Math and Matter

Condensation:

"The change of state from a gas to a liquid" • The opposite of evaporation. • Low-energy gas molecules collide with each other and stick together, forming a liquid. • This "sticking together" releases energy, so condensation is a warming process.

Johannes Kepler

"The world of nature, the world of man, the world of God—all these fit together." CAREFUL observation and measurement led Kepler to discern the laws of planetary motion.

Sublimation & Deposition

"solid to gas" Processes that skip a step » Sublimation : solid → gas ❖Dry ice (solid CO2) » Deposition : gas → solid ❖Snow/Frost

Boiling Point

"temperature at which a liquid changes to gas" *The temperature at which boiling occurs.* » Depends on atmospheric pressure. Higher pressure → higher boiling point Lower pressure → lower boiling point » At sea level (1 atm), water boils at 100 ℃. » On Everest (1/3 atm), it boils at 71℃. » Forming the bubbles of vapor works against the pressure above them.

Motion

*a change in the location of something relative to something else* • Reference Frame - the perspective from which the motion of something is measured

Temperature is measured using 3 scales:

*kelvin* (100-degree interval) 373 - water boils 273 - water freezes *celsius* (100-degree interval) 100 - water boils 0 - water freezes *Fahrenheit* (180-degree interval) 212 - water boils 32 - water freezes

Gas Laws:

*• Gases are described by four basic quantities* » Density » Pressure » Temperature » Volume *• As a gas undergoes some change, these quantities change.*

Energy Cost:

- *Heat of vaporization:* » Energy required to boil a liquid » Liquid → Gas - *Heat of fusion:* » Energy required to melt a solid » Solid → Liquid

chemical property

- A chemical property based on changes in how atoms are connected, observed during a chemical reaction (reactivity) - A chemical change: change in the identity (how atoms are connected) so new set of properties (burning wood)

Matter is classified by Extensive properties depend on the amount of the substance

- Volume Internal Energy - Mass Reaction Energy

• Newton's First Law

- an object that is either at rest or moving at a constant velocity will maintain its state of motion until it is acted upon by a net force • Inertia - the reluctance of an object to change its state of motion

States of Matter: *Liquids*

- close particles - not packed - not organized States of Matter: » definite volume » shape of its container

States of Matter: *Soilids*

- organized particles - tightly packed - crystal lattice arrangement - Vibrating States of Matter: » definite volume » definite shape

Kepler's Laws

1. Every planet has an elliptical orbit about the sun. 2. A straight line between any planet and the sun sweeps out equal areas in equal amounts of time.

Newton's Third Law:

: for every action force there is an equal and opposite reaction force. • Though the forces are the same, if the objects have different masses, they will experience different accelerations. • Action force : first object exerts on second • Reaction force : second object exerts on first

• Newton's Second Law

: the unbalanced net force acting on an object is equal to the object's mass times its acceleration • Force (F) = mass (m) X acceleration (a) • F=ma • Unit: Newton (N) = kg*m/s2 1 N = 0.225 lb 1 lb = 4.45 N

physical property:

A physical property observed without changing the identity (size, state of matter) - A physical change a change not affecting identity and atomic connections ex. shape or phase (melting ice to water, salt dissolving)

Matter is classified by: Intensive properties do not depend on the amount

Density Boiling point Melting Point Refractive Index Reactivity

Heating Stuff:

During a change of phase, adding or removing energy does not cause a temperature change. Heating Stuff Energy changes cause rearrangement of atoms or molecules.

*Pressure Example:* 4. A small woman with a mass of 50.0 kg is wearing high heels. The area of each heel is 0.500 cm2. What pressure does she exert with just 1 heel in Pa?

F=mg A=0.5cm2 Force comes from her weight

States of Matter: *Plasma*

Highest Energy

Speed

How fast an object moves • Distance covered per unit time • Speed has a derived unit: m/s, km/h, ...

Boiling:

Liquid to gas • Happens beneath the surface—prior to evaporation. • Bubbles of vapor form; and, when they're large enough, the buoyant force drives them toward the surface. • Also a cooling process.

States of Matter: *Gases*

Particles spread as far apart as possible States of Matter: » No definite volume » No definite shape

Heat of vaporization: (Energy Cost)

The amount of energy required for the liquid at its boiling point to become a gas » Energy required to boil a liquid » Liquid → Gas

Action and Reaction

The cannon when the cannonball is fired The oars to make the boat go forward

Temperature

Understand of Temp on the molecular level: • Average kinetic energies of all of the molecules that make up the object. - Sample has molecules with all different energies • Average is called the object's thermal energy. • We refer to how hot or how cold an object is. Atoms slow: Kinetic energy low -"cold" Atoms Fast: Kinetic energy high - "hot" Temperature is measured using 3 scales: kelvin, celsius, and Fahrenheit.

Pressure (molecular level)

Understand pressure on the molecular level - Pressure of a gas/liquid - number of hits per time on the walls of the container - Magnitude of pressure - how often and hard they strike Said in class: - temp goes up pressure goes up - temp goes down pressure goes down

Heat of fusion: (Energy Cost)

Amount of energy required to change a substance from the solid phase to the liquid phase at its melting point » Energy required to melt a solid » Solid → Liquid

Weight vs. Mass:

What is heavier, a ton of steel or a ton of feathers? - both same mass: the amount of a matter (measured with a balance, same anywhere in-universe) Weight - the impact of gravity on the mass (measured with a scale, depends on location)

Law of Momentum Conservation

When the sum of the forces working on a system is zero, the total momentum in the system cannot change. - -

A ball thrown into the air

accelerates downward

Common Densities

chart

Variable, Symbol, SI Units, Unit Symbol *Distance:* (Speed)

d, meter, m

Which of the following is NOT true of orbiting satellite? It..

has constant velocity

Imaginative Demonstration

laying on nails

Which is conserved when two objects collide?

momentum

States of Matter (Going from one phase to another requires energy)

plasma - highest energy gas liquid solid - lowest energy

Plicker Question: Which state of matter generally has the smallest energy?

solid?

