Paperwork

• Mastering Physics

• Course # DRKIDD880131

• Assignment Due tonight

• New Assignment up soon…

• Lab Reports due next Tuesday 5pm

Schedule Short Term

• Today – derive pressure/height, calculate

• Friday – Begin Chapter 19

• Monday – Chapter 19 / Solving

• Tuesday – Lab #2– Quiz#2 [Chapter 18, Labs]

• Thursday HMWK due 11pm

Pressure vs. Height

• Example 18.4

Thin object, mass m

Force = pA

Force = pA + (dp)A

For an object in a fluidPressure on sides of object is the same, so cancels (Book on desk is stationary)Assume pressure felt by top is slightly different than bottom (p+dp)

dy

Pressure vs. Height

• Example 18.4

Thin object, mass m

Force = pA

Force = pA + (dp)A

For an object in a fluidPressure on sides of object is the same, so cancels (Book on desk is stationary)Assume pressure felt by top is slightly different than bottom (p+dp)dp can be +, - or even zero. Just much smaller than p for thin objectLet’s say this object is stationary – floating in the fluid.What is sum of all forces on object?What are all forces on object?What if “Object” was just a portion of the fluid itself?

dy

Pressure vs. Height

• Example 18.4

mass = V = A(dy)

Force = pA

Force = pA + (dp)A

F = 0 = pA - [pA + (dp)A] – mg0 = pA – pA – (dp)A – Vg(dp)A = -Vg (dp)A = -(Ady)g(dp/dy) = - g

Implications?

dy

Pressure vs. Height

• Example 18.4

mass = V = A(dy)

Force = pA

Force = pA + (dp)A

F = 0 = pA - [pA + (dp)A] – mg0 = pA – pA – (dp)A – Vg(dp)A = -Vg (dp)A = -(Ady)g(dp/dy) = - g

dy

For Ideal Gas= m/V = pM/(RT) (dp/dy) = - g

Pressure vs. Height

• Example 18.4

mass = V = A(dy)

Force = pA

Force = pA + (dp)A

dy

For Fluid that is an Ideal Gas= m/V = pM/(RT)

Pressure vs. HeightAny Fluid(dp/dy) = - g

(dp/dy) = - pgM/(RT)

Pressure vs. Height

• (dp/dy) = - pgM/(RT)• Now need to set up equation to solve• (dp/p) = -(gM/RT)(dy)

– Assume a constant temperature (?)

0 0

1( )

pF yF

p y

Mgdp dy

p RT

Pressure vs. Height

• (dp/dy) = - pgM/(RT)• Now need to set up equation to solve• (dp/p) = -(gM/RT)(dy)

– Assume a constant temperature (?)

0 0

1( )

pF yF

p y

Mgdp dy

p RT

0 0

1( )

pF yF

p y

Mgdp dy

p RT

Pressure vs. Height

0 0

1( )

pF yF

p y

Mgdp dy

p RT

ln ln( 0) ( ) 0

ln ( ) 00

MgpF p yF y

RT

pF MgyF y

p RT

0 0

1( )

pF yF

p y

Mgdp dy

p RT

Pressure vs. Height

Let’s say integration was from sea level (p0=p0, y0 = 0)To a point pF = p, yF = yNeed to have known endpointsThen can derive equation for air pressure as a function of height above sea level

0

( )

0

( )

0

ln ln( 0) ( ) 0

ln ( ) 00

ln ( )

Mgy

RT

Mgy

RT

MgpF p yF y

RT

pF MgyF y

p RT

p Mgy

p RT

pe

p

p p e

Happy Equation: Should Check AccuracyImplications? Check at sea level.

Molecular Motion

• From Derivation in Section 18.3– KEAVG=(3/2)NkBT (N is # molecules)– pV = (2/3) KEAVG

– pV = NkBT

• Where does 3 come from?• Other implications?• Why do people care about root mean

square? [vrms]• Hint: zero?

Mean Free PathLifetime (Mean Free Time)

• Very Important Concept– Vacuum conditions– Behavior of electrons in solids– Any interacting (or not) particles

• Mean distance traveled before collision• MFP = v tMFP • Lifetime (mean free time) is time between

collisions• Why important for electrical conduction?

Lots of Averages…• Gas at temperature 500K• Average KE of One Mole

• KEAVG = (3/2)nRT = (3/2)RT– 8.31 J / (mole K)

• KEAVG = 6232 J

• Say gas is N2 (MM = 0.028kg / mole)

• KEAVG = (1/2)m(v2)AVG

2 221 m/sAVG

RMS AVG

KEv v

m

What is max speed?

Phase Diagram

Describes P&T conditions for materialsInteresting Points, What is this at STP?

Phase Diagram

Supercritical Fluid? Neat – can dissolve things like a liquid & Diffuse through solids like a gas…

Gas # molecules = n0

Temperature = T0

pressure = p0

Volume = V0

Discussion Q18.10Start

Gas Initial State# molecules = n0

Temperature = T0

pressure = p0

Volume = V0

Discussion Q18.10“Sudden” Hole in wall

Gas Final State# molecules = ?Temperature = ?pressure = ?Volume = ?

What Happens here?

Schedule Short Term

• Today – derive pressure/height, calculate

• Friday – Begin Chapter 19

• Monday – Chapter 19 / Solving

• Tuesday – Lab #2– Quiz#2 [Chapter 18, Labs]

• Thursday HMWK due 11pm