Particle model and pressure

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Apuntes de la lección

Kinetic Theory and Gas Pressure

Gas molecules are in constant random motion at high speeds.
Random motion means molecules travel in no specific path and change direction when they collide with the container walls or other molecules.
Gas pressure is the force exerted per unit area on the container walls, caused by molecules colliding with them.
The collisions produce a net force at right angles to the surface.
A gas at higher pressure has more frequent collisions and therefore a greater force per unit area.
The random motion of tiny particles in a fluid is called Brownian motion.

Gas particles colliding with a container wall

Temperature and Kinetic Energy

The temperature of a gas is related to the average kinetic energy of its molecules.
The hotter the gas, the higher the average kinetic energy and the faster the molecules move.
The cooler the gas, the lower the average kinetic energy and the slower the molecules move.
As temperature increases, molecules collide with the walls more frequently and with more force, increasing pressure.
At constant volume, an increase in temperature increases the pressure of a gas, and vice versa.

A large iceberg has more total kinetic (thermal) energy than a few small ice cubes of the same substance and temperature, because it is made of far more particles.

Absolute Zero and the Kelvin Scale

Absolute zero is the temperature at which particles have zero kinetic energy and exert no pressure.
Absolute zero is equal to −273 °C or 0 K.
It is not possible to have a temperature lower than 0 K; a Kelvin temperature is never negative.
The Kelvin scale starts at absolute zero, and a change of 1 K equals a change of 1 °C.
Convert Celsius to Kelvin: T(K) = θ(°C) + 273.
Convert Kelvin to Celsius: θ(°C) = T(K) − 273.

Pressure and Volume (Boyle's Law)

For a fixed mass of gas at constant temperature, pressure × volume = constant: pV = constant.
Pressure and volume are inversely proportional.
When volume decreases (compression), pressure increases.
When volume increases (expansion), pressure decreases.
The equation can be written for before and after a change: P₁V₁ = P₂V₂.
Key assumptions: temperature and mass (number of particles) remain constant.
Pressure is measured in pascals (Pa) and volume in metres cubed (m³).

Illustration of Boyle's Law showing a balloon expanding as pressure decreases in a bell jar.

Explaining Pressure Changes with the Particle Model

When a gas is compressed, the same number of particles occupy a smaller volume.
The density of the gas increases, so particles collide with the walls more frequently.
Each collision exerts the same force, but more frequent collisions give a greater force per unit area (pressure).
When a gas expands, particles collide with the walls less frequently, so pressure decreases.
The pressure produces a net force at right angles to the container walls.

Doing Work on a Gas

Work is the transfer of energy by a force.
Doing work on a gas increases its internal energy and can increase its temperature.
Compressing a gas with a piston does work on it, decreasing its volume.
The molecules move faster and have higher kinetic energy, so temperature rises.
If a gas expands, it does work and loses energy, so its temperature falls.
Example: a bicycle pump gets warm when compressed because work is done on the gas.
Example: releasing pressurised carbon dioxide causes it to expand, do work, and cool, forming dry ice.

Common Misconceptions to Avoid

Gas pressure is caused by collisions with the container walls, not by particles repelling each other.
Use kelvin for proportionality with pressure or volume, not degrees Celsius.
Particles do not lose energy when they collide with the walls.
Absolute zero is the point of minimum internal energy, not just 'very cold'.
Do not reverse the pressure–volume relationship: compression increases pressure.

