Act6_sol

Act6_sol - 6/13/05 Activity 6 Solutions: Entropy and The...

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6/13/05 1 Activity 6 Solutions: Entropy and The Laws of Thermodynamics 6.1 Order, Disorder, and Entropy 1) Ordered and Disordered Systems a) Deal three cards from the deck on your table. Do the three cards have the same picture? If not, return the cards to the deck, shuffle, and deal three cards again. Repeat until you have dealt three cards with the same picture (an ordered set). How many disordered sets did you deal before dealing an ordered set? ________ b) If you continued dealing sets of three cards, which type of set would you expect to deal more frequently: ordered sets or disordered sets? disordered sets c) How can you relate your results with the cards to ordered and disordered systems in nature? Which would you think are more common – ordered systems or disordered systems? __ disordered systems _ 2) Ordered and Disordered Checkers In the next activity, we use checkers on a four-square board to help explain why disordered systems are more common than ordered systems. To do this, we find the probability of drawing at random checkers whose colors match the colors of the squares on a four-square board. When you start the activity, the number of red and black checkers in the beaker is the same. Each time a checker is drawn from the beaker, we will act as if another checker of that color has been added to the beaker. That is, we will assume that before we draw each checker, there are equal numbers of red and black checkers in the beaker. a) Select one checker at random from the beaker. Place the selected checker on square #1 of the four-square board. Since there are two colors of checkers, what is the probability that the color of the checker you drew at random matches the color of square #1 on which it was placed? Since there are two colors of checkers, the probability that you selected the correct color at random is 1 in 2, or ½. b) Draw a second checker at random from the beaker and place it on square #2. What is the probability that the color of the second checker you drew matches the color of square #2? Again, the probability that you selected the correct color at random is 1 in 2, or ½. c) What is the probability that the colors of both of the checkers you have drawn at random match the colors of the squares on which each was placed? The total probability is the product of the individual probabilities: 4 1 2 1 2 1 x 2 1 2 = =

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6/13/05 2 d) Draw two more checkers at random, placing the first checker on square #3 and the second checker on square #4. What is the probability that the colors of all four checkers match the colors of the squares on which they were placed? The total probability is the product of the individual probabilities: 3) Combinations of Two Colors on Four Squares You can verify your results from part 2) using the 16 four-square boxes shown below.
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This note was uploaded on 06/11/2011 for the course PHYSICS 104 taught by Professor Staff during the Winter '11 term at Ohio State.

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Act6_sol - 6/13/05 Activity 6 Solutions: Entropy and The...

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