a low temperature (273oC)

Gases turn into liquids before this temperature is reached

The temperature 273oC is called absolute zero

Absolute temperature is temperature measured above absolute zero in degrees celsius (the Kelvin scale)

T1 V1

--- = ---- at constant pressure  Charles’ law

T2 V2


Ideal gas
Ideal Gas

Combined Boyle’s and Charles’ laws give the ideal gas law

p1 V1 p2 V2

------- = -------

T1 T2

At constant T (T1 = T2) we have Boyle’s law

At constant p (p1 = p2) we have Charles’ law

p V

----- = const

T


Kinetic theory of gases
Kinetic Theory of Gases

Basis: all matter is composed of tiny particles called molecules that are in constant motion.

Gas molecules:

are small compared with the average distances between them

collide without loss of kinetic energy

exert almost no forces on one another outside of collisions

Thus, a gas is mostly an empty space

The absolute temperature of a gas is proportional to the average kinetic energy of its molecules


Why molecules keep moving
Why Molecules Keep Moving?

Motion is affected by friction

When friction is applied, it converts kinetic energy into heat

Heat is molecular energy!

Thus, there is no change in molecular energy by friction  molecular motion is unstoppable


States of matter
States of Matter

Solid

Liquid

Gas

Matter can exist in these 3 states.

Changes of state may occur under specific conditions.

Liquid into Gas: evaporation and boiling

Solid into Liquid: melting

Solid into Gas: sublimation


Energy transformations

Heat can be turned into mechanical energy by a heat engine.

Energy Transformations

Heat cannot be converted into other forms of energy efficiently

The reason is random molecular motion

The maximum efficiency of a heat engine is a ratio of the (work output)/(energy input)

or 1  Tcold/Thot

(typical actual efficiency < 40%).


Thermodynamics
Thermodynamics

Thermodynamics is a science of heat transformations

  • 2 fundamental laws of thermodynamics:

  • Energy cannot be created or destroyed.

  • It is impossible to convert all the heat of a source into mechanical energy.

The second law is based on the fact that one cannot line up all the molecules in a volume.


Fate of the universe
Fate of the Universe

Other energy forms can be turned into heat, but heat cannot be efficiently converted back.

Thus, heat energy in the Universe increases with time.

Stars is the warm reservoir, everything else is the cool reservoir.

With time the temperature difference between the two decreases, and finally all the particles will have the same average energy  “heat death” of the Universe


Entropy
Entropy

Entropy is defined as a measure of the disorder of the molecules in a material body.

A liquid has more disorder than a solid.

A gas has more disorder than a liquid.

The entropy of an isolated system cannot decrease.


Summary

The concept of ideal gas is a good model to study properties of substances

Summary

  • The absolute zero temperature corresponds to the absence of molecular motion and cannot be reached.

  • Heat cannot be effectively converted into other forms of energy.

  • Entropy or disorder in isolated systems can only be increased.