Later in the semester, we will find that the probability that a system will occu
ID: 3202262 • Letter: L
Question
Later in the semester, we will find that the probability that a system will occupy an energy state with energy, E, is proportional to exp(-E/RT) if E is in energy per mole. Consider a sample system having only four possible energy states that we denote as States 1, 2, 3 and 4. The energies of the states are, in J/mol, 0, 1000, 2000 and 3000, respectively. Obtain a normalized probability for the system in state I and evaluate the normalization constant at T = 298 K. Calculate the average energy per system that a large number of systems would have at 298 K. Which energy state is the most heavily populated? What is the probability that the combined energy of two separate systems described by the given probability distribution will add to 3000 J/mol? Compute the average total energy the two systems in d.) will have at 298 K. What relationship docs this result have to that obtained in b.)?Explanation / Answer
The gas constant R is 8.314 J / mol. K
Given E is proportional to exp(-E/RT), E is energy per mole.
a) probability
b) mean =
mean= sum(Ep)/sum(p)
1017.789666
c) Probabilty is highest among the energy states. the population is higher if the probability is higher. Hence at energy state 0, probability is higher
d) Probabililty that combined energy add upto 3000J is 1000J and 2000J and addition of their probabilies = 0.66 + 0.44 = 1.1
e) average energy of system combined energy levels at 1000j and 2000j is 1418J
average energy of system combined energy levels at 1000j and 2000j is greater than total average energy
E exp(-E/RT) 0 1 1000 0.667897 2000 0.446087 3000 0.29794Related Questions
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