Question

1. Suppose you had 10 identical molecules enclosed by a box. At a given instant, one molecule has an energy of 100 Joules, and the others are all stationary. (A) What is the average kinetic energy of the 10 molecules? (B) Is this a situation of high or low entropy? (C) What happens to the energy and entropy of the molecules in the box as time passes? Does your answer depend on the insulation of the box?

2. Which is more disordered: a 1000 word paper with 1 word misspelled, or a 2000 word paper with 2 mistakes? Compare the entropy of the two situations.

Answer 1

1. (A) you have 10 molecules. The energy of one molecule is 100 Joules.

Then we calculate an average energy

KE_av = 100J (1molec) / 10molec. KE_av= 10 J per molecula

(B) The entropy depends on the disorder of the system. If we have only one of the 10 molecules moving the entropy of the system is low.

(C)  While the Temperatura is constant, la kinetic energy will remain unchanged over time. So yes, it all depends on the insulation of the box.

2. The relation between the two papers remains the same. Because 1000 to 1 is the same relation that 2000 to 2. So the entropy in the two situations is the same because is the same quantity of microstates.