Category: Schroeder’s TP Solutions

Problem 2.23 Consider a two-state paramagnet with elementary dipoles, with the total energy fixed at zero so that exactly half the dipoles point up and half point down.(a) How many microstates are “accessible” to this system?(b) Suppose that the microstate of this system changes a billion times per second. How many microstates will it explore…

Problem 2.22 This problem gives an alternative approach to estimating the width of the peak of the multiplicity function for a system of two large Einstein solids. (a) Consider two identical Einstein solids, each with N oscillators, in thermal contact with each other. Suppose that the total number of energy units in the combined system…

Problem 2.16 Suppose you flip 1000 coins. (a) What is the probability of getting exactly 500 heads and 500 tails? (Hint: First write down a formula for the total number of possible outcomes. Then, to determine the “multiplicity” of the 500-500 “macrostate,” use Stirling’s approximation. If you have a fancy calculator that makes Stirling’s approximation…

Problem 1.8 For a solid, we also define the linear thermal expansion coefficient, , as the fractional increase in length per degree: (a) For steel, is Estimate the total variation in length of a 1-km steel bridge between a cold winter night and a hot summer day.(b) The dial thermometer in Figure 1.2 uses a…

Problem 1.7 When the temperature of liquid mercury increases by one degree Celsius (or one kelvin), its volume increases by one part in 5500. The fractional increase in volume per unit change in temperature (when the pressure is held fixed) is called the thermal expansion coefficient, : (where is volume, is temperature, and signifies a…

Problem 1.6 Give an example to illustrate why you cannot accurately judge the temperature of an object by how hot or cold it feels to the touch. Solution: Problem 1.6 Solution (Download)

Problem 1.5 When you’re sick with a fever and you take your temperature with a thermometer, approximately what is the relaxation time? Solution: Problem 1.5 Solution (Download)

Problem 1.4 Does it ever make sense to say that one object is “twice as hot” as another? Does it matter whether one is referring to Celsius or kelvin temperatures? Explain. Solution: Problem 1.4 Solution (Download)

Problem 1.3 Determine the kelvin temperature for each of the following:(a) human body temperature;(b) the boiling point of water (at the standard pressure of 1 atm);(c) the coldest day you can remember;(d) the boiling point of liquid nitrogen (196 °C);(e) the melting point of lead (327 °C). Solution: Problem 1.3 Solution (Download)

Problem 1.2 The Rankine temperature scale (abbreviated °R) uses the same size degrees as Fahrenheit, but measured up from absolute zero like kelvin (so Rankine is to Fahrenheit as kelvin is to Celsius). Find the conversion formula between Rankine and Fahrenheit, and also between Rankine and kelvin. What is room temperature on the Rankine scale?…