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Preguntas de práctica

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1.Which statement best describes the motion of the molecules in a gas?
Easy
- AThey are in constant random motion at high speeds
- BThey are stationary and held in fixed positions
- CThey vibrate about fixed positions but do not move around
- DThey move in straight lines only, never changing direction
2.The temperature of a gas is related to the average kinetic energy of its molecules.
Easy
True or false?
3.A sealed container holds a fixed mass of gas at constant volume. What happens to the pressure of the gas when its temperature is increased?
Easy
- AThe pressure increases because the molecules collide with the walls more often
- BThe pressure decreases because the molecules collide with the walls less often
- CThe pressure stays the same because the volume is constant
- DThe pressure increases because the molecules repel each other
4.What is absolute zero?
Easy
- AThe temperature at which the molecules in a substance have zero kinetic energy
- BThe temperature at which water freezes
- CThe lowest temperature ever recorded on Earth
- DThe temperature at which a gas turns into a liquid
5.A fixed mass of gas is held at constant temperature. Its volume is decreased. What happens to its pressure, and why?
Medium
- AThe pressure increases because the molecules collide with the walls more frequently
- BThe pressure decreases because the molecules collide with the walls less frequently
- CThe pressure increases because the molecules push each other apart
- DThe pressure decreases because the molecules lose energy on collision with the walls
6.Which of the following statements about gas pressure are correct? (select all that apply)
Medium
- APressure is the force exerted per unit area
- BGas pressure is caused by molecules colliding with the walls of the container
- CGas pressure is caused by molecules repelling each other
- DThe force from the gas acts at right angles to the container walls
- EMolecules lose all their kinetic energy when they collide with the walls
7.A gas is compressed at a constant temperature. What happens to the density of the gas and why?
Medium
- AThe density increases because the same number of molecules occupies a smaller volume
- BThe density decreases because the molecules get smaller
- CThe density stays the same because the number of molecules is unchanged
- DThe density increases because new molecules are created
8.Match each term about gases to its correct definition.
Medium
- Pressure
- Absolute zero
- Brownian motion
- Boyle's Law
- The force exerted per unit area
- The temperature at which molecules have zero kinetic energy
- The random motion of tiny particles in a fluid
- pV = constant for a fixed mass of gas at constant temperature

