1. Thermodynamics

2. Intensive and extensive properties
Intensive properties:
System properties whose magnitudes are independent of the total amount, instead, they are dependent on the concentration of substances
Extensive properties
Properties whose value depends on the amount of substance present

3. State and Nonstate Functions
Euler’s Criterion
State functions
Pressure
Internal energy
Nonstate functions
Work
Heat

6. Energy Capacity to do work
Internal energy is the sum of the total various kinetic and potential energy distributions in a system.

16. Heat
The energy transferred between one object and another due to a difference in temperature.
In a molecular viewpoint, heating is:
The transfer of energy that makes use of disorderly molecular motion
Thermal motion
The disorderly motion of molecules

17. Exothermic and endothermic
Exothermic process
A process that releases heat into its surroundings
Endothermic process
A process wherein energy is acquired from its surroundings as heat.

19. Work Motion against an opposing force.
The product of an intensity factor (pressure, force, etc) and a capacity factor (distance, electrical charge, etc)
In a molecular viewpoint, work is:
The transfer of energy that makes use of organized motion

34. Free expansion
Isothermal
Isochoric
Isobaric
Adiabatic ΔU
q+w q
nRT ln 𝑉𝑓 𝑉𝑖
wrev
-nRT ln 𝑉𝑓 𝑉𝑖
wirrev
-pextΔV

35. Adiabatic Changes q=0! Therefore ΔU = w
In adiabatic changes, we can expect the temperature to change.
Adiabatic changes can be expressed in terms of two steps: the change in volume at constant temperature, followed by a change in temperature at constant volume.

36. Adiabatic changes
The overall change in internal energy of the gas only depends on the second step since internal energy is dependent on the temperature.
ΔUad = wad = nCvΔT for irreversible conditions

37. Adiabatic changes
How to relate P, V, and T? during adiabatic changes? Use the following equations!
ViTic = VfTfc
Where c = Cv/R
PiViγ = PfVfγ
Where γ = Cp/Cv

38. Adiabatic changes
What about for reversible work?
Wad,rev = 𝑛𝑅∆𝑇 1−γ

41. Free expansion Isochoric Isobaric Adiabatic
Isothermal
Isochoric
Isobaric
Adiabatic ΔU
nCvΔT
q+w w q
nRT ln 𝑉𝑓 𝑉𝑖
or -wirrev
nCpΔT or –wirrev
wrev
-nRT ln 𝑉𝑓 𝑉𝑖
- 𝑉𝑖 𝑉𝑓 𝑝d𝑉
𝑛𝑅∆𝑇 1−γ
wirrev
-pextΔV
=-nCvΔT
=-pextΔV
ViTic = VfTfc
Where c = Cv/R
Cp – Cv = R
PiViγ = PfVfγ
Where γ = Cp/Cv

42. Exercise
10 g of N2 is obtained at 17°C under 2 atm. Calculate ΔU, q, and w for the following processes of this gas, assuming it behaves ideally: (5 pts each)
Reversible expansion to 10 L under 2 atm
Adiabatic free expansion
Isothermal, reversible, compression to 2 L
Isobaric, isothermal, irreversible expansion to m3 under 2 atm
Isothermal free expansion
(Homework) 2 moles of a certain ideal gas is allowed to expand adiabatically and reversibly to 5 atm pressure from an initial state of 20°C and 15 atm. What will be the final temperature and volume of the gas? What is the change in internal energy during this process? Assume a Cp of 8.58 cal/mole K (10 pts)
1 cal = J
-46°C, 7.45 L

46. Enthalpy
As can be seen in the previous derivation, at constant pressure:
ΔH = nCpΔT
Provided that the system does not perform additional work.

47. Relating ΔH and ΔU in a reaction that produces or consumes gas
ΔH = ΔU + pΔV,
When a reaction produces or consumes gas, the change in volume is essentially the volume of gas produced or consumed.
pΔV = ΔngRT, assuming constant temperature during the reaction
Therefore:
ΔH = ΔU + ΔngRT

48. Dependence of Enthalpy on Temperature
The variation of the enthalpy of a substance with temperature can sometimes be ignored under certain conditions or assumptions, such as when the temperature difference is small.
However, most substances in real life have enthalpies that change with the temperature.
When it is necessary to account for this variation, an approximate empirical expression can be utilized

