1. Thermodynamics

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3. More Seriously Reviewing Chem 003
Thermodynamics is the study of the relationship between heat and other forms of energy in a chemical or physical process.
We will sometimes use thermochemistry to describe the thermodynamics of chemical reactions.
Thermodynamics became necessary at the end of the 18th century when steam engines were introduced.

4. Steam Engines and Thermodynamics
Steam engines turn heat energy to work. They require a source of heat, but also a cooling bath to condense the steam. The first goal of thermodynamics was to understand how this process could be made more efficient.
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Newcomen engine 1712
Watt engine ~1770

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6. Thermodynamics
The first important step was to realize that heat was a form of energy. Benjamin Thompson was the first to show this, but his experiments were crude.
James Joule measured an exact value for the mechanical equivalent of heat, by measuring the mechanical energy used to rotate a set of paddle wheels in a water container and simultaneously measuring the temperature rise

7. Dry Stuff
The language of thermodynamics can be very dry and uninteresting, but the results are important, and thermodynamics is a powerful tool for analyzing physical and chemical changes.
Thermodynamics divides the universe into a system and its surroundings.
An important characteristic of thermodynamics is the boundary between the system and its surroundings

8. Boundary
An important characteristic of the thermodynamics is the boundary between the system and its surroundings. We can differentiate systems by what can and cannot pass through the boundary.
A system where neither energy or matter can pass through the boundary is called isolated.
A system where energy, but not matter can pass through the boundary is called closed
A system where both energy and matter can pass through the boundary is called open
Thermodynamics cannot be used to calculate the energy of a system but it can calculate the energy passing thru the boundary

9. Internal Energy We know that all systems
are composed of atoms and molecules
that there are forces between these molecules (potential energy)
that the molecules can move (kinetic energy)
The internal energy, U, is the sum of the kinetic and potential energies of the particles making up the system. If there are no forces between the molecules, the energy of the gas is all in the form of kinetic energy
For an ideal atomic gas the total internal energy
U = 3/2 nRT
T is temperature, R, is the gas constant and n is the number of moles. The unit of energy is the Joule.

10. State Properties
The temperature is a property of the system. There are two types of system properties
Extensive, which depend on the size of the system
volume V,
number of moles, n,
internal energy U
Intensive, which are independent of the size of the system
Pressure, p
Temperature, T
These properties describe the state the system is in. They are called STATE properties

11. Boundary
An important characteristic of the thermodynamics is the boundary between the system and its surroundings. We can differentiate systems by what can and cannot pass through the boundary.
A system where neither energy or matter can pass through the boundary is called isolated.
A system where energy, but not matter can pass through the boundary is called closed
A system where both energy and matter can pass through the boundary is called open
Thermodynamics cannot be used to calculate the energy of a system but it can calculate the energy passing thru the boundary

12. Work
Let us talk first about work. For the purposes of this class, work done ON a system will be considered positive, and work done BY a system on its surroundings will be taken as negative.
This is consistent with the chemists point of view. Chemists are interested in the system, what is in the beaker, or flask. OTOH engineers are interested in how much work they can get out of a system, a boiler for example, and they take the sign of work done BY a system on its surroundings as POSITIVE.
We are also going to simplify our lives by ONLY considering pressure volume work, not electrical work, or magnetic interactions or other more esoteric physics type things.

13. Pressure Volume Work
If we have a piston in a cylinder, with a constant pressure P on the piston whose area is A, equals, P = F/A.
If the cylinder moves a distance h, the volume of the cylinder increases by DV=h A, but note that in this case the system piston does work on the surroundings! So the work is negative.
Since W =-Fh in this case W=-PA DV/A or cancelling the As, W=-PDV

14. Units of Work
Looking at the units of pressure and volume it becomes clearer why when pressure is in Pa, and volume in m3, R=8.314 J/mole-K, because then the product of PDV has units of Joules, the SI unit of work.
We must also point out that the pressure we are talking about when we calculate the work is the external pressure on the piston.
A consequence of this is that if there is NO external pressure P=0 and no work is done as the piston flies out of the cylinder

15. A Bit of Calculus
We can generalize this in the following way, for an infinitesimally small change in volume the change in the work
dw = -Pext dV
For the case of the external pressure being constant,
w = Pext DV
If the volume is constant then dV=0 and w = 0! No work is done in a constant volume process either.
If we know how the pressure varies as a function of volume we can calculate the work, for example if pV = nRT then using p=nRT/V we can find (using calculus) that
w = nRT ln(V1/V2)

16. Heat and Temperature
Work is a function not of the end points of the system, but of the path taken between the endpoints of the process.
What about heat.
We talked a bit at the beginning of the mechanical equivalent of heat that established that heat is a form of energy.
W defined temperature in Chem 003 using the ideal gas (thermometer).
By measuring pressure, volume and number of moles of an ideal gas (all things we can do), we can define absolute temperature as T = PV/RT.

