Indicate whether each statement is true or false. (a) ΔS is a state function. (b) If a system undergoes a reversible change, the entropy of the universe increases. (c) If a system undergoes a reversible process, the change in entropy of the system is exactly matched by an equal and opposite change in the entropy of the surroundings. (d) If a system undergoes a reversible process, the entropy change of the system must be zero.

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Welcome back everyone in this example we need to determine whether the below statements are either true or false. Beginning with statement A. It says that for a reversible process, the entropy change of the surroundings is equal to zero. So we want to recall the formula for a reversible process where the entropy change of our universe is equal to the sum of the entropy change of our system plus the entropy change of our surroundings which should all equal zero, meaning that when the statement A says that the entropy change of our surroundings is equal to zero. That is false because we see that the entropy change of our universe is what is equal to zero. So statement A is a false statement and that is our first answer. Moving on to statement B. We have for a reversible process. The value of entropy of the surroundings is equal and opposite to the change in entropy of the system. Based on our formula that we outlined above, we said that the change in entropy of our system added to the change in entropy of our surroundings should equal zero when they're added together. So to simplify so that we have the entropy change of our surroundings. On the other side we're going to subtract this from both sides, meaning that we would say that the entropy change of our system is indeed equal and opposite to the negative entropy change of our surroundings because the entropy change of our system is positive where the entropy change of our surroundings is negative and so B is going to be what we consider a true statement. So this is our second answer. Moving on to statement see it says that the change in entropy of a reaction is a path function. So we'll do the work for statements see here below following the arrow where we want to recall that entropy is going to be a measure of disorder in the system, meaning that it depends on our starting and ending states sorry and ending states of the system. And so we would say that therefore entropy is not a path function. It does not depend on the path taken meaning we would consider statements see as a false statement for our third answer for this example. Moving on to our last example, we have statement D which says that for a reversible process, the entropy of the universe is equal to zero. Again, based on that equation we outlined above our entropy of our universe is equal to the sum of the entropy of our system added to the entropy of our surroundings which should equal zero. Ultimately, so the entropy of our universe is indeed equal to zero for a reversible process. And that is exactly what statement D validates. So we would say that statement D is a true statement, meaning that this is our fourth final answer to complete this example. So everything highlighted in yellow represents the final answers to complete whether each statement was either true or false. I hope everything I went through is clear. If you have any questions, please leave them down below and I'll see everyone in the next practice video.

Verified Solution

Key Concepts

State Functions

Entropy and the Second Law of Thermodynamics

Reversible Processes