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Chapter 5: Q. 5.79 (page 208)
Most pasta recipes instruct you to add a teaspoon of salt to a pot
of boiling water. Does this have a significant effect on the boiling temperature?
Justify your answer with a rough numerical estimate.
There is hardly any effect on the boiling temperature of water.
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Consider a fuel cell that uses methane ("natural gas") as fuel. The reaction is
(a) Use the data at the back of this book to determine the values of and for this reaction, for one mole of methane. Assume that the reaction takes place at room temperature and atmospheric pressure.
(b) Assuming ideal performance, how much electrical work can you get out of the cell, for each mole of methane fuel?
(c) How much waste heat is produced, for each mole of methane fuel?
(d) The steps of this reaction are
What is the voltage of the cell?
In the previous section I derived the formula . Explain why this formula makes intuitive sense, by discussing graphs of F vs. V with different slopes.
Functions encountered in physics are generally well enough behaved that their mixed partial derivatives do not depend on which derivative is taken first. Therefore, for instance,
where each is taken with fixed, each is taken with fixed, and is always held fixed. From the thermodynamic identity (for) you can evaluate the partial derivatives in parentheses to obtain
a nontrivial identity called a Maxwell relation. Go through the derivation of this relation step by step. Then derive an analogous Maxwell relation from each of the other three thermodynamic identities discussed in the text (for ). Hold fixed in all the partial derivatives; other Maxwell relations can be derived by considering partial derivatives with respect to , but after you've done four of them the novelty begins to wear off. For applications of these Maxwell relations, see the next four problems.
Functions encountered in physics are generally well enough behaved that their mixed partial derivatives do not depend on which derivative is taken first. Therefore, for instance,
where each is taken with S fixed, each is taken with V fixed, and N is always held fixed. From the thermodynamic identity (for U ) you can evaluate the partial derivatives in parentheses to obtain
a nontrivial identity called a Maxwell relation. Go through the derivation of this relation step by step. Then derive an analogous Maxwell relation from each of the other three thermodynamic identities discussed in the text (for H, F, and G ). Hold N fixed in all the partial derivatives; other Maxwell relations can be derived by considering partial derivatives with respect to N, but after you've done four of them the novelty begins to wear off. For applications of these Maxwell relations, see the next four problems.
Write down the equilibrium condition for each of the following reactions:
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