Deck 20: Kinetic Theory of Gases

Question 1

Two tanks of gas, one of hydrogen, H2, and one of helium, He, contain equal numbers of moles of gas. The gram-molecular mass of He is twice that of H2. Both tanks of gas are at the same temperature, 293 K. Which statement(s) below is(are) correct when we ignore vibrational motion?

A)The total internal energy of the hydrogen is the same as that of the helium.
B)The total internal energy of the hydrogen is 1.4 times that of the helium.
C)The total internal energy of the helium is 1.4 times that of the hydrogen.
D)The total internal energy of the hydrogen is 1.67 times that of the helium.
E)The total internal energy of the helium is 1.67 times that of the hydrogen.

Answer 1

The total internal energy of the hydrogen is 1.67 times that of the helium.

Question 2

According to kinetic theory, a typical gas molecule in thermal equilibrium at room temperature has a kinetic energy K = 6.00 × 10⁻²¹ J, regardless of mass. Estimate the speed at room temperature of a hydrogen molecule H2 (m = 3.34 × 10⁻²⁷ kg) and a xenon atom (m = 2.00 × 10⁻²⁵ kg). [kB = 1.38 × 10⁻²³ J/K]

Answer 2

1895 m/s, 245 m/s

Question 3

One mole of hydrogen, one mole of nitrogen and one mole of oxygen are held in a 22.4 × 10³ cm³ enclosed vessel at 20°C. The pressure in the vessel, in N/m², is

A)109.
B)304.
C)326.
D)1.09 × 10⁵.
E)3.26 × 10⁵.

Answer 3

3.26 × 10⁵.

Question 4

An ideal gas is allowed to expand adiabatically until its volume increases by 50%. By approximately what factor is the pressure reduced? (γ = 5/3.)

A)1.5
B)2.0
C)2.5
D)3.0
E)3.5

Question 5

The root mean square speed of a gas molecule is greater than the average speed, because the former gives a greater weight to

A)lighter molecules.
B)heavier molecules.
C)lower speeds.
D)higher speeds.
E)more probable speeds.

Question 6

A 50-gram sample of dry ice (solid CO₂) is placed in a 4-liter container. The system is sealed and allowed to reach room temperature (20°C). By approximately how much does the pressure inside the container increase when the dry ice turns to gas? (Ignore the initial volume of the sample.)

Question 7

A container having a volume of 1.0 m³ holds 5.0 moles of helium gas at 50°C. If the helium behaves like an ideal gas, the average kinetic energy per molecule is

A)6.7 × 10⁻²⁰ J.
B)1.0 × 10⁻²¹ J.
C)1.0 × 10⁻²⁰ J.
D)6.7 × 10⁻²¹ J.
E)1.3 × 10⁻²⁰ J.

Question 8

The temperature of a quantity of an ideal gas is

A)one measure of its ability to transfer thermal energy to another body.
B)proportional to the average molecular kinetic energy of the molecules.
C)proportional to the internal energy of the gas.
D)correctly described by all the statements above.
E)correctly described only by (a) and (b) above.

Question 9

The average molecular translational kinetic energy of a molecule in an ideal gas is

A) kBT.
B) RT.
C) kBT.
D) RT.
E) kBT, where n = number of internal degrees of freedom.

Question 10

A container having a volume of 1.0 m³ holds 5.0 moles of helium gas at 50°C. If the helium behaves like an ideal gas, the total energy of the system is

A)2.0 × 10⁴ J.
B)2.5 × 10⁴ J.
C)1.7 × 10³ J.
D)1.5 × 10³ J.
E)4.0 × 10⁴ J.

Question 11

During the volcanic eruption of Mt. Pelee in 1902, an incredibly hot "burning cloud" rolled down the mountain and incinerated the town of Saint-Pierre. From the damage done, the temperature in the cloud was estimated at 700°C. If the air temperature was 20°C and a mole of air is 29 grams, estimate the molecular weight of the gas in the "burning cloud" that made it heavier than the surrounding air. (As a follow-on, estimate the most probable composition of the cloud. Some typical volcanic gases are H₂S, SO₂, H₂SO₄, CO₂, NO.)

Question 12

Which statement below is NOT an assumption made in the molecular model of an ideal gas?

A)The average separation between molecules is large compared with the dimensions of the molecules.
B)The molecules undergo inelastic collisions with one another.
C)The forces between molecules are short range.
D)The molecules obey Newton's laws of motion.
E)Any molecule can move in any direction with equal probability.

Question 13

Two tanks of gas, one of hydrogen, H2, and one of helium, He, contain equal masses of gas. The gram-molecular mass of He is twice that of H2. Both tanks of gas are at the same temperature, 293 K. Which statement(s) below is(are) correct when we ignore vibrational motion?

A)The total internal energy of the hydrogen is the same as that of the helium.
B)The total internal energy of the hydrogen is 167 times that of the helium.
C)The total internal energy of the helium is 1.67 times that of the hydrogen.
D)The total internal energy of the hydrogen is 3.33 times that of the helium.
E)The total internal energy of the helium is 3.33 times that of the hydrogen.

Question 14

A molecule in a uniform ideal gas can collide with other molecules when their centers are equal to or less than

A)one radius away from its center.
B)one diameter away from its center.
C)two diameters away from its center.
D)twice the cube root of volume away from its center.
E) diameters away from its center.

Question 15

When we consider a thin horizontal layer of the atmosphere, of thickness dy, of area A, with pressure P on the bottom, with an average mass m per molecule, and nV molecules per unit volume, the magnitude of the difference of the pressure at the top and bottom of the layer is given by dP =

A)mgdy.
B)mgnVdy.
C)mgAdy.
D)mgnVAdy.
E)mgnVAPdy.

Question 16

During an adiabatic compression, a volume of air decreases to 1/4 its original size. Calculate its final pressure if its original pressure was 1 atm. (Assume the air behaves like an ideal gas with γ = 1.4.)

A)7.0 atm
B)5.6 atm
C)3.5 atm
D)2.2 atm
E)0.14 atm

Question 17

The internal energy of n moles of an ideal gas depends on

A)one state variable T.
B)two state variables T and V.
C)two state variables T and P.
D)three state variables T, P and V.
E)four variables R, T, P and V.

Question 18

If CP for an ideal gas is 35.4 J/mol⋅K, which of the following is CV for this gas?

A)12.5 J/mol⋅K
B)20.8 J/mol⋅K
C)29.1 J/mol⋅K
D)27.1 J/mol⋅K
E)43.4 J/mol⋅K

Question 19

If the rms speed of helium atoms is vrms,He at temperature T, what is the rms speed of CO₂ at the same temperature?

A)
B)
C)
D)
E)