Thermodynamics Lecture 4 Flashcards
What are the Kelvin and Clausius statements? Explain them?
There are two statements that help build the second law of thermodynamics
Kelvin statement:
no process is possible in which the sole result is the absorption of heat from a reservoir and its complete conversion into work. This means that no system can convert all of its heat to work, for example, a heat engine has two reservoirs one with hot water that supplies work and the other with cold water where the rest of the heat would go to
Clausius statement:
Heat does not flow spontaneously from a cool body to a hot body. This means that work needs to be down inorder for heat to flow between a cold and a hot system toward the hot system.
These two statements are LOGICALLY the same
what is the second law of thermodynamics?
The entropy of an isolated system increases in the course of a spontaneous change (Stot > 0)
What is the thermodynamic definition of entropy? How is it used to calculate the entropy change of a sample of perfect gas when it expands isothermally?
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How can we calculate the change of entropy of the surroundings and how did we reach there?
Change of entropy surroundings = qsur/T
This is brought by taking the fact that the entropy of surroundings is considered over a small infinitesimal transfer of heat (qsur), and since the surroundings have a constant volume the energy supplied by heating is known as Usur which is independent of the weather the reaction is reversible or irreversible giving us Usur = qsur.
How do Kelvin’s and Clausis’s statements agree with the second law of thermodynamics?
For Kelvin - if all of the heat was transferred to energy as work, then that means that there is no change in entropy, meaning it is not a spontaneous reaction!!
For Clausis- If heat travels from cold reserve to a hot one then there is no change in entropy therefore no spontaneous
What is the statistical definition of entropy?
entropy = k ln W, k - Boltzmann constant and W - the number of microstates: The number of ways the molecules of the system can be distributed over energy level for the specified total energy
This definition shows how with the more disorderly distribution of matter and a greater dispersal of energy the number of microstates increases.
Why is Entropy inversely proportional to the temperature?
s when you transfer heat to the system new energy states become available which then increases entropy.
The transfer of heat in a system with a high temperature will lead to only a few new energy states meaning that the change in W is small, but the transfer of heat in a low temp system leads to many more energy states becoming available increasing W
Following S = klnW shows that the entropy is inversely proportional to the temperature
What is the Carnot cycle? Explain how it shows entropy as a state function.
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What are the different expressions for efficiency?
Efficiency = Work done/heat absorbed from the hot source
This can be rewritten in terms of heat transaction on its own as the work done equals the difference between the heat supplied to the system and the heat returned to the cold sink
n = (qh - qc)/qh = 1 - qc/qh
Efficiency can also be written in terms of temp since (qc/qh) = (Tc/Th):
n = 1 - Tc/Th
Explain how two coupled systems can have efficiency regardless of their construction.
Given two engines A and B where A is said to have a higher efficiency than B, and B is set to have certain energy transferred as heat from the cold sink as qc then converted to qh and given to the hot sink. A is then more efficient than B so the work that A does is more than the work needed to supply heat Qc to B so the remaining energy is supplied as work and the cold sink remains unchanged between them. This means that heat has been converted into only work going against Kelvin’s statement and indicating the efficiency of A is not more than the efficiency of B.
What is the thermodynamic temperature scale?
It is when an engine works reversibly between a hot source Th and a cold skin with a temperature T, which can be defined as follows:
T = Th(1-n)
What is Clausius’s inequality? What are its uses?
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When energy is lost from the system to the surroundings what is the expression of the entropy of the surroundings? Also when isothermal expansion occurs freely what is the expression of the entropy of the surroundings
For energy is lost from the system
since heat is lost from the system to the surrounds dqsur = -dq therefore:
Ssur = -nRlnVf/Vi
where the sum of Ssur and S system equals zero
for free expansion:
No work will be done (since w = o) and since isothermal expansion U = 0 therefore qsur = 0, so Ssur =0 and the total entropy = Ssys = nRlnVf/Vi, where Stot > 0 (expected for irreversible expansion)
What is the normal transition temperature, Ttrs? How can we Express the transition entropy by this temp? (explain what happens for endo and exo systems)
The normal transition temperature is the temperature at which two phases are at equilibrium, where any transfer of heat between the system and its surroundings is reversible
At a constant pressure p = the change of enthalpy at the transition state, we can express the molar entropy as q = trsH/Ttrs.
For an exothermic process H < 0 the Ssys is negative and the Ssur is equally positive giving us Stot=0 and vice versa for endothermic process
What is the Expression for the entropy at a final Temperature Tf? (When the system goes through a change from Ti to Tf)
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