The total number of microstates for N molecules.

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Answer 1

Question

Chapter 19, Problem 68P

(a)

To determine

The total number of microstates for N molecules.

(b)

To determine

The number of microstates with half the molecules on each side of the box.

(c)

To determine

The ratio of probability that all the molecules will be found on one side of the box to the probability that there will be equal number on both sides.

(d)

To determine

The probability ratio for N=4 and N=100 .

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In this problem you are to consider an adiabaticexpansion of an ideal diatomic gas, which means that the gas expands with no addition or subtraction of heat. Assume that the gas is initially at pressure p0, volume V0, and temperature T0. In addition, assume that the temperature of the gas is such that you can neglect vibrational degrees of freedom. Thus, the ratio of heat capacities is γ=Cp/CV=7/5. Note that, unless explicitly stated, the variable γshould not appear in your answers--if needed use the fact that γ=7/5 for an ideal diatomic gas. Find an analytic expression for p(V), the pressure as a function of volume, during the adiabatic expansion. Express the pressure in terms of V and any or all of the given initial values p0, T0, and V0. p(V) = __________

In this problem you are to consider an adiabaticexpansion of an ideal diatomic gas, which means that the gas expands with no addition or subtraction of heat. Assume that the gas is initially at pressure p0, volume V0, and temperature T0. In addition, assume that the temperature of the gas is such that you can neglect vibrational degrees of freedom. Thus, the ratio of heat capacities is γ=Cp/CV=7/5. Note that, unless explicitly stated, the variable γshould not appear in your answers--if needed use the fact that γ=7/5 for an ideal diatomic gas. A) Find an analytic expression for p(V), the pressure as a function of volume, during the adiabatic expansion. Express the pressure in terms of V and any or all of the given initial values p0, T0, and V0. p(V) = __________ B) At the end of the adiabatic expansion, the gas fills a new volume V1, where V1>V0. Find W, the work done by the gas on the container during the expansion. Express the work in terms of p0, V0, and V1. Your…

Give the temperature T of 1 mole of ideal gas as a function of the pressure P, volume V, and the gas constant R and give the internal energy U of a rigid diatomic ideal gas as a function of its temperature T and the gas constant R.

Answer 2

Question

Chapter 19, Problem 68P

(a)

To determine

The total number of microstates for N molecules.

(b)

To determine

The number of microstates with half the molecules on each side of the box.

(c)

To determine

The ratio of probability that all the molecules will be found on one side of the box to the probability that there will be equal number on both sides.

(d)

To determine

The probability ratio for N=4 and N=100 .

Expert Solution & Answer

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Answer 3

Question

Chapter 19, Problem 68P

(a)

To determine

The total number of microstates for N molecules.

(b)

To determine

The number of microstates with half the molecules on each side of the box.

(c)

To determine

The ratio of probability that all the molecules will be found on one side of the box to the probability that there will be equal number on both sides.

(d)

To determine

The probability ratio for N=4 and N=100 .

Expert Solution & Answer

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Check out a sample textbook solution

See solution

Answer 4

Question

Chapter 19, Problem 68P

(a)

To determine

The total number of microstates for N molecules.

(b)

To determine

The number of microstates with half the molecules on each side of the box.

(c)

To determine

The ratio of probability that all the molecules will be found on one side of the box to the probability that there will be equal number on both sides.

(d)

To determine

The probability ratio for N=4 and N=100 .

Expert Solution & Answer

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Check out a sample textbook solution

See solution

Answer 5

Chapter 19, Problem 68P

(a)

To determine

The total number of microstates for N molecules.

(b)

To determine

The number of microstates with half the molecules on each side of the box.

(c)

To determine

The ratio of probability that all the molecules will be found on one side of the box to the probability that there will be equal number on both sides.

(d)

To determine

The probability ratio for N=4 and N=100 .

Answer 6

Chapter 19, Problem 68P

(a)

To determine

The total number of microstates for N molecules.

Answer 7

Chapter 19, Problem 68P

(a)

To determine

The total number of microstates for N molecules.

Answer 8

(b)

To determine

The number of microstates with half the molecules on each side of the box.

Answer 9

(b)

To determine

The number of microstates with half the molecules on each side of the box.

Answer 10

(c)

To determine

The ratio of probability that all the molecules will be found on one side of the box to the probability that there will be equal number on both sides.

Answer 11

(c)

To determine

The ratio of probability that all the molecules will be found on one side of the box to the probability that there will be equal number on both sides.

Answer 12

(d)

To determine

The probability ratio for N=4 and N=100 .

Answer 13

(d)

To determine

The probability ratio for N=4 and N=100 .

Answer 14

Expert Solution & Answer

Answer 15

Expert Solution & Answer

Answer 16

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Answer 17

Ch. 19.1 - Which of these processes is irreversible? (a)...Ch. 19.2 - The low temperature for a practical heat engine is...Ch. 19.3 - A clever engineer decides to increase the...Ch. 19.4 - In each of the following processes, does the...Ch. 19 - Could you cool the kitchen by leaving the...Ch. 19 - Prob. 2FTD Ch. 19 - Should a car get better mileage in the summer or...Ch. 19 - Prob. 4FTD Ch. 19 - Name some irreversible processes that occur in a...Ch. 19 - Your power company claims that electric heat is...

The total number of microstates for N molecules.

Solution Summary: The author explains how the total number of microstates for N molecules is given by 2N.

The total number of microstates for N molecules.

The number of microstates with half the molecules on each side of the box.

The ratio of probability that all the molecules will be found on one side of the box to the probability that there will be equal number on both sides.

The probability ratio for N=4 and N=100 .

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Chapter 19 Solutions