Entropy Flashcards
What is the mathematical relationship between entropy and the number of microstates?
S = KBln omega, where omega = # of microstates
What is Boltzmann’s constant?
R/NA; ratio of the ideal gas constant to Avogadro’s number
Which steps in this Carnot cycle diagram are isothermal, and which are adiabatic? When is the system doing positive work, and when are the surroundings doing positive work?
A and B are the expansion stages; in this case, the system is doing positive work on the surroundings, and the surroundings are doing negative work
C and D are the compression stages; volume is decreasing. The surroundings are doing positive work on the system.
The net work done ON the system is the negative of the area under the curve
Isothermal paths: A and C
Adiabatic Paths: B and D
Net work performed by the system is positive, and equals the area under A and B minus the area unde
What is the change in internal energy in the Carnot cycle?
As with any cyclic process, the total change in internal energy is 0, so the amount of heat put into the system exactly balances the work done by the system
What part of this diagram represents the amount of heat added to the system? How does this relate to the efficiency?
The area under A represents the heat put into the system at the higher temperature. The ratio of the enclosed area to the total area under A represents the efficiency of the system
What is the significance of the Carnot efficiency?
Showed that the efficiency is proportional to the difference in temperature between the two reservoirs, and the temperature of one would have to be infinitely high or infinitely low for it to be 100% efficient; therefore, this places a fundamental limit on efficiency
The most important result: q/T is a state function, and this is defined as entropy; it is independent of path
What is the mathematical defintion of entropy?
integral (dq/T)
What is the change in entropy of the surroundings?
Because we can assume that the temperature remains constant, it equals: - ΔHsys/T
In an exothermic reaction, the enthalpy change to the system is negative, and the entropy change to the surroundings is positive
Is more work done by an irreversible or reversible expansion?
The work performed by a system expanding irreversibly (due to a sudden drop in external pressure) is always less than it would be if the expansion had been carried out reversibly
Because the external pressure is low throughout, the negative work done on the system is smaller
However, because internal energy is a state function, reversible and irreversible processes have the same ΔU; therefore, the irreversible process must absorb less heat
Is more heat absorbed in an irreversible or reversible expansion?
More heat is absorbed in a reversible one, because there is a greater amount of work being done due to the higher external pressure
What is the inequality of Clausius and how is it defined?
Entropy is defined as the qrev/T
For an irreversible isothermal process, qirrev < qrev,so we conclude that:
ΔS > qirrev/T
Meaning: in any spontaneous proces, the heat absorbed by the system from the surroundings at the same temperature is always less than TΔS
What happens to the total entropy in a reversible and irreversible process?
- In a reversible process, the total entropy of a system plus its surroundings is unchaged
- In an irreversible (spontaneous) process, the entropy of the system plus surroundings increases
Why does Gibbs Free Energy change with temperature?
Example: phase transitions, temperature of transition = 273 K
The entropy change of the system is essentially independent of temperature – it’s equal to the heat transferred when the process is in equilibrium, so it equals q/273, and this value doesn’t really change
On the other hand, the entropy of the surroundings depends on the actual temperature at which it’s carried out – so if the reaction occurred at 200K, the entropy change would be q/200, and the increase in entropy of the surroundings would exceed the decrease in entropy of the system
