Exam 20: The Micromacro Connection

An ice cube at 0°C is placed in a very large bathtub filled with water at 30°C and allowed to melt, causing no appreciable change in the temperature of the bath water. Which one of the following statements is true?

What is the average kinetic energy of an ideal gas molecule at 569°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 speed?

If we double the root-mean-square speed (thermal speed) of the molecules of a gas, then

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 × 10²³ molecules/mole, and the ideal gas constant is = 0.0821 L ∙ atm/mol ∙ K.

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

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?

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 50.0°C, the average translational kinetic energy of a gas molecule is K. If the temperature is now increased to 100.0°C, the average translational kinetic energy of a molecule will be closest to

As a result of any natural process, the total entropy of any system plus that of its environment

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 × 10²³ 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 to

A 0.10- gas tank holds 5.0 moles of nitrogen gas (N₂), 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 to

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

The root-mean-square speed (thermal speed) of the molecules of a gas is 200 m/s at a temperature 23.0°C. What is the mass of the individual molecules? 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?

What is the mean free path of a gas of randomly-moving hard spheres of radius 2.00 × 10^-9 m when the density of spheres is 3.00 × 10¹⁹ per cubic meter?

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.

The average molecular kinetic energy of a gas can be determined by knowing

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?

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 × 10^-26 kg. The Boltzmann constant is 1.38 × 10^-23 J/K.