Define the kinetic theory of gases .

The kinetic theory of gases models the thermodynamic behaviour of gases by linking the microscopic properties of particles (mass and speed) to the macroscopic properties of the gas (pressure and volume).

State four assumptions of the kinetic theory of gases model.

Molecules are identical , or all have the same mass Molecules are hard, perfectly elastic spheres The volume of the molecules is negligible compared to the container The time of a collision is negligible compared to the time between collisions There are no intermolecular forces between molecules, except during impact Molecules move in continuous random motion

In the kinetic theory model, the volume of gas molecules is .......... compared with the volume of the container.

In the kinetic theory model, the volume of gas molecules is negligible compared with the volume of the container.

True or False? Gas molecules lose kinetic energy when they collide with each other.

False. Collisions between gas molecules are perfectly elastic , so no kinetic energy is lost; only the direction of the molecules' motion changes.

Why is the average behaviour of gas molecules considered, rather than the behaviour of individual molecules?

Because a gas contains a very large number of molecules, the average behaviour (for example, average speed) is a more useful and reliable measure than any single molecule's behaviour.

Define root-mean-square (r.m.s.) speed .

The square root of the mean square speed of the particles in a gas, given the symbol c r.m.s. .

True or False? Mean square speed and root-mean-square speed have the same units.

False. Mean square speed has units of m 2 s -2 , while root-mean-square speed has units of m s -1 , since it is the square root of the mean square speed.

The root-mean-square speed has units of .......... .

The root-mean-square speed has units of m s -1 .

Why must the velocities of gas particles be squared before averaging, rather than added directly?

Velocity is a vector , and particles move randomly in all directions, so positive and negative values cancel to give a net zero . Squaring the velocities removes the negative signs, allowing a meaningful average speed to be found.

The Boltzmann constant is defined as the molar gas constant divided by .......... .

The Boltzmann constant is defined as the molar gas constant divided by Avogadro's constant .

What are the units of the Boltzmann constant, and why?

Its units are J K -1 , because the Boltzmann constant links an energy (J) to a temperature (K).

True or False? The Boltzmann constant has a large numerical value because the kinetic energy of a molecule changes significantly for each degree increase in temperature.

False. The Boltzmann constant is very small because the increase in kinetic energy of a molecule is very small for every incremental increase in temperature.

When using the average kinetic energy equation, temperature must always be given in .......... .

When using the average kinetic energy equation, temperature must always be given in kelvin .

True or False? The equation E = (3/2) kT gives the total kinetic energy of all the molecules in a gas.

False. This equation gives the average kinetic energy of one molecule only; to find the total kinetic energy of all the molecules, multiply by N , the total number of molecules.

Define the internal energy of an ideal gas .

The total kinetic energy of all the particles inside the gas.

True or False? The internal energy of an ideal gas includes both the kinetic and potential energy of its particles.

False. For an ideal gas, electrostatic forces between particles are negligible except during collisions, so there is no electrostatic potential energy . Internal energy is due to kinetic energy only.

For an ideal gas, electrostatic forces between particles are considered .......... , except during collisions.

For an ideal gas, electrostatic forces between particles are considered negligible , except during collisions.

If the thermodynamic temperature of an ideal gas is doubled, what happens to its internal energy?

The internal energy also doubles , since internal energy is directly proportional to thermodynamic temperature.

A LevelPhysicsOCRFlashcards5. Newtonian World & AstrophysicsKinetic Theory of Gases

Kinetic Theory of Gases (OCR A Level Physics): Flashcards

Exam code: H556

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FrontKinetic Theory of Gases
Define the kinetic theory of gases.
FrontKinetic Theory of Gases
State four assumptions of the kinetic theory of gases model.
BackKinetic Theory of Gases
Molecules are identical, or all have the same mass
Molecules are hard, perfectly elastic spheres
The volume of the molecules is negligible compared to the container
The time of a collision is negligible compared to the time between collisions
There are no intermolecular forces between molecules, except during impact
Molecules move in continuous random motion

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Cards in this collection (30)