49. Dependence of Enthalpy on Temperature
𝑑𝐻=𝐶𝑝𝑑𝑡
𝐻 (𝑇𝑖) 𝐻 (𝑇𝑓) 𝑑𝐻= 𝑇𝑖 𝑇𝑓 𝐶𝑝 𝑑𝑡
Where the empirical parameters a, b, and c are independent of temperature and are specific for each substance
Integrate resulting equation for Cp appropriately in order to get ΔH

50. ΔU nCvΔT q+w w q nRT ln 𝑉𝑓 𝑉𝑖 or -wirrev nCpΔT or –wirrev wrev
Free expansion
Isothermal
Isochoric
Isobaric
Adiabatic ΔU
nCvΔT
q+w w q
nRT ln 𝑉𝑓 𝑉𝑖
or -wirrev
nCpΔT or –wirrev
wrev
-nRT ln 𝑉𝑓 𝑉𝑖
𝑛𝑅∆𝑇 1−γ
wirrev
-pextΔV
- 𝑉𝑖 𝑉𝑓 𝑝d𝑉
=-nCvΔT
=-pextΔV ΔH
0 (for ideal gas)
=ΔU + pΔV
=nCvΔT
=nCpΔT

51. Problem
Calculate the change in molar enthalpy of N2 when it is heated from 25°C to 100°C.
N2(g) Cp,m (J/mol K) a =28.58; b = 3.77x10-3 K;
c = x105 K2

52. Problem
Water is heated to boiling under a pressure of 1.0 atm. When an electric current of 0.50 A from a 12V supply is passed for 300 s through a resistance in thermal contact with it, it is found that g of water is vaporized. Calculate the per mole changes in internal energy and enthalpy at the boiling point.
* 1 A V s = 1 J

53. Thermochemistry
The study of energy transfer as heat during chemical reactions.
This is where endothermic and exothermic reactions come in.
Standard enthalpy changes of various kinds of reactions have already been determined and tabulated.

54. Standard Enthalpy Changes
Defined as the change in enthalpy for a process wherein the initial and final substances are in their standard states
The standard state of a substance at a specified temperature is its pure form at 1 bar
Standard enthalpy changes are taken to be isothermal changes, except in some cases to be discussed later.

55. Enthalpies of Physical Change
The standard enthalpy change that accompanies a change of physical state is called the standard enthalpy of transition
Examples: standard enthalpy of vaporization (ΔvapHƟ) and the standard enthalpy of fusion (ΔfusHƟ)

58. Enthalpies of chemical change
These are enthalpy changes that accompany chemical reactions.
We utilize a thermochemical equation for such enthalpies, a combination of a chemical equation and the corresponding change in standard enthalpy.
Where ΔHƟ is the change in enthalpy when the reactants in their standard states change to the products in their standard states.

61. Hess’s Law
Standard enthalpies of individual reactions can be combined to acquire the enthalpy of another reaction. This is an application of the First Law named the Hess’s Law
“The standard enthalpy of an overall reaction is the sum of the standard enthalpies of the individual reactions into which a reaction may be divided.”

62. Hess’s Law: Example

63. Standard Enthalpies of Formation
The standard enthalpy of formation, denoted as ΔfHƟ, is the standard reaction enthalpy for the formation of 1 mole of the compound from its elements in their reference states.
The reference state of an element is its most stable state at the specified temperature and 1 bar.
Example: Benzene formation
6 C (s, graphite) + 3 H2(g)  C6H6 (l) ΔfHƟ = 49 kJ/mol

66. The temperature dependence of reaction enthalpies
dH = CpdT
From this equation, when a substance is heated from T1 to T2, its enthalpy changes from the enthalpy at T1 to the enthalpy at T2.

68. Kirchhoff’s Law
It is normally a good approximation to assume that ΔrCpƟ is independent of temperature over a limited temperature range, but when the temperature dependence of heat capacities must be taken into account, we can utilize another equation

69. Dependence of Enthalpy on Temperature
𝑑𝐻=𝐶𝑝𝑑𝑡
𝐻 (𝑇𝑖) 𝐻 (𝑇𝑓) 𝑑𝐻= 𝑇𝑖 𝑇𝑓 𝐶𝑝 𝑑𝑡
Where the empirical parameters a, b, and c are independent of temperature and are specific for each substance
Integrate resulting equation for Cp appropriately in order to get ΔH

70. Kirchhoff’s Law: Example

71. Exercise