Más preguntas

9.Place the steps in order to explain how increasing the temperature of a gas at constant volume increases its pressure.
Medium
- The temperature of the gas increases
- The average kinetic energy of the molecules increases
- The molecules collide with the container walls more frequently
- The force per unit area on the walls increases
10.A bicycle pump is used to inflate a tyre. The air inside the pump gets warm. Which statement explains why?
Medium
- AWork is done on the gas, increasing its internal energy and temperature
- BWork is done by the gas, so its temperature falls
- CThe gas expands and does work on the surroundings
- DThe gas loses energy to the pump, so it heats up
11.When a gas is allowed to expand and do work, its temperature decreases.
Easy
True or false?
12.A sealed syringe contains air. The piston is pushed in so the volume of the air decreases. What happens to the pressure of the air?
Easy
- AThe pressure increases
- BThe pressure decreases
- CThe pressure stays the same
- DThe pressure increases then returns to its original value
13.A fixed mass of gas is heated inside a sealed, rigid container. Which of the following statements are correct? (select all that apply)
Medium
- AThe average speed of the molecules increases
- BThe average kinetic energy of the molecules increases
- CThe molecules collide with the container walls more frequently
- DThe molecules lose energy each time they hit the walls
- EThe volume of the gas increases
14.At absolute zero the molecules of a substance have zero kinetic energy.
Easy
True or false?
15.Match each quantity or statement about gases to its correct description.
Medium
- Pressure
- Absolute zero
- Boyle's Law
- Brownian motion
- Force exerted per unit area
- The temperature at which molecules have zero kinetic energy
- pV = constant for a fixed mass at constant temperature
- The random motion of tiny particles in a fluid
16.Place the steps in order to explain why compressing a gas at constant temperature increases its pressure.
Medium
- The volume of the container decreases
- The same number of molecules move in a smaller space
- The molecules collide with the walls more frequently
- The force per unit area on the walls increases
17.A gas is held at constant temperature. Its volume is doubled. What happens to its pressure?
Medium
- AThe pressure halves
- BThe pressure doubles
- CThe pressure stays the same
- DThe pressure falls to zero
18.A pressurised carbon dioxide cylinder is opened and the gas is suddenly released, expanding rapidly. Which statement best explains what happens to the gas?
Hard
- AThe gas does work as it expands, loses energy and its temperature falls, so it can form dry ice
- BThe gas has work done on it as it expands, so its temperature rises
- CThe gas expands at constant temperature because no work is done
- DThe gas loses particles as it expands, so its pressure falls to zero
19.A gas is trapped in a syringe at constant temperature. The piston is pulled out so that the volume of the gas increases. Which statement describes what happens to the pressure of the gas and why?
Medium
- AThe pressure decreases because the molecules collide with the walls less frequently
- BThe pressure increases because the molecules collide with the walls more frequently
- CThe pressure decreases because the molecules lose kinetic energy on each collision with the walls
- DThe pressure stays the same because the number of molecules in the syringe has not changed
20.A student plots a graph of the pressure of a fixed mass of gas against its temperature in °C, keeping the volume constant. The graph is a straight line. At what temperature would the line cross the temperature axis (pressure = 0)?
Medium
- A−273 °C
- B0 °C
- C273 °C
- D−373 °C
21.A fixed mass of gas is trapped in a sealed, rigid container. The container is warmed. Which of the following statements are correct? (select all that apply)
Medium
- AThe average speed of the molecules increases
- BThe average kinetic energy of the molecules increases
- CThe molecules collide with the container walls more frequently
- DThe molecules exert a smaller force on the container walls
- EThe volume of the gas increases
22.A sealed boiling tube containing gas is placed in an ice bath. What happens to the speed and the kinetic energy of the gas particles?
Easy
- ABoth the speed and the kinetic energy decrease
- BBoth the speed and the kinetic energy increase
- CThe speed decreases but the kinetic energy stays the same
- DThe speed stays the same but the kinetic energy decreases
23.A student records the pressure of a fixed mass of gas as its volume is changed at constant temperature. She finds that when the volume is halved, the pressure doubles. Which statement describes the relationship shown by her data?
Medium
- APressure is inversely proportional to volume
- BPressure is directly proportional to volume
- CPressure is proportional to volume squared
- DPressure is independent of volume
24.When a gas at constant volume is heated, the temperature in kelvin must be used when comparing it with the pressure of the gas.
Easy
True or false?
25.A student's results for a gas at constant temperature are shown. Volume = 0.50 m³, pressure = 120 Pa. The gas is then compressed to a volume of 0.20 m³. Which value is closest to the new pressure?
Hard
- A300 Pa
- B48 Pa
- C120 Pa
- D600 Pa
26.A diesel engine compresses a mixture of fuel and air very suddenly. Which statement explains why the mixture ignites?
Hard
- AWork is done on the gas, increasing its internal energy and raising its temperature
- BWork is done by the gas, decreasing its internal energy and raising its temperature
- CThe gas expands, so its molecules gain kinetic energy from the surroundings
- DThe pressure of the gas decreases, so the molecules move faster
27.Place the steps in order to explain why the pressure of steam trapped in a rigid boiler increases as it is heated.
Medium
- The average kinetic energy of the molecules increases
- The molecules hit the walls of the boiler more often
- The temperature of the steam rises
- The force per unit area on the walls increases
28.A pressurised carbon dioxide cylinder is opened and the gas expands rapidly out of the nozzle. Which of the following statements are correct? (select all that apply)
Medium
- AThe gas does work as it expands
- BThe gas loses energy and its temperature falls
- CThe gas may cool enough to form dry ice
- DThe pressure of the gas inside the cylinder increases as it leaves
- EThe molecules of the gas stop moving
29.Absolute zero is the temperature at which the molecules of a substance have zero kinetic energy.
Easy
True or false?
30.A sealed syringe contains air at room temperature. The piston is pushed in quickly so that the air is compressed, and the air becomes warmer. Which statement best explains this?
Medium
- AWork is done on the gas, increasing its internal energy
- BHeat flows into the gas from the surroundings
- CThe molecules of the gas collide with each other less often
- DThe gas does work on the piston, so its temperature rises
31.A student plots a graph of the pressure of a fixed mass of gas against its volume at constant temperature. Which shape of graph is obtained?
Hard
- AA straight line through the origin
- BA curve that falls as the volume increases
- CA straight line with a negative gradient that crosses the volume axis
- DA horizontal straight line
32.A student plots a graph of the pressure of a fixed mass of gas against its temperature in kelvin, keeping the volume constant. The graph is a straight line. What does the line show?
Medium
- APressure is directly proportional to temperature in kelvin
- BPressure is inversely proportional to temperature in kelvin
- CPressure is directly proportional to temperature in degrees Celsius
