# handout11 - 4.6 Spontaneous Processes in Isolated Systems...

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4.6 Spontaneous Processes in Isolated Systems REMINDER: In an ongoing thermodynamic process, entropy increases until equilibrium is reached. In general, a process will change the system itself as well as its surroundings have to look at entropy of both ( Δ S = Δ S e + Δ S i ). In an isolated system, only need to look at the system at hand, i.e. Δ S i . In an isolated system, a process will occur spontaneously only if Δ S i > 0 . A spontaneous process is irreversible. NOTE: Spontaneous processes need not be particularly fast. For example, we can store H 2 and O 2 together for centuries without anything happening. Only when we provide a spark, does the reaction occur. On the other hand, water molecules do not spontaneously decompose. EXAMPLE: A hot block of metal is added to cold water. The system is isolated. What is the final temperature T f in of the water and metal if we add n m = 2mol of iron at a temperature of T i m = 100 C = 373.1K to n w = 20mol of water at T i w = 20 C = 293.1K ? What is the entropy change of this process? Is it spontaneous? 4–22

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ANSWER: We know how to calculate T f in ! 0 = Δ Q = Δ Q m + Δ Q w (4.59) Δ Q m = - Δ Q w (4.60) n m C m p T f in - T i m = - n w C w p T f in - T i w (4.61) n m C m p T f in + n w C w p T f in = n m C m p T i m + n w C w p T i w . (4.62) So then T f in = n m C m p T i m + n w C w p T i w n m C m p + n w C w p (4.63) = 2mol × 25.10 J mol K 373.1K + 20mol × 75.33 J mol K 293.1K 2mol × 25.10 J mol K + 20mol × 75.33 J mol K = 295.68K = 22.58 C . (4.64) For the total entropy change (assume an isobaric process), we apply Eq. 4.34 for the metal and water separately; then the entropy change is Δ S = Δ S w + Δ S m (4.65) = n w C w p log e T f in T i w + n m C m p log e T f in T i m (4.66) = 20mol × 75.33 J mol K log e 295.68K 293.1K 4–23
+ 2mol × 25.10 J mol K log e 295.68K 373.1K (4.67) = 13.2 J K - 11.7 J K (4.68) = 1.53 J K > 0 . (4.69) The entropy is positive; this is a spontaneous process as expected. EXAMPLE: n mol of an ideal gas at temperature T 0 is partitioned into one half of an isolated chamber. 2V V V QUESTION: What is the change in entropy after the partition is removed without doing any work?

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