1. Thermodynamics
Chapter 12

2. Thermodynamics Vocabulary
Thermo (heat) dynamics (transfer)
Thermodynamic systems describe many many particles (molecules) which obey Newton’s laws for dynamics but which would be difficult to analyze due to their numbers.
We use macroscopic means for analysis of these systems of many particles - involving quantities such as pressure, volume and temperature.

3. Thermodynamics Vocabulary
System – a definite quantity of matter enclosed by boundaries or surfaces. Boundaries need not have definite shape or volume.
Thermally Isolated System – system in which no heat is transferred into or out of the system.
Heat Reservoir – a large separate system with unlimited heat capacity (any amount of heat can be withdrawn or added without appreciably changing the temperature).

4. State of a System
Kinematics equations describe the motion of an object using variables which change but are related (displacement, velocity, acceleration). Motion can be described at any moment using these quantities.
Thermodynamic systems can be described similarly using relationships between pressure, volume and temperature. Relationships between these variables are called Equations of State, and describe the state of the system at any moment.

5. p-V Diagrams
A pressure-volume diagram shows how pressure changes as a function of volume.
Each coordinate (V, p) specifies a state of the system. Pressure and volume are given and temperature may be found indirectly.
A process is any change in the state of a system. Processes may be reversible or irreversible.

6. p-V Diagrams

7. First Law of Thermodynamics
First Law describes how heat transferred to a system, Q, relates to internal energy of the system, U, and work done by the system, W.
Recall, Q = heat added; W = work done; U = internal energy (see page 360)
First Law of Thermo: Q = ΔU + W

8. First Law of Thermodynamics
Q = ΔU + W
If a system absorbs 2000J of heat and does 800J of work (expanding perhaps) then the internal energy will increase by 1200J.

9. Example 1
A 65 kg worker shovels coal for 3.0 hours. During this process he does work at a rate of 20 W and loses heat to the environment at a rate of 480 W. Ignoring the loss of water by perspiration, how much fat will the worker lose? The energy value of fat is 9.3 kcal/g/

10. Keep Track of Signs
Positive work is done when force and displacement are in the same direction (expanding gas).
Q is positive when heat is added, negative when heat is lost.

11. Work from a p-V Diagram Work = F·Δx pA ·Δx pΔV
On a pressure-volume diagram, work done by a system is equal to the area under the p-V curve.

12. Isothermal Process Isothermal means constant temperature.
Internal Energy remains constant if temperature remains constant.
Q = ΔU + W ; ΔU=0
Q = W

13. Isothermal Process First Law of Thermo: Q = ΔU + W But for isothermal,
Q = W
All added heat goes into
work done by expanding gas.
Work = nRT ln(Vf/Vi)

14. Isobaric Process A constant pressure process is called isobaric.
Work in isobaric process is
W = p(V2 – V1) = pΔV
So Q = ΔU + pΔV

15. Example
Two moles of a monatomic ideal gas initially at 0° and 1.0 atm are expanded to twice their original volume using two different processes. They are expanded isothermally and then, starting in the same initial state, they are expanded isobarically. During which process does the gas do more work? Find the work done in each case.

16. Isometric Process
Isometric means isovolumetric … it describes a process at constant volume.
If volume doesn’t change, no work is done.
Q = ΔU

17. Example
Many ‘empty’ aerosol cans contain remnant propellant gases under approximately 1 atm of pressure and 20°C. They display the warning “Do not dispose of this can in an incinerator”. What is the change in internal energy of such a gas if 500J of heat is added to it, raising the temperature to 2000°F? What is the final pressure of the gas?

18. Adiabatic Process
Adiabatic means no heat is transferred into or out of the system.
Q = 0 so first law of thermodynamics becomes
ΔU = -W
If internal energy increases, work has been done

19. Adiabatic Process adiabatic expansion
Pressure and volume are related along an adiabat by p1V1γ = p2V2γ
Work done in an adiabatic process can be found using
Wadiabatic = (p1V1 – p2V2) / (γ - 1)
γ = 1.67 for monotonic gas, 1.40 for diatomic

20. Summary Isothermal T = constant ΔU = 0 Q = W Isobaric p = constant
Process
Characteristic
Result
First Law
Isothermal
T = constant
ΔU = 0
Q = W
Isobaric
p = constant
W = pΔV
Q = ΔU + pΔV
Isometric
V = constant
W = 0
Q = ΔU
Adiabatic
Q = 0
ΔU = -W

21. Example
Blowing Air
A sample of helium expands to triple its initial volume adiabatically in one case and isothermally in another. It starts from the same initial state in both cases. The sample contains 2.00mol of helium initially at 20 ºC and 1.0 atm.
a) during which process does the gas do
more work?
b) Calculate the work done in each process.

22. Second Law of Thermodynamics
Second Law provides a way to predict the direction in which thermal processes proceed.
Heat flows spontaneously from a warmer body to a cooler body
Heat energy cannot be completely transformed into mechanical work

23. Entropy Entropy is a measure of a system’s ability to do work.
Entropy is a measure of disorder.
A system naturally moves towards greater disorder. More order = lower entropy; more disorder = higher entropy.
ΔS>0 for natural processes

24. Entropy
ΔS = Q / T [Joules / Kelvin] gives a change in entropy at a constant temperature, T.
ΔS = increase in entropy
Entropy increases if Q is positive; temperature must be measured in Kelvin.

25. Examples
While doing physical exercise at 34°C, an athlete loses kg of water per hour by evaporation of perspiration from his skin. Estimate the change in entropy of the water as it vaporizes. Latent heat of vaporization for perspiration is
24.2X105 J/kg

26. Heat Engines Heat engines convert heat energy into useful work
Examples are electric turbines (power plants) and internal combustion engines (automobiles).
‘Heat in’ generates work; gas must be brought to original state via a compression which takes work.
Wnet is the enclosed area.

27. Heat Engines Net Work = Work done by gas - Work done on gas
Wnet = Wexp – Wcom
For a cycle, ΔU = 0 so…
Wnet = Qh – Qc

28. Efficiency Efficiency is the ratio of net work out to heat in.
ε = Wnet / Qin
ε = (Qh – Qc) / Qh
ε = 1 – Qc/Qh

29. Efficiency
No engine is perfectly efficient! More heat (energy) is required (Qh) than useful work created!!
Why???

30. Example
A leaf-blower engine absorbs 800J of heat energy from a high temperature reservoir (the ignited gas-air mixture) and exhausts 700J to a low temperature reservoir (the outside air). What is the efficiency?

31. Example
You have mol of an ideal monatomic gas that follows the cycle shown. The pressure and temperature on the lower left is 1.00 atm and 20 °C. Assume that the pressure doubles during the isometric pressure increase and the volume doubles during the isobaric expansion. Find the efficiency.

32. Otto Cycle – 4 Stroke Engine

33. Carnot Cycle
A Carnot cycle is a cycle consisting of two isotherms and two adiabats.
Sadi Carnot discovered that efficiency can be maximized by a cycle absorbing heat from a constant high temperature reservoir, Th (isotherm), and exhausting it to a constant low temperature reservoir, Tc (isotherm).

34. Carnot Cycle Efficiency of a Carnot Cycle: ε = (Th – Tc)/Th
= 1 – Qc/Qh