- DPressure does not depend on temperature
33.A student investigates the pressure of a fixed mass of air trapped in a flask as it is heated in a water bath. Which of the following are valid control variables? (select all that apply)
Hard
- AThe mass of air trapped in the flask
- BThe volume of the flask
- CThe temperature of the water bath
- DThe pressure of the air
- EThe colour of the flask
34.A sealed, rigid container holds a fixed mass of gas. The gas is cooled. What happens to the pressure of the gas, and why?
Medium
- AThe pressure decreases because the particles move more slowly and collide with the walls less often
- BThe pressure decreases because the particles become smaller
- CThe pressure increases because the particles move more slowly and collide with the walls more often
- DThe pressure stays the same because the volume is constant
35.A fixed mass of gas is heated at constant volume. The temperature rises from 27 °C to 54 °C. Which statement correctly describes the change in pressure?
Hard
- AThe pressure doubles because the temperature in degrees Celsius doubles
- BThe pressure increases by a factor of 327/300 because the kelvin temperature increases in that ratio
- CThe pressure stays the same because the volume is constant
- DThe pressure decreases because the temperature increases
36.A student compresses a gas in a sealed syringe quickly. The gas becomes warmer. Which statement best explains this?
Medium
- AWork is done on the gas, transferring energy to it and increasing its internal energy
- BThe gas does work on the surroundings, so it gains energy
- CThe particles gain energy by colliding with the walls and bouncing off
- DThe pressure of the gas decreases, which increases the temperature
37.A pressurised carbon dioxide cylinder is opened and the gas expands rapidly through the nozzle, forming dry ice. Which statements are correct? (select all that apply)
Hard
- AThe gas does work as it expands
- BThe gas loses internal energy and its temperature falls
- CThe gas gains internal energy from the surroundings
- DThe temperature of the gas rises as it expands
- EThe rapid cooling can cause the carbon dioxide to freeze
38.At absolute zero, the particles of a substance have zero kinetic energy.
Easy
True or false?
39.Match each term about gases to its correct description.
Medium
- Absolute zero
- Pressure
- Boyle's Law
- Work done on a gas
- The temperature at which particles have zero kinetic energy
- Force exerted per unit area
- pV = constant for a fixed mass of gas at constant temperature
- Transfer of energy by a force that increases the internal energy of the gas
40.Place the steps in order to explain why the pressure of a gas trapped in a rigid container increases when it is heated.
Medium
- The particles collide with the container walls more frequently and with greater force
- The temperature of the gas increases
- The pressure of the gas increases
- The average kinetic energy and speed of the particles increase
41.The temperature of a room is 300 K. What is this temperature in degrees Celsius?
Medium
42.Complete the sentences about kinetic theory.
Easy
Molecules in a gas are in constant random motion at high ____. Random motion means that the molecules do not travel in a specific path and undergo sudden changes in their motion if they collide with the ____ of the container or with other molecules. The temperature of the gas is related to the average ____ energy of the molecules.
43.A gas occupies a volume of 0.70 m³ at a pressure of 200 Pa. It is compressed to a volume of 0.15 m³ at constant temperature. Calculate the new pressure of the gas.
Hard
44.A gas occupies a volume of 0.50 m³ at a pressure of 120 Pa. It is compressed at constant temperature to a volume of 0.20 m³. Calculate the new pressure of the gas, in pascals.
Medium
45.Complete the sentences about the kinetic theory of gases.
Easy
Molecules in a gas are in constant random motion at ____ speeds. The temperature of a gas is related to the average ____ energy of its molecules. At a constant volume, an increase in temperature ____ the pressure of the gas.
46.What name is given to the temperature at which the molecules of a substance have zero kinetic energy?
Medium
47.A temperature is measured as 350 K. Calculate this temperature in degrees Celsius.
Medium
48.A car tyre exerts a pressure of 203 kPa on the ground. The contact area between the tyre and the ground is 0.021 m². Calculate the force that the tyre exerts on the ground, in newtons.
Medium
49.A fixed mass of gas at constant temperature occupies a volume of 0.022 m³ at a pressure of 1.53 MPa. It expands until its pressure is 101 kPa. Calculate the final volume of the gas, in m³.
Medium
50.A canister supplies 20 000 cm³ of helium at a pressure of 2400 kPa. Each balloon has a volume of 1200 cm³ and is filled to atmospheric pressure, 100 kPa. Calculate how many balloons can be filled, assuming the temperature stays constant.
Medium
51.Complete the sentences about the pressure of a gas, using the correct scientific terms.
Medium
Gas pressure is caused by gas molecules colliding with the ____ of the container. These collisions produce a net force at ____ angles to the wall. Pressure is defined as the force exerted per unit ____.
52.Complete the sentences about the Kelvin temperature scale.
Medium
Absolute zero is equal to ____ K, which is the same as ____ °C. A temperature of 350 K is equal to ____ °C.
53.Explain, in terms of particles, why the pressure of a gas increases when its volume decreases at constant temperature.
Hard
54.Explain, in terms of particles, how the air inside a sealed, rigid container exerts a pressure on the container walls.
Hard
55.A student investigates how the pressure of a fixed mass of air changes as its volume changes at constant temperature. Describe how she could obtain reliable pressure and volume readings, and state one control variable in the investigation.
Hard
56.A sealed, rigid container holds a fixed mass of gas. The gas is heated. Explain, in terms of the particles, why the pressure of the gas increases.
Hard
57.A student investigates how the pressure of a fixed mass of air changes as its volume changes at constant temperature. Describe how she could obtain reliable pressure and volume readings.
Medium
58.The temperature of a room is 300 K. What is this temperature in degrees Celsius?
Medium
- A24 °C
- B30 °C
- C27 °C
- D33 °C
59.A gas occupies a volume of 0.70 m³ at a pressure of 200 Pa. It is compressed to a volume of 0.15 m³ at constant temperature. Calculate the new pressure of the gas.
Hard
- A1026.6 Pa
- B933.3 Pa
- C1119.9 Pa
- D840 Pa
60.A gas occupies a volume of 0.50 m³ at a pressure of 120 Pa. It is compressed at constant temperature to a volume of 0.20 m³. Calculate the new pressure of the gas, in pascals.
Medium
- A270 Pa
- B330 Pa
- C300 Pa
- D360 Pa
61.A temperature is measured as 350 K. Calculate this temperature in degrees Celsius.
Medium
- A69 °C
- B77 °C
- C93 °C
- D85 °C
62.A car tyre exerts a pressure of 203 kPa on the ground. The contact area between the tyre and the ground is 0.021 m². Calculate the force that the tyre exerts on the ground, in newtons.
Medium
- A3837 N
- B4689 N
- C5115 N
- D4263 N
63.A fixed mass of gas at constant temperature occupies a volume of 0.022 m³ at a pressure of 1.53 MPa. It expands until its pressure is 101 kPa. Calculate the final volume of the gas, in m³.
Medium
- A0.333 m³
- B-0.667 m³
- C1.333 m³
- D2.333 m³
64.A canister supplies 20 000 cm³ of helium at a pressure of 2400 kPa. Each balloon has a volume of 1200 cm³ and is filled to atmospheric pressure, 100 kPa. Calculate how many balloons can be filled, assuming the temperature stays constant.
Medium
- A360 balloons
- B440 balloons
- C400 balloons
- D480 balloons

