PHY 2311

PHYSICS 231Lecture 25: Viscosity (ch.9) and

Temperature (ch. 10)

Remco ZegersWalk-in hour: Thursday 11:30-13:30 am

Helproom

PHY 2312

Applications of Bernoulli’s law: the golf ball

P1

P2

Neglecting the small change in height between thetop and bottom of the golf ball:

P1+½v12= P2+½v2

2

P1-P2= ½(v22- v1

2)

P1

P2

P1-P2= ½(v22- v1

2)=0v2=v1

No pressure difference, no lift

P1-P2= ½(v2-v)2-(v1+ v) 2=0

P2>P1 so:Upward force: the ball goes higherand thus travels faster

PHY 2313

Viscosity

Viscosity: stickiness of a fluidOne layer of fluid feels a largeresistive force when slidingalong another one or along asurface of for example a tube.

PHY 2314

ViscosityContact surface A

fixed

movingF=Av/d

=coefficient of viscosityunit: Ns/m2

or poise=0.1 Ns/m2

PHY 2315

Poiseuille’s Law

How fast does a fluid flowthrough a tube?

Rate of flow Q= v/t=R4(P1-P2)

8L(unit: m3/s)

PHY 2316

Example

PP=106 Pa P=105 Pa

Flow rate Q=0.5 m3/sTube length: 3 m=1500E-03 Ns/m2

What should the radius of the tube be?

Rate of flow Q=R4(P1-P2)

8L

R=[8QL/((P1-P2))]1/4=0.05 m

PHY 2317

Chapter 10 Temperature

R

Potential Energy

0

R

2 atom/molecules

-Emin

The curve depends onthe material, e.g. Emin isdifferent for water andiron

Kinetic energy ~ T

PHY 2318

Solid (low T)

R

Potential Energy

0

Kinetic energy ~ T

-Emin

The temperature (and thus kinetic energy)is so small that the atoms/molecules can onlyoscillate around a fixed position Rmin

Rmin

PHY 2319

Liquid (medium T)

R

Potential Energy

0

Kinetic energy ~ T

-Emin

Rmin

On average, the atoms/molecules like tostick together but sometimes escape andcan travel far.

PHY 23110

Gas (high T)

R

Potential Energy

0

Kinetic energy ~ T

-Emin

Rmin

The kinetic energy is much larger thanEmin and the atoms/molecules move aroundrandomly.

PHY 23111

What happens if the temperature of a substance is increased?

R

0

Kinetic energy ~ T

-Emin

Rmin=Rave(T=0)

T=0: Average distance between atoms/molecules: Rmin

Rave(T>0) > Rmin

T>To: The average distance between atoms/molecules is larger than Rmin:

the substance expands

PHY 23112

Temperature scales

ConversionsTcelsius=Tkelvin-273.5Tfahrenheit=9/5*Tcelcius+32

We will use Tkelvin.

If Tkelvin=0, the atoms/moleculeshave no kinetic energy and everysubstance is a solid; it is called theAbsolute zero-point.

Kelvin

Celsius Fahrenheit

PHY 23113

Thermal expansion

L=LoT

L0

L

T=T0T=T0+T

A=AoT =2

V=VoT =3

length

surface

volume

Some examples:=24E-06 1/K Aluminum=1.2E-04 1/K Alcohol

: coefficient of linear expansion different for each material

PHY 23114

Thermal equilibrium

Low temperatureLow kinetic energyParticles move slowly

High temperatureHigh kinetic energyParticles move fast

Thermal contact

Transfer of kinetic energy

Thermal equilibrium: temperature is the same everywhere

PHY 23115

Zeroth law of thermodynamics

If objects A and B are both in thermal equilibriumwith an object C, than A and B are also in thermalequilibrium.

There is no transfer of energy between A, B and C

PHY 23116

Thermal expansion: an example

In the early morning (T=30oF=272.4K) a person is askedto measure the length of a football field with an aluminummeasure and finds 109.600 m. Another person does the same in the afternoon (T=60oF=289.1K) usingthe same ruler and finds 109.566 m. What is the coefficientof linear expansion of the ruler?

L=LoT so = L/(L0T) T=16.7K L0=109.60 L=109.644-109.600=0.044So: =24E-06 1/K

PHY 23117

A heated ring

A metal ring is heated. What is true:a) The inside and outside radii become largerb) The inside radius becomes larger, the outside

radius becomes smallerc) The inside radius becomes smaller, the outside

radius becomes largerd) The inside and outside radii become smaller

PHY 23118

Demo: bimetallic strips

Application: contact in a refrigerator

top

bottom

top<bottom if the temperature increases,

The strip curls upward, makes contact and switcheson the cooling.

PHY 23119

Demo’s

Bimetallic coil

Expanding and contracting rod

PHY 23120

Water: a special case

Coef. of expansion isnegative: If T dropsthe volume becomeslarger

Coef. Of expansion ispositive: if T drops the volume becomes smaller

Ice is formed (it floats on water)

PHY 23121

Ice

liquid

ice

(g/cm3)

1

0.917

Phase transformation

Ice takes a larger volume than water!