Variable, Symbol, SI Units, Unit Symbol *Time:* (Speed)

t, seconds, s

Change of State

the change of a substance from one physical state to another

Variable, Symbol, SI Units, Unit Symbol *Speed:* (Speed)

v=d/t, meters/second, m/s

Force:

• *A net "push" or "pull" that changes the acceleration of an object* -*Net Force:* the sum of all of the forces acting on the object -*Balanced Forces:* occurs when the net force is zero, meaning no acceleration -*Unbalanced Forces:* occurs when the net force is nonzero, meaning acceleration

Heating by Radiation:

• *Anything that absorbs light* • Some materials absorb light better than others. Examples: » A black shirt » A white T-shirt

Heating by Convection:

• *Fluids (liquids and gases)* • Our atmosphere is heated by convection » Warm air rises. Why? » Important for fluctuations in climate and weather. • Which way does your ceiling fan turn in hot weather? In cold weather?

Heating by Conduction:

• *Solids* • Materials differ in their thermal conductivity. » How easily something transmits heat. » Conductors » Insulators

Finding Volume

• *The amount of space occupied by an object*. • *For simple geometries* » V = length * width * height • *For complicated geometries* » Immerse the object in a liquid. » The volume of liquid displaced is equal to the volume of the object! V(object) = V(object + mass) - V (liquid)

Pressure

• *The force per unit area that an object exerts on a surface* • p = F / A • Unit of pressure » Pascal (Pa) = N / m2

Density:

• *The ratio of an object's mass to its volume* » D = m / V • *Unit of density* » kg / m3 • *Usually instead reported in g/mL or g/cm3*

Pressure in a Liquid

• ... depends on the object's depth • p = Dliquid x g x depth

Other Units of Pressure:

• 1 atm = 101.325 kPa = 760 mm Hg • 760 mm Hg = 760 torr = 30 in Hg • 1 atm = 1013 mbar = 1.013 bar • 1 kPa = 0.145 psi (he wrote on board 14psi) he said to memorize the 1 atm = 760 and 760 mm Hg = 760 Torr

Newton's Law of Gravity

• Affected by: - Mass: the greater the mass the greater the gravitational attraction. - Distance: the greater the distance between the objects the lower the gravitational attraction. (the equation was on the slide)

Buoyancy

• Because pressure depends on depth, there is a net upward pressure on any object immersed in a liquid. • The force associated with this pressure is called the buoyant force. • buoyant force = weight of the liquid it displaces

Ways to Heat Something:

• By conduction solids (molecular collisions) • By convection fluids/gases (actual motion of the substance) • By radiation emission and absorption of light

Evaporation

• Collisions at the surface of a liquid cause evaporation. • The kicked out molecules take energy with them, so evaporation is a cooling process. • What gets cooler?

Momentum

• Depends on the objects mass and velocity • Two types: linear and angular • Momentum (p) = mass (m) x velocity (v) p = m x v • Derived SI unit: kg⋅m/s

Newton's Laws of Motion: (memorize the first, second, and third law)

• Describe how forces cause motion. • Newton's First Law - an object that is either at rest or moving at a constant velocity will maintain its state of motion until it is acted upon by a net force • Inertia - the reluctance of an object to change its state of motion

Converting Temperuature:

• Equations: » ◦F = (1.8 x ◦C) + 32 » ◦C =(◦F - 32)/1.8 » K = ◦C + 273 » ◦C = K- 273 • If your algebra is good, just remember one of each.

Common Forces:

• Friction - a contact force • Air Resistance - friction between the surface of an object and air molecules • Gravity - the force of attraction between or among objects having mass

Gravity- Free Fall

• On earth g = 9.8 m/s2 for any object in free fall. • Free fall occurs when gravity is the only force acting on an object. - v = gt - Can use to find height (equation was shown on the slide)

Gravity

• Once the motion of the planets was predicted by Kepler's Laws, the next question was why? • The planets must be held into orbit by a force. • Isaac Newton first addressed the idea of gravitational attraction. • Newton discovered "The Law of Gravity."

Friction

• Sometimes ignored—but is always present in some way. • The direction of the friction force is always opposite that of the motion. • Friction is bad: it dissipates energy. • Friction is good: it allows us to roll, turn, and stop!

Gravity

• The force of attraction that exists between objects having mass. • Fundamental Force : the strongest is strong and teh weakest is gravity on the chart

Terminal Speed

• The maximum speed reached by a falling object • When air resistance upward balances gravity downward • About 120 mi/hr for people - Ex: if you fall off a building gyou would get to a terminal velocity. When you wan to go faser, put yourself into a dice position.

Heat

• The transfer of thermal energy from one object to another. » Unit is a Joule. (It's an energy transfer.) » The transfer is always from a body of higher temperature to one of lower temperature. • Changes the internal energy of each object.

Measuring Pressure

• Use a barometer. • Pressure of the earth's atmosphere » 1 atm = 760 mm Hg

Weight

• Weight = mass x (acceleration due to gravity) • w = mg • In pounds (lb) or Newtons (N) • N= kg x m/s2 • 1 N =0.225 lb

Density can be used to....

• identify an unknown. • find the thickness of a thin sheet of foil. • determine the buoyancy of something. (whether it will sink or float) - sink = density is high - float = density is less