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Слайды и текст к этой презентации:
№2 слайд
![Irreversibility of processes](/documents_6/6c69ec5fba0bfac61e7de55a4bcffbd4/img1.jpg)
Содержание слайда: Irreversibility of processes
There exist many processes that are irreversible:
the net transfer of energy by heat is always from the warmer object to the cooler object, never from the cooler to the warmer
an oscillating pendulum eventually comes to rest because of collisions with air molecules and friction. The mechanical energy of the system converted to internal energy in the air, the pendulum, and the suspension; the reverse conversion of energy never occurs.
№8 слайд
![The Second Law of](/documents_6/6c69ec5fba0bfac61e7de55a4bcffbd4/img7.jpg)
Содержание слайда: The Second Law of Thermodynamics
The Kelvin form:
It is impossible to construct a cyclic engine that converts thermal energy from a body into an equivalent amount of mechanical work without a further change in its surroundings.
Thus it says that for a heat engine it’s impossible for QC=0, or heat engine efficiency e=100%.
№14 слайд
![So, using the last expression](/documents_6/6c69ec5fba0bfac61e7de55a4bcffbd4/img13.jpg)
Содержание слайда: So, using the last expression and the expression for efficiency:
So, using the last expression and the expression for efficiency:
Thus we have proved that the Carnot Efficiency equals
Carnot Engine does not depend on the use of the ideal gas as a working substance.
Carnot Engine is Reversible – it can be used as a refrigerator or heat pump.
Carnot Cycle is the most efficient cycle for given two temperatures Th and Tc.
№17 слайд
![Entropy Measures the amount](/documents_6/6c69ec5fba0bfac61e7de55a4bcffbd4/img16.jpg)
Содержание слайда: Entropy
Measures the amount of disorder in thermal system.
It is a function of state, and only changes in entropy have physical significance.
Entropy changes are path independent.
Another statement of the Second Law of Thermodynamics: The total entropy of an isolated system that undergoes a change cannot decrease.
For infinitesimal changes:
№18 слайд
![Entropy change calculations](/documents_6/6c69ec5fba0bfac61e7de55a4bcffbd4/img17.jpg)
Содержание слайда: Entropy change calculations
Entropy is a state variable, the change in entropy during a process depends only on the end points and therefore is independent of the actual path followed. Consequently the entropy change for an irreversible process can be determined by calculating the entropy change for a reversible process that connects the same initial and final states.
№19 слайд
![So for infinitesimal changes](/documents_6/6c69ec5fba0bfac61e7de55a4bcffbd4/img18.jpg)
Содержание слайда: So for infinitesimal changes:
So for infinitesimal changes:
The subscript r on the quantity dQr means that the transferred energy is to be measured along a reversible path, even though the system may actually have followed some irreversible path. When energy is absorbed by the system, dQr is positive and the entropy of the system increases. When energy is expelled by the system, dQr is negative and the entropy of the system decreases.
Thus, it’s possible to choose a particular reversible path over which to evaluate the entropy in place of the actual path, as long as the initial and final states are the same for both paths.
№20 слайд
![Change of Entropy in a Carnot](/documents_6/6c69ec5fba0bfac61e7de55a4bcffbd4/img19.jpg)
Содержание слайда: Change of Entropy in a Carnot Cycle
Carnot engine operates between the temperatures Tc and Th. In one cycle, the engine takes in energy Qh from the hot reservoir and expels energy Qc to the cold reservoir. These energy transfers occur only during the isothermal portions of the Carnot cycle thus the constant temperature can be brought out in front of the integral sign in expression
Thus, the total change in entropy for one cycle is
№22 слайд
![Reversible Cycle Now consider](/documents_6/6c69ec5fba0bfac61e7de55a4bcffbd4/img21.jpg)
Содержание слайда: Reversible Cycle
Now consider a system taken through an arbitrary (non-Carnot) reversible cycle. Because entropy is a state variable —and hence depends only on the properties of a given equilibrium state —we conclude that
S=0
for any reversible cycle. In general, we can write this condition in the mathematical form
the symbol indicates that the integration is over a closed path.
№23 слайд
![Ideal Gas Reversible Process](/documents_6/6c69ec5fba0bfac61e7de55a4bcffbd4/img22.jpg)
Содержание слайда: Ideal Gas Reversible Process
Suppose that an ideal gas undergoes a quasi-static, reversible process from an initial state Ti, Vi to a final state Tf, Vf .
1st law of thermodynamics: dQr = ΔU + W,
Work: W=pdV,
Internal Energy change: ΔU=nCvdT, (n – moles number)
Equation of state for an Ideal Gas: P=nRT/V,
Thus: dQr = nCvdT + nRTdV/V
Then, dividing the last equation by T, and integrating we get the next formula:
№24 слайд
![- This expression](/documents_6/6c69ec5fba0bfac61e7de55a4bcffbd4/img23.jpg)
Содержание слайда: - This expression demonstrates that S depends only on the initial and final states and is independent of the path between the states. The only claim is for the path to be reversible.
-S can be positive or negative
- For a cyclic process (Ti= Tf, Vi = Vf), S=0. This is further evidence that entropy is a state variable.
№25 слайд
![The Second Law of](/documents_6/6c69ec5fba0bfac61e7de55a4bcffbd4/img24.jpg)
Содержание слайда: The Second Law of Thermodynamics
The total entropy of an isolated system that undergoes a change cannot decrease.
If the process is irreversible, then the total entropy of an isolated system always increases. In a reversible process, the total entropy of an isolated system remains constant.
№26 слайд
![Microscopic States Every](/documents_6/6c69ec5fba0bfac61e7de55a4bcffbd4/img25.jpg)
Содержание слайда: Microscopic States
Every macrostate can be realized by a number of microstates.
Each molecule occupies some microscopic volume Vm. The total number of possible locations of a single molecule in a macroscopic volume V is the ratio
w =V/Vm.
Number w represents the number of ways that the molecule can be placed in the volume, or the number of microstates, which is equivalent to the number of available locations.
If there are N molecules in volume V, then there are
W = wN = (V /Vm)N
microstates, corresponding to N molecules in volume V.
№29 слайд
![Entropy is a measure of](/documents_6/6c69ec5fba0bfac61e7de55a4bcffbd4/img28.jpg)
Содержание слайда: Entropy is a measure of Disorder
The more microstates there are that correspond to a given macrostate, the greater is the entropy of that macrostate.
Thus, this equation indicates mathematically that entropy is a measur measure of disorder. Although in our discussion we used the specific example of the free expansion of an ideal gas, a more rigorous development of the statistical interpretation of entropy would lead us to the same conclusion.
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