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Exam 17: Thermal Properties of Matter

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Question 21

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Eleven molecules have speeds 16, 17, 18, . . . , 26 m/s. Calculate the root-mean-square of this group of molecules.

A) 21.2 m/s
B) 21.0 m/s
C) 21.5 m/s
D) 21.7 m/s

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Question 22

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A fixed amount of ideal gas is held in a rigid container that expands negligibly when heated. At 20°C the gas pressure is p. If we add enough heat to increase the temperature from 20°C to 40°C, the pressure will be

A) impossible to determine since we do not know the number of moles of gas in the container.
B) greater than 2p.
C) less than 2p.
D) equal to 2p.
E) impossible to determine since we do not know the volume of gas in the container.

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Question 23

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A mole of oxygen (O₂) molecules and a mole of carbon dioxide (CO₂) molecules at the same temperature and pressure have

A vertical tube that is closed at the upper end and open at the lower end contains an air pocket. The open end of the tube is under the water of a lake, as shown in the figure. When the lower end of the tube is just under the surface of the lake, where the temperature is 37°C and the pressure is 1.0 × 10⁵ Pa, the air pocket occupies a volume of 630 cm³. Suppose now that the lower end of the tube is at a depth of 86 m in the lake, where the temperature is 7.0°C. What is the volume of the air pocket under these conditions? The density of the water in the lake is 1000 kg/m³.

A sealed container holds 0.020 moles of nitrogen (N₂) gas, at a pressure of 1.5 atmospheres and a temperature of 290 K. The atomic mass of nitrogen is 14.0 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 mass density of the gas is closest to

A 3.2-L volume of neon gas (Ne) is at a pressure of 3.3 atm and a temperature of 330 K. The atomic mass of neon is 20.2 g/mol, Avogadro's number is 6.022 · 10²³ molecules/mol, and the ideal gas constant is R = 8.314 J/mol · K = 0.0821 L · atm/mol · K. The mass of the neon gas is closest to

A 5.0-liter gas tank holds 1.4 moles of helium (He) and 0.70 moles of oxygen (O₂) , 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 × 10²³ 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 to

Which contains more moles of material: 80 grams of helium gas (He, having atomic weight 4.0 g/mol) or 400 grams of argon gas (Ar, having atomic weight 40 g/mol) ?

What is the root-mean-square value of the following velocity components: 2.0 m/s, -3.0 m/s, and 4.0 m/s?

A 0.10-m³ gas tank holds 5.0 moles of nitrogen gas (N₂) , at a temperature of 370 K. 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 to

How many moles of water (H₂O) molecules are in a 4.00 m3 container at a pressure 8.00 × 10⁵ N/m² and temperature 600°C? The ideal gas constant is R = 8.314 J/mol•K = 0.0821 L ∙ atm/mol ∙ K.

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 × 10²³ 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 to

At what temperature would the root-mean-square speed (thermal speed) of oxygen molecules be 13.0 m/s? Assume that oxygen approximates an ideal gas. The mass of one O₂ molecule is 5.312 x 10^-26 kg. The Boltzmann constant is 1.38 × 10^-23 J/K.

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?

If the temperature of a fixed amount of an ideal gas is increased, it NECESSARILY follows that

For a fixed amount of gas, if the absolute temperature of the gas is doubled, what happens to the pressure of the gas?

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.

Dust particles are pulverized rock, which has density 2500 kg/m³. 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 400°C? (The Boltzmann constant is 1.38 × 10^-23 J/K.)

A container is filled with a mixture of helium (light molecules) and oxygen (heavy molecules) gases. A thermometer in the container reads 22°C. Which gas molecules have the greater average kinetic energy?

Sometimes an experiment requires a certain pure gas to be used at reduced pressure. One way to achieve this is to purchase a sealed glass container filled with the gas, and to introduce the gas into a vacuum by attaching the glass container to the vacuum chamber and breaking the tip of the glass container using a metallic bean and a magnet. If the volume of the glass container is 1.0 L and it is at a pressure of 1.0 × 10⁵ Pa and if the vacuum chamber has a volume of 2.0 L, what will the pressure be after the gas, which is to be assumed to be an ideal gas, is released into the vacuum chamber and the temperature has returned to its original value? (Note that the glass container remains part of the system.)