The most probable state is the ten particles divided into two equal parts, in this situation, the number of microstates Is largest, =252, therefore the answer is(D) 5)55 5. For which of the following processes is the entropy change zero? (C) (A)Isobaric B)Isothermal ( C)Adiabatic (D)Constant volume None of these, since AS>0 for all processes Solution If these processes are quasi-static reversible, according to the definition of entropy A5 rd@ 6. One mole of an ideal gas is originally at Po, Vo, and To. The gas is heated at constant volume to 2To, then allowed to expand at constant temperature to 2Vo, and finally it is allowed to cool at constant pressure to To. The net entropy change for this ideal gas is (A)△S=(SR/2)n2(B)△S=5R/2(C)△S=Rln2(D)△S=3R2(E)△S-0 Solution For the entropy is a state variable of a thermodynamic system, the net entropy change of the ideal gas iS(e) 7. A block of aluminum originally at 80C is places into an insulated container of water originally at 25C. After a while the system reaches an equilibrium temperature of 31C. During this process (A)△Saam (B)△ satuminunn (C)△ saluinun0 The total entropy change of the block of aluminum is As 304K mcalumingm dT <0J. the answer 353K should be(C) 8. Which of the following is a consequence of the second law of thermodynamics? A)Heat can flow only from high temperature to low temperature B)Objects in contact will tend toward having the same temperature (C) Any system that produces order from disorder must have an external influence Solution The second law of thermodynamics tells that if there is no external effect, an isolated system will always change from order to disorder. The answer is(C) I. Filling the blanksThe most probable state is the ten particles divided into two equal parts, in this situation, the number of microstates is largest, 252 5!5! 10! 5 10 = = ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ ，therefore the answer is (D). 5. For which of the following processes is the entropy change zero? （ C ） (A) Isobaric (B) Isothermal (C) Adiabatic (D) Constant volume (E) None of these, since ∆S>0 for all processes. Solution: If these processes are quasi-static reversible, according to the definition of entropy ∫ ∆ = T Q S d , the answer is (C). 6. One mole of an ideal gas is originally at P0, V0, and T0. The gas is heated at constant volume to 2T0, then allowed to expand at constant temperature to 2V0, and finally it is allowed to cool at constant pressure to T0. The net entropy change for this ideal gas is （ E ） (A) ∆S=(5R/2)ln2 (B) ∆S=5R/2 (C) ∆S=Rln2 (D) ∆S=3R/2 (E) ∆S=0 Solution: For the entropy is a state variable of a thermodynamic system, the net entropy change of the ideal gas is (E). 7. A block of aluminum originally at 80°C is places into an insulated container of water originally at 25°C. After a while the system reaches an equilibrium temperature of 31°C. During this process （ C ） (A) ∆Saluminum>0. (B) ∆Saluminum=0. (C) ∆Saluminum<0. Solution: The total entropy change of the block of aluminum is 0 J 304K d 353K min ∫ ∆ = < T mc T S alu um , the answer should be (C). 8. Which of the following is a consequence of the second law of thermodynamics? ( C ) (A) Heat can flow only from high temperature to low temperature. (B) Objects in contact will tend toward having the same temperature. (C) Any system that produces order from disorder must have an external influence. Solution: The second law of thermodynamics tells that if there is no external effect, an isolated system will always change from order to disorder. The answer is (C) II. Filling the Blanks