Thermodynamics
I. Temperature
1. Thermal equilibrium. Zeroth law of thermodynamics
a) We need a thermometer
b) Thermal equilibrium
c) Zeroth law:
If C is in thermal equilibrium with both A and B,
then A and B are also in thermal equilibrium with each other
d) Temperature
Two systems are in thermal equilibrium if and only if they
have the same temperature
2. Temperature scales
TC:
0°C - freezing of water,
TF = (9/5) TC+32
Tk = TC +273.15
100°C - boiling of water
TC = (5/9) (TF - 32)
The temperature of an ideal monatomic gas is a
measure related to the average kinetic energy
of its atoms as they move. In this animation, the
size of helium atoms relative to their spacing is
shown to scale under 1950 atmospheres of
pressure. These room-temperature atoms have
a certain, average speed (slowed down here
two trillion fold).
Heating a body, such as a segment of
protein alpha helix, tends to cause its
atoms to vibrate more, and to cause it
to expand or change phase.
http://en.wikipedia.org/wiki/Temperature
Question
Two thermometers are in thermal
equilibrium with each other. One
reads in ˚C and one reads in ˚F.
At what temperature do they read the
same number? That is, at what
temperature is T(˚C) = T(˚F)?
1.
2.
3.
4.
5.
40
20
0
-20
-40
2a. The absolute (Kelvin) scale and gas thermometer
The Gay-Lussaec law
For an ideal gas at V=const:
P1/T1= P2/T2
P
T(°C)
-273.15°C
P/T=const
0°C
P
V1
V2 > V1
P
0
273.15
T(K)
Definition:
Ttriple = 273.16 K = 0.01 ºC
T(K)
P
P
T  Ttriple
 273.16
Ptriple
Ptriple
3. Thermal expansion
T0, L0
T = T0 + ΔT,
ΔL = α L0ΔT
L = L0 + ΔL
L - L0 = α L0ΔT
L = L0 (1 + α ΔT)
ΔV = β V0ΔT
V = V0 (1 + β ΔT)
β = 3α
V=L3
L
V = L3 =[L0 (1 + α ΔT)]3 = L0 3 (1 + α ΔT) 3 ~
~ L0 3 (1 + 3α ΔT)
ΔA = 2 α A0ΔT
A= A0 (1 + 2 α ΔT)
L
L A=L2
L
Example 1: An aluminum flagpole is 33m high. By how mach
does its length increase as the temperature increases by 15 °C?
L0 = 33 m
ΔT = 15°C
α = 25x10-6 (C ° )-1
ΔL - ?
ΔL = α L0ΔT
ΔL = [25x10-6 (C ° )-1]x (33 m) x (15°C) =1.2x10-2 m
Example 2: A donut shaped piece of metal is cooled and its temperature
decreases. What happened with inner and outer radii after cooling?
Both radii decrease!
Question
A steel measuring tape is 10.000 m
long at 20 ˚C.
The increase in length of the
measuring tape upon heating to 40 ˚C
is ___ mm.
(For steel,  = 1.2 x 105/˚C)
1.
2.
3.
4.
0.8
1.6
2.4
3.2