Category: Schroeder’s TP Solutions

Problem 1.1 The Fahrenheit temperature scale is defined so that ice melts at and water boils at (a) Derive the formulas for converting from Fahrenheit to Celsius and back.(b) What is absolute zero on the Fahrenheit scale? Solution: Problem 1.1 Solution (Download)

Problem 2.14 Write in the form , for some . Solution: Problem 2.14 Solution (Download)

Problem 2.13 Fun with logarithms.(a) Simplify the expression . (That is, write it in a way that doesn’t involve logarithms.)(b) Assuming that , prove that . (Hint: Factor out the a from the argument of the logarithm, so that you can apply the approximation of part (d) of the previous problem.) Solution: Problem 2.13 Solution…

Problem 2.12 The natural logarithm function, ln, is defined so that for any positive number x.(a) Sketch a graph of the natural logarithm function.(b) Prove the identities and .(c) Prove that (d) Derive the useful approximation ,which is valid when . Use a calculator to check the accuracy of this approximation for x = 0.1…

Problem 2.10 Use a computer to produce a table and graph, like those in this section, for the case where one Einstein solid contains 200 oscillators, the other contains 100 oscillators, and there are 100 units of energy in total. What is the most probable macrostate, and what is its probability? What is the least…

Problem 2.3 Suppose you flip 50 fair coins.(a) How many possible outcomes (microstates) are there?(b) How many ways are there of getting exactly 25 heads and 25 tails?(c) What is the probability of getting exactly 25 heads and 25 tails?(d) What is the probability of getting exactly 30 heads and 20 tails?(e) What is the…

Problem 2.1 Suppose you flip four fair coins.(a) Make a list of all the possible outcomes, as in Table 2.1.(b) Make a list of all the diferent “macrostates” and their probabilities.(c) Compute the multiplicity of each macrostate using the combinatorial formula 2.6, and check that these results agree with what you got by brute force…

Problem 1.54 A 60-kg hiker wishes to climb to the summit of Mt. Ogden, an ascent of 5000 vertical feet (1500 m). (a) Assuming that she is 25% efficient at converting chemical energy from food into mechanical work, and that essentially all the mechanical work is used to climb vertically, roughly how many bowls of…

Problem 1.50 Consider the combustion of one mole of methane gas: The system is at standard temperature (298 K) and pressure ( Pa) both before and after the reaction. (a) First imagine the process of converting a mole of methane into its elemental consituents (graphite and hydrogen gas). Use the data at the back of…

Problem 1.47 Your 200-g cup of tea is boiling-hot. About how much ice should you add to bring it down to a comfortable sipping temperature of ? (Assume that the ice is initially at . The specific heat capacity of ice is .) Solution: Problem 1.47