Define the kinetic theory of gases.
The kinetic theory of gases models the thermodynamic behaviour of gases by linking the microscopic properties of particles (mass and speed) to the macroscopic properties of the gas (pressure and volume).
State four assumptions of the kinetic theory of gases model.
- Molecules are identical, or all have the same mass
- Molecules are hard, perfectly elastic spheres
- The volume of the molecules is negligible compared to the container
- The time of a collision is negligible compared to the time between collisions
- There are no intermolecular forces between molecules, except during impact
- Molecules move in continuous random motion
In the kinetic theory model, the volume of gas molecules is .......... compared with the volume of the container.
In the kinetic theory model, the volume of gas molecules is negligible compared with the volume of the container.
True or False?
Gas molecules lose kinetic energy when they collide with each other.
False.
Collisions between gas molecules are perfectly elastic, so no kinetic energy is lost; only the direction of the molecules' motion changes.
Why is the average behaviour of gas molecules considered, rather than the behaviour of individual molecules?
Because a gas contains a very large number of molecules, the average behaviour (for example, average speed) is a more useful and reliable measure than any single molecule's behaviour.
A gas molecule of mass m and velocity v collides elastically with a container wall, rebounding with the same speed in the opposite direction. Calculate its change in momentum.
$Δ p = (- m v) - (m v) = - 2 m v$
How does Newton's third law explain the origin of gas pressure?
When a gas particle exerts a force on the container wall, the wall exerts an equal and opposite force on the particle (Newton's third law). The combined effect of many such collisions, acting over the container's surface area, produces the gas pressure:
$p = \frac{F}{A}$
Define root-mean-square (r.m.s.) speed.
The square root of the mean square speed of the particles in a gas, given the symbol c_r.m.s..
True or False?
Mean square speed and root-mean-square speed have the same units.
False.
Mean square speed has units of m² s^-2, while root-mean-square speed has units of m s^-1, since it is the square root of the mean square speed.
The root-mean-square speed has units of ...........
The root-mean-square speed has units of m s^-1.
Why must the velocities of gas particles be squared before averaging, rather than added directly?
Velocity is a vector, and particles move randomly in all directions, so positive and negative values cancel to give a net zero. Squaring the velocities removes the negative signs, allowing a meaningful average speed to be found.
Write the kinetic theory of gases equation linking pressure, volume, number of molecules, mass and mean square speed.
$p V = \frac{1}{3} N m \bar{c^{2}}$
Write the equation linking gas pressure to density and mean square speed.
$p = \frac{1}{3} ρ \bar{c^{2}}$
Define density, as used in the kinetic theory equations.
$ρ = \frac{m a s s}{v o l u m e} = \frac{N m}{V}$
Define the Boltzmann constant.
$k = \frac{R}{N_{A}}$
It relates the microscopic properties of particles (for example, the kinetic energy of a gas molecule) to their macroscopic properties (for example, temperature), and has a value of 1.38 × 10^-23 J K^-1.
The Boltzmann constant is defined as the molar gas constant divided by ...........
The Boltzmann constant is defined as the molar gas constant divided by Avogadro's constant.
Calculate the value of the Boltzmann constant, using R = 8.31 J mol^-1 K^-1 and N_A = 6.02 × 10²³ mol^-1.
$k = \frac{8.31}{6.02 \times 10^{23}} = 1.38 \times 10^{- 23} {J K}^{- 1}$
What are the units of the Boltzmann constant, and why?
Its units are J K^-1, because the Boltzmann constant links an energy (J) to a temperature (K).
True or False?
The Boltzmann constant has a large numerical value because the kinetic energy of a molecule changes significantly for each degree increase in temperature.
False.
The Boltzmann constant is very small because the increase in kinetic energy of a molecule is very small for every incremental increase in temperature.
Define the equation for the average kinetic energy of a gas molecule.
$E = \frac{1}{2} m \bar{c^{2}} = \frac{3}{2} k T$
State the relationship between the average kinetic energy of a gas molecule and its thermodynamic temperature.
The average kinetic energy of a gas molecule is directly proportional to its thermodynamic temperature: $E \propto T$
When using the average kinetic energy equation, temperature must always be given in ...........
When using the average kinetic energy equation, temperature must always be given in kelvin.
Write the average kinetic energy equation in terms of the molar gas constant, R, and the Avogadro constant, N_A, instead of the Boltzmann constant.
$E = \frac{3 R T}{2 N_{A}}$
True or False?
The equation E = (3/2)kT gives the total kinetic energy of all the molecules in a gas.
False.
This equation gives the average kinetic energy of one molecule only; to find the total kinetic energy of all the molecules, multiply by N, the total number of molecules.
The equations pV = NkT and pV = (1/3)Nm $\bar{c^{2}}$ can both be used to describe an ideal gas. Combine these equations to show that $m \bar{c^{2}} = 3 k T$ .
Equating the two expressions for pV and cancelling N from both sides gives:
$\frac{1}{3} m \bar{c^{2}} = k T$
Multiplying both sides by 3:
$m \bar{c^{2}} = 3 k T$
Define the internal energy of an ideal gas.
The total kinetic energy of all the particles inside the gas.
True or False?
The internal energy of an ideal gas includes both the kinetic and potential energy of its particles.
False.
For an ideal gas, electrostatic forces between particles are negligible except during collisions, so there is no electrostatic potential energy. Internal energy is due to kinetic energy only.
For an ideal gas, electrostatic forces between particles are considered .........., except during collisions.
For an ideal gas, electrostatic forces between particles are considered negligible, except during collisions.
Write the equation for the change in internal energy, ΔU, of an ideal gas in terms of N, k and ΔT.
$Δ U = \frac{3}{2} N k Δ T$
If the thermodynamic temperature of an ideal gas is doubled, what happens to its internal energy?
The internal energy also doubles, since internal energy is directly proportional to thermodynamic temperature.

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