12.  In each cycle of its operation, a thermal engine absorbs 1000 J of heat from a large heat reservoir at 400 K and discharges heat to another large heat sink at 300 K.  Calculate:
(a) The thermodynamic efficiency of the heat engine, operated reversibly.
       To determine the efficiency of a carnot engine that is running reversibly we use the equation:
                        E = T_h - T_l
                                  T_h
                            =  400 K - 300 K
                                        400 K
                            =  1/4 = 25%
(b) The quantity of heat discharged to the low-temperature sink each cycle.
        In the engine the change in energy is equal to zero.  Therefore we use the equation:
                    dE = 0 = q_ab + q_cd + w
                            q_cd = q_ab + w
                                   = 1000 J + (-1000J / 4)
                                   = 750 J
(c) The maximum amount of work the engine can perform each cycle.
        The equation we use for work would be the product of the negative efficiency and the energy.
                            W = -Eq_ab
                                 = (-.25)(1000 J) = -250 J
26.  All of the halogens react directly with H2(g) to give binary compounds.  The reactions are
        F₂(g) +  H₂(g) --->  2 HF(g)
        Cl₂(g) + H₂(g) ---> 2 HCl(g)
        Br₂(g) + H₂(g) ---> 2 HBr(g)
        I₂(g)  +  H₂(g) ---> 2 HI(g)
Using the data from Appendix D, compute the change in entropy of formation of each reaction and identify a periodic trend, if any.
        The change in entropy for each of the reactants and products can be found in the book.  Using those for each reaction, we can determine the change of entropy of formation by subtracting the reactants from the products.  Therefore the changes in entropy for each of the reactions are:
               Reaction              Change in Entropy (J/K)
                    1                                        14.1
                    2                                        20.0
                    3                                        24.26
                    4                                        21.81

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