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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

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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

Force = pA + (dp)A

dy

Thin object, mass m

Force = pA

For an object in a fluid

Pressure 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)

Pressure vs. Height
• Example 18.4

Force = pA + (dp)A

dy

Thin object, mass m

Force = pA

For an object in a fluid

Pressure 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 object

Let’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?

Pressure vs. Height
• Example 18.4

Force = pA + (dp)A

dy

mass = rV = rA(dy)

Force = pA

SF = 0 = pA - [pA + (dp)A] – mg

0 = pA – pA – (dp)A – rVg

(dp)A = -rVg

(dp)A = -r(Ady)g

(dp/dy) = - rg

Implications?

Pressure vs. Height
• Example 18.4

Force = pA + (dp)A

dy

mass = rV = rA(dy)

Force = pA

SF = 0 = pA - [pA + (dp)A] – mg

0 = pA – pA – (dp)A – rVg

(dp)A = -rVg

(dp)A = -r(Ady)g

(dp/dy) = - rg

For Ideal Gas

r = m/V = pM/(RT)

(dp/dy) = - rg

Pressure vs. Height
• Example 18.4

Force = pA + (dp)A

dy

mass = rV = rA(dy)

Force = pA

Pressure vs. Height

Any Fluid

(dp/dy) = - rg

For Fluid that is an Ideal Gas

r = m/V = pM/(RT)

(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 (?)
Pressure vs. Height
• (dp/dy) = - pgM/(RT)
• Now need to set up equation to solve
• (dp/p) = -(gM/RT)(dy)
• Assume a constant temperature (?)
Pressure vs. Height

Let’s say integration was from sea level (p0=p0, y0 = 0)

To a point pF = p, yF = y

Need to have known endpoints

Then can derive equation for air pressure as a function of height above sea level

Happy Equation: Should Check Accuracy

Implications? 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
• lMFP = 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

What is max speed?

Phase Diagram

Describes P&T conditions for materials

Interesting Points, What is this at STP?

Phase Diagram

Supercritical Fluid?

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

Discussion Q18.10Start

Gas

# molecules = n0

Temperature = T0

pressure = p0

Volume = V0

Discussion Q18.10“Sudden” Hole in wall

Gas Initial State

# molecules = n0

Temperature = T0

pressure = p0

Volume = V0

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