1. PHYSICS 231 Lecture 23: Temperature
Remco Zegers
Walk-in hour: Tue 4-5 pm
Helproom
PHY 231

2. quiz A boat carrying a large rock is floating on a lake.
The rock is thrown overboard and sinks. The water
level in the lake (with respect to the shore) rock >> water
rises
drops
remains the same
rock in boat:
B=Mg
Vdispl  waterg =(Mboat+Mrock)g
Vdispl=(Mboat+Mrock)/water
=Mboat/water+Mrock/water
rock overboard:
boat:
Vdispl=Mboat/water
rock under water:
Vrock=Mrock/rock
<<Mrock/water
so lower total displaced volume
PHY 231

3. Kinetic energy ~ T Chapter 10 Temperature Potential Energy -Emin R
-Emin R
The curve depends on
the material, e.g. Emin is
different for water and
iron R
2 atom/molecules
PHY 231

4. Solid (low T) Kinetic energy ~ T Potential Energy Rmin R -EminR
-Emin
The temperature (and thus kinetic energy)
is so small that the atoms/molecules can only
oscillate around a fixed position Rmin
PHY 231

5. Liquid (medium T) Potential Energy Kinetic energy ~ T Rmin R -EminR
-Emin
On average, the atoms/molecules like to
stick together but sometimes escape and
can travel far.
PHY 231

6. Gas (high T) Kinetic energy ~ T Potential Energy Rmin -Emin R
-Emin R
The kinetic energy is much larger than
Emin and the atoms/molecules move around
randomly.
PHY 231

7. What happens if the temperature of a substance is increased?
Rmin=Rave(T=0)
Kinetic energy ~ T
Rave(T>0) > Rmin
T>To: The average distance
between atoms/molecules is
larger than Rmin:
the substance expands R
T=0: Average distance between
atoms/molecules: Rmin
-Emin
PHY 231

8. Temperature scales Conversions Tcelsius=Tkelvin-273.5
Tfahrenheit=9/5*Tcelcius+32
We will use Tkelvin.
If Tkelvin=0, the atoms/molecules
have no kinetic energy and every
substance is a solid; it is called the
Absolute zero-point.
Celsius
Fahrenheit
Kelvin
PHY 231

9. Thermal expansion L=LoT A=AoT =2 V=VoT =3 
length L
L=LoT
surface
A=AoT =2
volume
V=VoT =3  L0
: coefficient of linear expansion
different for each material
Some examples:
=24E-06 1/K Aluminum
=1.2E-04 1/K Alcohol
T=T0
T=T0+T
PHY 231

10. Water: a special case Coef. of expansion is negative: If T drops
the volume becomes
larger
Coef. Of expansion is
positive: if T drops the volume becomes smaller
Ice is formed (it floats on water)
PHY 231

11. Ice  (g/cm3) liquid 1 Phase transformation 0.917 ice
Ice takes a larger volume than water!
PHY 231

12. water=1000 kg/m3, so 1 liter is M=1 kg. ice=917 kg/m3=M/Vice=1/Vice
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 231

13. Thermal equilibrium Thermal contact High temperature Low temperature
High kinetic energy
Particles move fast
Low temperature
Low kinetic energy
Particles move slowly
Transfer of kinetic energy
Thermal equilibrium: temperature is the same everywhere
PHY 231

14. Zeroth law of thermodynamics
If objects A and B are both in thermal equilibrium
with an object C, than A and B are also in thermal
equilibrium.
There is no transfer of energy between A, B and C
PHY 231

15. Thermal expansion: an example
In the early morning (T=30oF=272.4K) a person is asked
to measure the length of a football field with an aluminum
measure and finds m. Another person
does the same in the afternoon (T=60oF=289.1K) using
the same ruler and finds m. What is the coefficient
of linear expansion of the ruler?
L=LoT so = L/(L0T)
T=16.7K L0= L= =0.044
So: =24E-06 1/K
The ruler has become larger by m, so the
person measures a length smaller by the same amount
PHY 231

16. A heated ring A metal ring is heated. What is true:
The inside and outside radii become larger
The inside radius becomes larger, the outside radius becomes smaller
The inside radius becomes smaller, the outside radius becomes larger
The inside and outside radii become smaller
PHY 231

17. Demo: bimetallic strips
top
bottom
Application: contact in a refrigerator
top<bottom if the temperature increases,
The strip curls upward, makes contact and switches
on the cooling.
PHY 231

18. Demo’s
Bimetallic coil
Expanding and contracting rod
PHY 231