An Introduction to Thermal Physics 1st Edition solutions

An Introduction to Thermal Physics 1
Problem 22P If you poke a hole in a container full of gas, the gas will start leaking out. In this problem you will make a rough estimate of the rate at which gas escapes through a hole. (This process is called effusion, at least when the hole is sufficiently small.) (a) Consider a small portion (are

An Introduction to Thermal Physics 1
Problem 12P Calculate the average volume per molecule for an ideal gas at room temperature and atmospheric pressure. Then take the cube root to get an estimate of the average distance between molecules. How does this distance compare to the size of a small molecule like N2 or H2O?

An Introduction to Thermal Physics 1
Problem 37P Using the same method as in the text, calculate the entropy of mixing for a system of two monatomic ideal gases, A and B, whose relative proportion is arbitrary. Let N be the total number of molecules: and let x be the fraction of these that are of species B. You should find ?Smixing = Nk

An Introduction to Thermal Physics 1
Problem 35P According to the Sackur-Tetrode equation, the entropy of a monatomic ideal gas can become negative when its temperature (and hence its energy) is sufficiently low. Of course this is absurd, so the Sackur-Tetrode equation must be invalid at very low temperatures. Suppose you start with a s

An Introduction to Thermal Physics 1
Problem 16P The exponential atmosphere. (a) Consider a horizontal slab of air whose thickness (height) is dz. If this slab is at rest, the pressure holding it up from below must balance both the pressure from above and the weight of the slab. Use this fact to find an expression for dP/dz, the variati

An Introduction to Thermal Physics 1
Problem 23P Consider a two-state paramagnet with 1023 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

An Introduction to Thermal Physics 1
Problem 2P Suppose you flip 20 fair coins. (a) How many possible outcomes (microstates) are there? ________________ (b) What is the probability of getting the sequence HTHHTTTHTHHHTHHHHTHT (in exactly that order)? ________________ (c) What is the probability of getting 12 heads and 8 tails (in an

An Introduction to Thermal Physics 1
Problem 54P 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 m

An Introduction to Thermal Physics 1
Problem 1P Suppose you flip four fair coins. (a) Make a list of all the possible outcomes, as in below Table. ________________ (b) Make a list of all the different macrostates and their probabilities. ________________ (c) Compute the multiplicity of each macrostate using the combinatorial formula

An Introduction to Thermal Physics 1
Problem 57P Home owners and builders discuss thermal conductivities in terms of the R value (R for resistance) of a material, defined as the thickness divided by the thermal conductivity: (a) Calculate the R value of a 1/8-inch (3.2 mm) piece of plate glass, and then of a 1 mm layer of still air.

An Introduction to Thermal Physics 1
Problem 5P For an Einstein solid with each of the following values of N and q, list all of the possible microstates, count them, and verify below formula. (a) N = 3, q = 4 (b) N = 3, q = 5 (c) N = 3, q = 6 (d) N = 4, q = 2 (e) N = 4, q = 3 (f) N = 1, q = anything (g) N = anything, q = 1 Formula:

An Introduction to Thermal Physics 1
Problem 1P Use Table 3.1 to compute the temperatures of solid A and solid B when qA = 1. Then compute both temperatures when qA = 60. Express your answers in terms of ?/k, and then in kelvins assuming that ? = 0.1 eV.

An Introduction to Thermal Physics 1
Problem 24P Calculate the total thermal energy in a gram of lead at room temperature, assuming that none of the degrees of freedom are frozen out (this happens to be a good assumption in this case).

An Introduction to Thermal Physics 1
Problem 24P For a single large two-state paramagnet, the multiplicity function is very sharply peaked about N? = N/2. a) Use Stirlings approximation to estimate the height of the peak in the multiplicity function. ________________ b) Use the methods of this section to derive a formula for the multi

An Introduction to Thermal Physics 1
Problem 25P The mathematics of the previous problem can also be applied to a one-dimensional random walk: a journey consisting of N steps, all the same size, each chosen randomly to be either forward or backward. (The usual mental image is that of a drunk stumbling along an alley.) a) Where are you m

An Introduction to Thermal Physics 1
Problem 10P An ice cube (mass 30 g) at 0C is left sitting on the kitchen table, where it gradually melts. The temperature in the kitchen is 25C. (a) Calculate the change in the entropy of the ice cube as it melts into water at 0C. (Dont worry about the fact that the volume changes somewhat.) ________

An Introduction to Thermal Physics 1
Problem 34P Show that during the quasistatic isothermal expansion of a monatomic ideal gas, the change in entropy is related to the heat input Q by the simple formula In the following chapter Ill prove that this formula is valid for any quasistatic process. Show, however, that it is not valid for

An Introduction to Thermal Physics 1
Problem 21P During a hailstorm, hailstones with an average mass of 2 g and a speed of 15 m/s strike a window pane at a 45 angle. The area of the window is 0.5 m2 and the hailstones hit it at a rate of 30 per second. What average pressure do they exert on the window? How does this compare to the press

An Introduction to Thermal Physics 1
Problem 60P A frying pan is quickly heated on the stovetop to 200C. It has an iron handle that is 20 cm long. Estimate how much time should pass before the end of the handle is too hot to grab with your bare hand. (Hint: The cross sectional area of the handle doesnt matter. The density of iron is abo

An Introduction to Thermal Physics 1
Problem 42P A black hole is a region of space where gravity is so strong that nothing, not even light, can escape. Throwing something into a black hole is therefore an irreversible process, at least in the everyday sense of the word. In fact, it is irreversible in the thermodynamic sense as well: Add