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che359_sp10_hw2_soln - Solutions prepared by Chris Singer...

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Page 1 of 4 ChE 359 Homework #2 Solutions prepared by Chris Singer 1. (10 points) Suppose two objects A and B , with heat capacities C A and C B and initial temperatures T A and T B are brought into thermal contact. If C A > C B , state whether the equilibrium temperature T would be closer to T A or T B , and justify your choice. When two objects are brought into thermal contact, but are otherwise isolated from the surroundings, both objects will have the same temperature at equilibrium. Since they are isolated, there is no net change in the energy of the total system: dU tot = dU A + dU B = 0 , or Δ U A + Δ U B = 0 . The change in energy of A is given by the heat capacity: Δ U A = C A dT T A T = C A T T A ( ) . The change in energy of B is given by the heat capacity: Δ U B = C B dT T B T = C B T T B ( ) . Thus, we substitute back into our expression to get: C A T T A ( ) + C B T T B ( ) = 0 , which we can rearrange to get an expression for the equilibrium temperature: T = C A T A + C B T B C A + C B . If C A > C B , we can make the assumption: T C A T A + C B T B C A = T A + C B T B C A T A , so the equilibrium temperature would be closer to T A . 2. (25 points) Two moles of an ideal gas undergo an irreversible isothermal expansion from V 1 = 100 L to V 2 = 300 L at T = 300 K . a. (5 points) List the natural variables that govern this process, and the fundamental thermodynamic equation for a property that is a function of these variables. The variables that are specified/controlled at the system boundary are T , V , and N . Thus, the fundamental thermodynamic equation corresponding to these natural variables is F T , V , N ( ) , or dF = SdT PdV + μ j dN j j = 1 M b. (5 points) During this process process, state whether this property would stay the same, increase, or decrease, and justify your choice. During this process, we want to maximize entropy and minimize free energy. Thus, the Helmholtz free energy would decrease during this process. Also this can be seen from dF = PdV for this isothermal closed process.
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ChE 359 SP2010 - Homework #2 Page 2 of 4 c. (5 points) Find an expression for entropy as a function of this property. We note that S ≡ − F T Λি Νয় Μ৏ Ξ৯ Πਏ Ο৿ V , N d. (5 points) Calculate the change in entropy [J/K] during this process. We want to find the change in entropy during the expansion process, which is a change in volume. Thus, we need to calculate S V Λি Νয় Μ৏
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