Question
please answer the question number 3
without any restraining tension and allowed to jump back to its original length L During this last process, the spring evolves 2.50 Jof heat. a) What is the entropy change for the stretching of the spring? b) What is the entropy change for the collapse of the spring? c) What is the entropy change of the universe for the total process (stretching plus collapse)? (30 points) A cube consisting of one mole of Al metal initially at 300 K is put into thermal contact with a cube consisting of one mole of Pb metal at 290 K. This process takes spontaneously. The heat place in a vacuum. After a time the system comes to equilibrium capacity at constant pressure (Ci) for Al Is 23.5 Jdeg-mole and that for Pb 25.7 a) Determine the entropy change for the Al metal. b) Determine the entropy change for the universe. c) (10 Points, extra credit only do this problem if you have successfully completed the first two parts). Suppose both cubes are ofthe same material, say Al. more two temperatures Ti and T2 Using the fact that (a+b) 4ab for any real a b (a not equal to b) prove that Asumiv >0. (Note that by considering -a -2ab t b2 a +2ab ba -4ab (a (a-b)? 4ab 0, it is easy to show (a 4abl. 4. (10 points) a A deck of five cards (all clubs) is originally in the order (A, 2, 3,4, 5) What is the entropy of this deck? (in units of k) randomized. What is the change b) The deck is shuffled many times until the order is completely in entropy for this process?
Explanation / Answer
a) Entropy change for aluminium
CP=heat capacity, T temperature in 0C
note: 300K=26.850C
S=Q/T=23.5/26.85=0.875 Joules/0C
b) Entropy change for universe
The entropy change of the universe is the total entropy change of the system and its surroundings.
Su = Ssur + Ssys
Heat flowing into the surroundings increases the entropy. Note Hsys is negative for an exothermic process so the following equation requires a minus sign.
Ssur = - Hsys / T=-0.875 /298Kor 24.850C=-0.875 /24.85= -0.0352
Su = Ssur + Ssys
= -0.0352+0.875
= 0.8398 Joules/0C
C) information is not sufficient
