Toni L2 Flashcards
(15 cards)
Describe the statistical basis of entropy in an isolated system
The entropy tends to a maximum as an isolated system approaches equilibrium. Small fluctuations around the observed value are expected but on average the entropy increases until equilibrium is reached
What do we expect that entropy is proportional to and what does this suggest
We expect that the entropy is proportional to the number of molecules, Na. This suggests that entropy and probability are connected by an equation like
S ∝ ln(probability)
What is an ensemble
An ensemble is a hypothetical collection of chemical systems in all the different possible quantum states consistent with fixed value of macroscopic quantities such as N,V,T
What are microstates
A microstate is a specific, detailed configuration of a system meaning the exact positions, energies, and momenta of all particles in the system at a given moment.
Why do microstates matter
Even if two systems have the same macroscopic properties (like temperature, pressure, and volume), they can be made up of many different microstates.
What are macrostates
A macrostate is the overall, large-scale description of a system, defined by a few observable, average properties
What is written below different microstates and what does in mean
Below different microstates will be denoted by a subscript i or j. pi is the probability of a system being picked from the ensemble being in state i with energy Ei
Describe how we calculate the average internal energy using ensembles
Internal energy: U= ∑PiEi
Pi is the probability of a system being picked from the ensemble being in state i with energy Ei
Describe how we calculate the average volume using ensembles
Volume: V= ∑PiVi
Pi is the probability of a system picked from the ensemble being in state i with volume i
What is the gibbs’ formula for the entropy
S= -Kb ∑PilnPi
Kb is the Boltzmann constant
Describe the gibbs formula for the entropy in isolated systems
Entropy of an isolated system never decreases when it reaches the max value the system is in equilibrium. This happens when every state is equally likely if there are Ω different possible states then pi = 1/Ω
S= kbln Ω
How do we measure disorder
We measure disorder by the number of ways the insides can be arranged so that from the outside it looks the same. The logarithm of that number of ways is the entropy
Describe the effect on the macrostate if all the quantum microstates are different
Although the quantum microstates may be different the macrostates (overall behaviour) is going to behave chemically in the same way
What does probability always sum to
1
What is another way of writing R
R = NaKB
Where Na is avogadros constant and Kb is the Boltzmann constant
