## Physics for Scientists

Physics & Astronomy

## Quiz 20 :

The Micromacro Connection

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Q16 Q16 Q16

What is the total translational kinetic energy in a test chamber filled with nitrogen (N

_{2}) at and The dimensions of the chamber are The ATOMIC weight of nitrogen is 28.0 g/mol, Avogadro's number is 6.022 × 10^{23}molecules/mol and the Boltzmann constant is 1.38 × 10^{-23}J/K.Free

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Short Answer

Q17 Q17 Q17

A 5.0-liter gas tank holds 1.4 moles of helium (He) and 0.70 moles of oxygen (O

_{2}), at a temperature of 260 K. The atomic masses of helium and oxygen are 4.0 g/mol and 16.0 g/mol, respectively. Avogadro's number is 6.022 × 10^{23}molecules/mol and the Boltzmann constant is 1.38 × 10^{-23}J/K. The total random translational kinetic energy of the gas in the tank is closest toFree

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Multiple Choice

Q18 Q18 Q18

A 5.0-liter gas tank holds 1.7 moles of monatomic helium (He) and 1.10 mole of diatomic oxygen (O

_{2}), at a temperature of 260 K. The ATOMIC masses of helium and oxygen are 4.0 g/mol and 16.0 g/mol, respectively. What is the ratio of the root-mean-square (thermal) speed of helium to that of oxygen?Free

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Multiple Choice

Q19 Q19 Q19

An ideal gas is kept in a rigid container that expands negligibly when heated. The gas starts at a temperature of 20.0°C, and heat is added to increase its temperature. At what temperature will its root-mean-square speed (thermal speed) be double its value at 20.0°C?

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Multiple Choice

Q21 Q21 Q21

A 0.10- gas tank holds 5.0 moles of nitrogen gas (N

_{2}), at a temperature of The atomic mass of nitrogen is 14 g/mol, the molecular radius is 3.0 × 10^{-10}m, and the Boltzmann constant is 1.38 × 10^{-23}J/K. The root-mean-square speed (thermal speed) of the molecules is closest toFree

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Multiple Choice

Q23 Q23 Q23

The root-mean-square speed (thermal speed) of a certain sample of carbon dioxide molecules, with a molecular weight of 44 g/mol, is 396 m/s. What is the root-mean-square speed (thermal speed) of water vapor molecules, with a molecular weight of 18 g/mol, at the same temperature?

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Multiple Choice

Q25 Q25 Q25

A sealed container holds 0.020 moles of nitrogen (N

_{2}) gas at a pressure of 1.5 atmospheres and a temperature of 290 K. The atomic mass of nitrogen is 14 g/mol. The Boltzmann constant is 1.38 × 10^{-23}J/K and the ideal gas constant is R = 8.314 J/mol ∙ K = 0.0821 L ∙ atm/mol ∙ K. The average translational kinetic energy of a nitrogen molecule is closest toFree

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Multiple Choice

Q28 Q28 Q28

A cubic box with sides of 20.0 cm contains 2.00 × 10

^{23}molecules of helium with a root-mean-square speed (thermal speed) of 200 m/s. The mass of a helium molecule is 3.40 × 10^{-27}kg. What is the average pressure exerted by the molecules on the walls of the container? The Boltzmann constant is 1.38 × 10^{-23}J/K and the ideal gas constant is R = 8.314 J/mol ∙ K = 0.0821 L ∙ atm/mol ∙ K.Free

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Multiple Choice

Q31 Q31 Q31

Dust particles are pulverized rock, which has density 2500 kg/m

^{3}. They are approximately spheres 20 μm in diameter. Treating dust as an ideal gas, what is the root-mean-square speed (thermal speed) of a dust particle at (The Boltzmann constant is 1.38 × 10^{-23}J/K.)Free

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Multiple Choice

Q32 Q32 Q32

An oxygen molecule falls in a vacuum. From what height must it fall so that its kinetic energy at the bottom equals the average energy of an oxygen molecule at 800 K? (The Boltzmann constant is 1.38 × 10

^{-23}J/K, the molecular weight of oxygen is 32.0 g/mol, and Avogadro's number is 6.022 × 10^{23}molecules/mol.)Free

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Multiple Choice

Q36 Q36 Q36

What is the mean free path for the molecules in an ideal gas when the pressure is 100 kPa and the temperature is 300 K given that the collision cross-section for the molecules of that gas is 2.0 × 10

^{-20}m^{2}? The Boltzmann constant is 1.38 × 10^{-23}J/K, Avogadro's number is 6.02 × 10^{23}molecules/mole, and the ideal gas constant is R = 8.314 J/mol ∙ K = 0)0821 L ∙ atm/mol ∙ K.Free

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Multiple Choice

Q37 Q37 Q37

Assuming the radius of diatomic molecules is approximately for what pressure will the mean free path in room-temperature (20°C) nitrogen be 4.6 m? The Boltzmann constant is 1.38 × 10

^{-23}J/K, Avogadro's number is 6.02 × 10^{23}molecules/mole, and the ideal gas constant is = 0.0821 L ∙ atm/mol ∙ K.Free

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Multiple Choice

Q38 Q38 Q38

The mean free path of an oxygen molecule is 2.0 × 10

^{-5}m, when the gas is at a pressure of 120 Pa and a temperature of 275 K. The atomic mass of oxygen is 16.0 g/mol, the Boltzmann constant is 1.38 × 10^{-23}J/K, Avogadro's number is 6.02 × 10^{23}molecules/mole, and the ideal gas constant is J/mol ∙ K = 0.0821 L ∙ atm/mol ∙ K. The radius of an oxygen molecule is closest toFree

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Multiple Choice

Q39 Q39 Q39

The mean free path of an oxygen molecule is 2.0 × 10

^{-5}m, when the gas is at a pressure of 120 Pa and a temperature of 275 K. The molecular mass of oxygen is 32.0 g/mol and the Boltzmann constant is 1.38 × 10^{-23}J/K, Avogadro's number is 6.02 × 10^{23}molecules/mole, and the ideal gas constant is R = 8.314 J/mol ∙ K = 0.0821 L ∙ atm/mol ∙ K. Assuming that the molecules are moving at their root-mean-square speeds, the average time interval between collisions of an oxygen molecule is closest toFree

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Multiple Choice

Q40 Q40 Q40

On a hot summer day, the temperature is 40.0°C and the pressure is 1.01 × 10

^{5}Pa. Let us model the air as all nitrogen of molecular mass 28.0 g/mol having molecules of diameter 0.500 nm that are moving at their root-mean-square speed. Avogadro's number is 6.02 × 10^{23}molecules/mol, the ideal gas constant is 8.31 J/mol ∙ K, and the Boltzmann constant is 1.38 × 10^{-23}J/K. Calculate reasonable estimates for (a) the root-mean-square speed of the nitrogen molecules. (b) the average distance a typical molecule travels between collisions. (c) the average time a molecule travels between collisions, assuming that the molecules are moving at their root-mean-square speeds. (d) the number of collisions an average molecule undergoes per second.Free

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Essay

Q41 Q41 Q41

What is the mean free path of molecules in an ideal gas in which the mean collision time is 3.00 × 10

^{-10}s, the temperature is 300 K, and the mass of the molecules is 6.00 × 10^{-25}kg? Assume that the molecules are moving at their root-mean-square speeds. The Boltzmann constant is 1.38 × 10^{-23}J/K.Free

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Multiple Choice