Thermodynamics

1
Thermodynamics

• An Introduction

2
Total energy

• E U K Eint
• U potential energy
• K kinetic energy
• Eint internal or thermal energy

3
Temperature

• Measure of kinetic energy of molecules.
• Difference in temperature causes heat energy to
  be exchanged between bodies in contact.

4
Heat

• Internal energy transferred between bodies in
  contact.
• Temperature difference drives heat transfer.

5
Thermal Equilibrium

• Occurs when two bodies are at the same
  temperature.
• No heat is transferred between bodies in thermal
  equilibrium.

6
Ideal Gas Law

• P1V1/T1 P2V2/T2
• P1, P2 initial and final pressure
• V1, V2 initial and final volume
• T1, T2 initial and final temperature (in Kelvin!)

7
Ideal Gas Equation

• PV nRT
• P pressure
• V volume
• n number of moles
• R gas law constant
• T temperature in Kelvin

8
Ideal Gas Equation

• PV NkT
• P pressure
• V volume
• N number of molecules
• k Boltzmans constant
• T temperature in Kelvin

9
Ideal Gas Equation

• R NAk
• R ideal gas constant
• 8.31 J/mol K
• NA Avagadros number
• k Boltzmans constant
• 1.38 x 10-23 /mol K

10
1

• Gases consist of a large number of molecules that
  make elastic collisions with each other and the
  walls of the container.

11
2

• Molecules are separated, on average, by large
  distances and exert no forces on each other
  except when they collide.

12
3

• There is no preferred position for a molecule in
  the container, and no preferred direction for the
  velocity.

13
Average Kinetic Energy

• Kave 3/2 kBT
• Kave average kinetic energy (Joules)
• kB Boltzmanns Constant (1.38 x 10-23 J/K)
• T Temperature (K)

14
System
Environment
15
Boundary

• Doesnt let mass in or out.
• May or may not let in heat.
• May or may not let the system be compressed or
  allow it to expand.

16
First Law of Thermodynamics

• ?U Q W
• ?U change in internal energy of system
• Q heat added to the system
• W work done on the system

17
Isothermal Process
PV nRT
DT 0 (constant T)
18
Isobaric Process
PV nRT
DP 0 (constant P)
19
Isometric Process
PV nRT
DV 0 (constant V)
20
Adiabatic process
Q 0 (insulated)
21
Work done BY gases
Wgas p?V
Positive work
?V
Wenv -p?V
Negative work
22
Work done ON gases
Wgas p?V
Negative since ?V is negative
Wext -p?V
Positive since ?V is negative
23
Work at constant pressure
WAB gt WCD
P
P2
Where we are considering work done BY the gas

WAB p2?V
P1
WCD p1?V
V
24
Work is path dependent
WABD gt WACD
P
Where we are considering work done BY the gas
WABD
WACD
V
25
Second Law of Thermodynamics

• No process is possible whose sole result is the
  complete conversion of heat from a hot reservoir
  into mechanical work.
• - Kelvin-Plank statement

26
Second Law of Thermodynamics

• No process is possible whose sole result is the
  transfer of heat from a cooler to a hotter body.
• - Clausius statement

27
Heat Engines

• Convert heat into useful work.
• Always have waste heat.
• Efficiency can be used to tell how much heat is
  needed to produce a given amount of work.

28
Heat Transfer
QH QC
29
Heat Engines
Engine
QH QC W
30
Clarification

• A heat engine is not something that produces
  heat. A heat engine transfers heat from hot to
  cold, and does mechanical work in the process.

31
Isothermal vs Adiabatic Expansion of Gases
W ?U
32
Carnot Cycle
QH QC W Efficiency W/QH
Work
33
Efficiency of Heat Engine

• Efficiency W/QH
• (QH - QC)/QH
• Carnot Efficiency (TH - TC)/TH
• Efficiency Efficiency100

34
Entropy

• is disorder, or randomness. The entropy of the
  universe is increasing.
• Sort of like the entropy in your room.

35
Entropy

• ?S Q/T
• ?S Change in entropy (J/K)
• Q Heat going into system (J)
• T Kelvin temperature (K)