17. Heat
If we take two bodies at different temperature, heat is the energy that will flow from the hotter (TH) to the colder (TC) when they are brought into contact (Remember the song).
As a result of losing energy, the hotter body will cool and the colder one warm until they are at the same temperature. There is no heat flow between two bodies at the same temperature. The symbol for heat is q.

18. Units of Work
As with work, the amount of heat going into or out of a system is a function of the process which we are using. In the simplest case, an adiabatic process, no heat flows in or out of a system and q = 0. On the other hand, if we look at a cylinder with a torch under it
Some of the energy that flows into the system as heat, can flow out as work as the volume expands (DV > 0  -PDV < 0 and work is negative, ie, the system does work on the surroundings). Finally, if we lock the piston in place, then the situation is isochoric, and no work can be done so all of the energy that flows into the system stays there.

19. First Law of Thermodynamics
Finally we come to the First Law of Thermodynamics. Remember, the First Law, work is heat and heat is work, so the change in the internal energy is the sum of the work and heat in any process or
DU = q + w

20. First Law
We start by looking at closed and isolated systems, ie, systems where energy can flow in and out, but not particles or molecules.
What forms can energy flow in and out in; well, for the purpose of thermodynamics, in the forms of heat and work. ONLY!! That is all there is.
The change in internal energy (we will use the symbols Uor E for internal energy), does not depend on the path, but the amount of heat absorbed or emitted, and/or the amount of work done by or on the system does. Thus, we have the first law of thermodynamics
dU= q + w = q – PextdV
where dU is independent of the path between the
end points, but the heat exchanged with the
surroundings, q, and the work done on the system,
or by the system, w depends on HOW we get
between points 1 and 2.

21. Vocabulary Constant temperature – isothermal
Constant pressure – isobaric
Constant volume – isochoric
No heat flow across the boundary – adiabatic

22. Ideal Gas The energy of an ideal gas is
The internal energy of the ideal gas depends ONLY on temperature, ie. if you change the temperature of an ideal gas you change the internal energy, if you don’t, you don’t. The result is from the kinetic theory of gases, not from thermodynamics, but it has important consequences for thermodynamics. It means that the only way to change the internal energy of an ideal gas is to change its temperature. In that case it is simple to see that
DU = U2 – U1 = 3/2 nRT2 - 3/2 nRT1 = 3/2 nRDT = 3/2 CV DT

23. Specific Heat of an Ideal Gas
We can now define the specific heat of the ideal gas
The specific heat of a body is the change in the internal energy for a change in temperature. CV is different for diatomic and polyatomic molecules because they vibrational and rotational energy, not only kinetic energy, it is a bit different for a real gas because of the attraction and repulsion of molecules for one another, and it is obviously different for solids and gases. Still, in many cases the specific heat of a body is a constant.

24. Adiabatic and Isochoric Processes
If we have an adiabatic process, by definition q=0, and
w= DU =Cv(T) DT
For an isochoric process DV = 0 and
q= DU =Cp(T) DT

25. Enthalpy If we restrict ourselves to pressure volume work then
DU=q –pDV
So that for a constant VOLUME process DU=q
Very handy IF we lived in a constant volume chamber….but we live in a constant (reasonably) PRESSURE environment
We can put together a state function as a sum of other state functions
H = U + PV
which we call the enthalpy

26. H = q –p D V + p D V + V D p = q + V D p
Why is the Enthalpy Useful
Now we can look at the differential element of the enthalpy
DH = D U + p D V + V D p
Not very interesting until we substitute the first law equation above into this one
H = q –p D V + p D V + V D p = q + V D p
The interesting thing about this function is that at constant PRESSURE
D H = qP

27. Enthalpy and Internal Energy
We can also look at H = U + PV and ask what happens at constant pressure. Then the change in the enthalpy and the change in the internal energy are related by
DH = DU + PconstDV
So for a situation where the change in volume is small (heating a solid or a liquid, a phase change between a solid and a liquid) the change in the internal energy is about the same as the change in the enthalpy.
OTOH, for a process where the change in volume is LARGE (sublimation or vaporization or heating a gas, there will be a substantial difference between the changes in internal energy and enthalpy.

28. Specific Heat at Constant Pressure
For an ideal gas PV = nRT, so we could substitute this into
H = U + PV = U + nRT
Then for one mole