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Chapter 5: Q 5.8 (page 158)
Derive the thermodynamic identity for (equation 5.23), and from it the three partial derivative relations 5.24.
The expression for change in G is and the relations are
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The formula for Cp-Cv derived in the previous problem can also be derived starting with the definitions of these quantities in terms of U and H. Do so. Most of the derivation is very similar, but at one point you need to use the relation .
Use the Clausius-Clapeyron relation to derive equation 5.90 directly from Raoult's law. Be sure to explain the logic carefully.
A muscle can be thought of as a fuel cell, producing work from the metabolism of glucose:
(a) Use the data at the back of this book to determine the values of and for this reaction, for one mole of glucose. Assume that the reaction takes place at room temperature and atmospheric pressure.
(b) What is maximum amount of work that a muscle can perform , for each mole of glucose consumed, assuming ideal operation?
(c) Still assuming ideal operation, how much heat is absorbed or expelled by the chemicals during the metabolism of a mole of glucose?
(d) Use the concept of entropy to explain why the heat flows in the direction it does?
(e) How would your answers to parts (a) and (b) change, if the operation of the muscle is not ideal?
Express in terms of the volumes of solutions of reactants and products, for a chemical reaction of dilute solutes. Plug in some reasonable numbers, to show that a pressure increase of 1 atm has only a negligible effect on the equilibrium constant.
The first excited energy level of a hydrogen atom has an energy of 10.2 eV, if we take the ground-state energy to be zero. However, the first excited level is really four independent states, all with the same energy. We can therefore assign it an entropy of S =kln(4) , since for this given value of the energy, the multiplicity is 4. Question: For what temperatures is the Helmholtz free energy of a hydrogen atom in the first excited level positive, and for what temperatures is it negative? (Comment: When F for the level is negative, the atom will spontaneously go from the ground state into that level, since F=0 for the ground state and F always tends to decrease. However, for a system this small, the conclusion is only a probabilistic statement; random fluctuations will be very
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