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Unformatted text preview: 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 ( S = S e + S i ). In an isolated system, only need to look at the system at hand, i.e. S i . In an isolated system, a process will occur spontaneously only if S i > . 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 fin 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? 422 ANSWER: We know how to calculate T fin ! = Q = Q m + Q w (4.59) Q m = Q w (4.60) n m C m p T fin T i m = n w C w p T fin T i w (4.61) n m C m p T fin + n w C w p T fin = 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 S = S w + S m (4.65) = n w C w p log e T fin T i w + n m C m p log e T fin T i m (4.66) = 20mol 75.33 J mol K log e 295.68K 293.1K 423 + 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....
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This note was uploaded on 12/05/2010 for the course CHBE 251 taught by Professor Scotty during the Winter '09 term at The University of British Columbia.
 Winter '09
 scotty
 Equilibrium

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