Download Internal energy is a characteristic of a given state – it is the same no

Internal energy is a characteristic of a given state – it is the same no matter how you arrived at that state.
So if you want to know how much the internal energy of your system changed from one state to another,
you can follow any reasonable path between the two states.
There are a few simple paths that we can look at and find some basic rules:
Isobaric: P = 0
So you can raise temp (and therefore internal energy), but volume has to increase so that pressure does
not change (that means that the system has to do work)
Q = U + W but work done is W = Fd = PAd = PV
Isometric: V = 0
So you can change the pressure and the temperature together, but the system does not move. That
means that no work is done!
Q = U
Isothermal: T = 0 therefore U = 0
The temperature does not change so the system can’t gain any internal energy. Therefore any heat put
into the system will be used to do work
Q=W
Adiabatic: Q = 0
This happens when there is no heat passing into or out of the system. Practically, such a situation is
impossible – heat always passes between objects at different temperature. However, some processes
happen so fast that there isn’t time for significant heat transfer or there could be very well insulated
systems that slow down heat transfer a lot, so that they are very close to adiabatic. Examples include the
expansion stroke in your car
0 = U + W
or
U = -W
Second Law of Thermodynamics:
When you put an ice cube in a glass of boiling water, the ice cube melts and the water gets colder. Can
you imagine the opposite happening: a glass of water spontaneously getting warm as an ice cube forms
in its midst. That is perfectly consistent with the first law, but we never see it happen.
The second law attempts to address this inconsistency. Several variations in statement:
Heat will not spontaneously from a cool object to a hot object.
In a cycle of thermodynamic processes, heat energy cannot be completely transformed into mechanical
work.
It is impossible to construct a perpetual motion machine (?)
Entropy:
Second law is later connected to a quantity that Rudolf Clausius constructs – entropy
Entropy is a function of the state of the system. (I believe)
S = Q/T
T in kelvin
Calculate entropy change in phase change or calculate entropy change with small temperature change
(approximate with average temperature)
Small temp change or small energy transfer between two objects at different temps. Look at total
entropy!
The equations show that the entropy for a closed system never decreases! And there are very few
limited situations where it doesn’t increase. (This is equivalent to second law of thermodynamics.)
Boltzmann links entropy with microscopic states of the system:
S = k ln (n) Where n is the number of microstates that link to the particular macrostate observed. k is
boltzmann’s constant – shows up in lots of places.
Efficiency
Since the concept of entropy shows us that engines inevitably use up their energy supply – by rendering
it mixed and useless.
Kelvin’s statement of second law:
No cyclic heat engine can convert its heat input completely to work.
If this is true, we might ask how well they use the energy given.
Efficiency: Work done for the amount of energy put in
 = Wout/Ein = Wout/Qin
Q = U + W and we should look at a full cycle Qnet = Qhot-Qcold = 0 + Wnet
 = (Qhot – Qcold)/Qhot
Ideal engine sought by Sadi Carnot – created idealized engine which we call Carnot engine (Two
isothermal processes and two adiabatic processes). This engine is the most efficient engine possible.
Since all heat transferred during isothermal processes so we can apply our entropy equation to simplify
the efficiency formula:
C = (ThotS – TcoldS)/ThotS = (Thot – Tcold)S/ ThotS = (Thot – Tcold)/Thot = 1 - Tcold/Thot
Questions for review
http://www.ac.wwu.edu/~vawter/PhysicsNet/Topics/ProblemsLists/ProblemsList.html#Thermal
http://www.uvi.edu/Physics/SCI3xxWeb/Energy/TDProblems.html
http://www.dctech.com/physics/help/thermodynamics/
http://www.physics.uc.edu/~sitko/CollegePhysicsIII/12-Thermodynamics/Thermodynamics.htm