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19 Chemical Thermodynamics Solutions to Exercises (c) The gas will spontaneously adopt the state with maximum disorder, the state with the most possible arrangements for the molecules. 19.92 (a) Microstates are possible arrangements for the system. For each die, there are six possibilities for the top face, resulting in (6)(6) = 36 possible arrangements or microstates. (The face that appears on top of one die is not related to or determined by the face on top of the other die.) The two arrangements of top faces shown in the exercise are two of the 36 possible microstates. (b) The left pair of dice belongs to state III; the right pair belongs to state VII. (c) There are eleven possible states (II through XII; I is not a possibility) (d) The state with the most microstates has the highest entropy. State VII has six microstates and the highest entropy. The microstates are (1+6), (2+5), (3+4), (4+3), (5+2) and (6+1). States VI and VIII, on either side of VII, have five microstates. Moving farther away from VII, the number of microstates decreases until we reach the two extremes, II and XII, which each have one microstate. (e) States II and XII, with one microstate each, have the lowest entropy. 19.93 If dissolves spontaneously in water, G = AH - TAS. If G is negative and AH is positive, the sign of must be positive. Furthermore, TAS > AH at. room temperature. 19.94 (a) The sign of q for expansion is (+). Vaporization is an endothermic process; the enthaphy of the system increases and q is positive. Our system is the refrigerant. Because the expansion does not occur at constant pressure, q is not exactly equal to but it's sign is positive. (b) The sign of q for compression is (-). Compression is the reverse of expansion, and it has the opposite sign. (c) The expansion chamber is inside the house and the compression chamber is outside. During expansion, qsys increases and qsur decreases. The air surrounding the expansion chamber is cooled, and then distributed througout the house to cool it. If expansion occurred outside, the cool air would be wasted. Compression releases heat to the surroundings; it occurs outside so that the released heat can be dissipated by the outside air. (d) No. Heat can flow reversibly between a system and its surroundings only if the two have an infinitesimally small difference in temperature and the amount of heat transferred is infinitesimally small. There is no mechanism in our system to regulate the amount of heat transferred. When the liquid flows into the low pressure chamber, all of the liquid vaporizes, not an infinitesimally small amount. (e) A spontaneous process occurs without outside intervention. In an air conditioner, expansion (vaporization) of the refrigerant is spontaneous, but compression (condensation) to the liquid state is nonspontaneous. Cooling the house from 31 °C to 24 °C is nonspontaneous. [Note that all spontaneous processes are irreversible, but not all irreversible processes are spontaneous.] 600