PHY 2311

PHYSICS 231Lecture 23: Temperature

Remco ZegersWalk-in hour: Tue 4-5 pm

Helproom

PHY 2312

quiz

A boat carrying a large rock is floating on a lake.The rock is thrown overboard and sinks. The waterlevel in the lake (with respect to the shore) rock >> water

a) risesb) dropsc) remains the same

rock in boat:B=MgVdispl waterg =(Mboat+Mrock)gVdispl=(Mboat+Mrock)/water

=Mboat/water+Mrock/water

rock overboard:boat:B=MgVdispl=Mboat/water

rock under water:Vrock=Mrock/rock

<<Mrock/water

so lower total displaced volume

PHY 2313

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 2314

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 2315

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 2316

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 2317

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 2318

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 2319

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 23110

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 23111

Ice

liquid

ice

(g/cm3)

1

0.917

Phase transformation

Ice takes a larger volume than water!

PHY 23112

expanding ice

Someone puts a bottle of water of 1 liter (1E-03 m3)in the freezer. If there is 25cm3 space left in the bottle without water, what will happen when it freezes?

water=1000 kg/m3, so 1 liter is M=1 kg.ice=917 kg/m3=M/Vice=1/Vice

Vice=1/917=1.09E-03 m3=1.09E+03 cm3

(10% larger!). The volume becomes 90cm3

larger, but only 25cm3 is left.The bottle will break.

PHY 23113

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 23114

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 23115

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 109.556 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

The ruler has become larger by 0.044 m, so theperson measures a length smaller by the same amount

PHY 23116

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 23117

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 23118

Demo’s

Bimetallic coil

Expanding and contracting rod