- #1
domephilis
- 54
- 6
- Homework Statement
- Exercise 11.30 Find the change in entropy if 500g of water at 80C is added to 300g of water at 20C. (Fundamentals of Physics I by R. Shankar)
- Relevant Equations
After re-reading the book, I did figure out what I was supposed to do. Take both waters through a series of reservoirs to bring them down to their final temperature while allowing for a quasi-static process. Thus, . And I did get the correct answer, 3.2 cal/K.
But, before that, I tried a different method; and, my question is why I'm wrong. The method is as follows. I also thought that I needed a reversible (or quasi-static) process. So I imagined the hotter water slowly dripping into the colder water while allowing equilibrium at almost every moment. Then, . T(m) can be easily determined through some calorimetric work. We can then integrate both sides to get the change in entropy. (Units are in calories, grams, and Kelvin. I have omitted the specific heat because it is one for water.) Hence, . A similar logic applies to the change in entropy of the hotter water being cooled down by the cold water. Here, I assume that entropy is additive (which was given in the book). The final answer I got was 14.77 cal/K. Setting aside the gory details of the calculations, is there anything wrong with the logic?
But, before that, I tried a different method; and, my question is why I'm wrong. The method is as follows. I also thought that I needed a reversible (or quasi-static) process. So I imagined the hotter water slowly dripping into the colder water while allowing equilibrium at almost every moment. Then,