1. 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. TC: 0°C - freezing of water, 100°C - boiling of water
2. Temperature scales
TC: 0°C - freezing of water, 100°C - boiling of water
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 TC = TF?

3. 3. Thermal expansion ΔL = α L0ΔT
T0, L0
T = T0 + ΔT, L = L0
+ ΔL
ΔL = α L0ΔT
α – linear coefficient of thermal expansion
L = L0 (1 + α ΔT)
ΔA = 2 α A0ΔT
A=L2 L
A = A0 (1 + 2 α ΔT) L
ΔV = β V0ΔT
V=L3
V = V0 (1 + β ΔT)
β = 3α L L
β – volumetric coefficient of thermal expansion

4. Example: An aluminum flagpole is 30 m high
Example: An aluminum flagpole is 30 m high. By how much does its length increase as the temperature increases by 20°C? For aluminum the linear coefficient of thermal expansion is 25x106(1/˚C).
ΔL = α L0ΔT
ΔL - ?
A) 0.8
B) 1.6
C) 2.4
D) 3.2
Question 1: A steel measuring tape is m long at 20.0 ˚C.
The increase in length of the measuring tape upon heating to 40.0 ˚C is ___ mm. For steel,  = 1.2 x 105(1/˚C)
Question 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!

5. II. Ideal gases n = m/μ PV=const P1V1= P2V2 Equation of state
n - number of moles
m - total mass of gas
μ - molar (atomic) mass (“weight”)
1. Isotherms (Boyle’s law): T=const P
PV=const
T2 > T1
P1V1= P2V2 T1 V

6. V/T=const V1/T1= V2/T2 P/T=const P1/T1= P2/T2
2. Isobars (Charles’s law): P=const
V/T=const
V1/T1= V2/T2 V P1
P2 > P1 V
T(K)
T(C) °C
3. Isochors (Gay-Lussaec ): V=const
P/T=const P V1
P1/T1= P2/T2
V2 > V1 P
T(K)
T(°C) °C
0°C

7. Example 1: The temperature of an amount of an ideal gas has been increased twice, while the volume has been increased four times. What happened with the pressure?
T2 = 2T1
V2 = 4V1
P2 /P1 - ?
Example 2: What is the volume of 1 mole of an ideal gas at “standard temperature and pressure”?
n = 1 mol
T = 273 K (0° C)
P = 1 atm = 1.013x105 Pa
V - ?

8. 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.