Problem 1 - microscopic definition of entropy In Fig. 20.1 of the textbook, the

Question

Problem 1 - microscopic definition of entropy In Fig. 20.1 of the textbook, the process described is an irreversible adiabatic expansion of an ideal gas into a vacuum (namely, into an evacuated flask). In our analysis of this problem in class from a microscopic viewpoint, we established that the entropy increases for this process because the equilibrium state of the system before the expansion (all gas particles in the left flask) has a smaller W factor than the equilibrium state of the system after expansion (half the gas particles in each flask). Now, if we double the volume of the right flask, the entropy increase is even greater (see question 2). Provide a convincing argument to establish this from the microscopic viewpoint. mic

Explanation / Answer

The entropy (S) is the measure of the number of microscopic states (N) available to be occupied by a system. When the volume of the right flask is doubled, there is an increase is the number of states that can be occupied by a particle of our system. Initially the sytem was in a flask of volume V that expands to a volume 2V. But now it expands to a volume of 3V. Thus giving an even higher W factor and higher entropy value.

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