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Chapter 9: Q3CQ (page 402)

Given an arbitrary thermodynamic system, which is larger. the number of possible macro-states. or the numberof possible microstates, or is it impossible to say? Explain your answer. (For most systems, both are infinite, but il is still possible to answer the question,)

Short Answer

Expert verified

None can be measured; we know that there are more possible microstates

Step by step solution

01

microstates

Microstate is a term that describes the microscopic properties of a thermodynamic system.

02

possible number of microstates

Greater number is of the possible microstates, this is only theoretical simply because no one can keep track of each molecule and its position.

Knowing the number of molecules on each side would be knowing the macro-state of the system, but knowing each molecule where it is, specifying the actual molecule, is giving more options - microstates.

Although none can be measured, we know that there are more possible microstates.

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Most popular questions from this chapter

To obtain the Maxwell speed distribution, we assumed a uniform temperature. kinetic-only energy of E=mvx2+vy2+vz2, and we assumed that we wished to find the average of an arbitrary function of X. Along the way, we obtained probability per unit height speed,P(v).

a) Assuming a uniform temperature and an energy ofE=12mvx2+vy2+vz3+mgyand assuming we wish to find the average of an arbitrary function of Y, obtain a probability per unit height,P(y) .

b) Assuming a temperature of300K. how much less the density of the atmosphere'sat an altitude of(about3000ft) than at sea level'?

(c) What of theO2in the atmosphere?

Not surprisingly. in a collection of oscillators, as in other thermodynamic systems, raising the temperature causes particles' energies to increase. Why shouldn’t point be reached where there are more panicles in some high energy state than in a lower energy. state? (The fundamental idea, not a formula that might arise from it. is the object.)

The Debye temperature of copper is 45K .

(a) Estimate its molar heat capacity at 100 K using the plot in Figure 9.33(b) .

(b) Determine its corresponding specific heat and compare it with the experimental value of 0.254J/g·K.

You have six shelves, one above the other and all above the floor, and six volumes of an encyclopedia, A, B, C, D, E and F.

(a) list all the ways you can arrange the volumes with five on the floor and one on the sixth/top shelf. One way might be(ABCDE_,_,_,_,_F).

(b) List all the ways you can arrange them with four on the floor and two on the third shelf.

(c) Show that there are many more ways, relative to pans (a) and (b), to arrange the six volumes with two on the floor and two each on the first and second shelves. (There are several ways to answer

this, but even listing them all won't take forever it's fewer than.)

(d) Suddenly, a fantastic change! All six volumes are volume X-it's impossible to tell them apart. For each of the three distributions described in parts (a), (b), and (c), how many different (distinguishable) ways are there now?

(e) If the energy you expend to lift a volume from the floor is proportional to a shelf's height, how do the total energies of distributions (a), (b), and (c) compare?

(I) Use these ideas to argue that the relative probabilities of occupying the lowest energy states should be higher for hosons than for classically distinguishable particles.

(g) Combine these ideas with a famous principle to argue that the relative probabilities of occupying the lowest states should he lower for fermions than for classically distinguishable particles.

The electromagnetic intensity thermally radiated by a body of temperature Tis given by I=σT4whereσ=5.67×10−8W/m2⋅K4

This is known as the Stefan-Boltzmann law. Show that this law follows from equation (9-46). (Note: Intensity, or power per unit area, is the product of the energy per unit volume and distance per unit time. But because intensity is a flow in a given direction away from the blackbody, the correct speed is not c. For radiation moving uniformly in all directions, the average component of velocity in a given direction is14c .)
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