Tarjetas

Describe the motion of molecules in a gas.

Molecules in a gas are in constant random motion at high speeds. They travel in no specific path and undergo sudden changes in motion when they collide with the walls of their container or with other molecules.

What is Brownian motion?

Brownian motion is the random motion of tiny particles in a fluid. It provides evidence for the kinetic particle model of matter.

How is the temperature of a gas related to the motion of its molecules?

The temperature of a gas is related to the average kinetic energy of its molecules. The hotter the gas, the higher the average kinetic energy and the faster the molecules move.

Explain how gas molecules produce pressure on the walls of their container.

Gas molecules collide with the container walls. Each collision exerts a force on the wall. The total force per unit area is the pressure.

What is the definition of pressure?

Pressure is the force exerted per unit area. It is measured in pascals (Pa).

What happens to the pressure of a gas at constant volume when its temperature increases?

The pressure increases. The molecules move faster, so they collide with the walls more frequently and with more force.

Why does compressing a gas at constant temperature increase its pressure?

When the volume decreases, the same number of molecules are in a smaller space. They collide with the walls more frequently, increasing the force per unit area (pressure).

State the equation linking pressure and volume for a fixed mass of gas at constant temperature.

pV = constant, or p1V1 = p2V2, where p is pressure in pascals (Pa) and V is volume in cubic metres (m³).

What is Boyle's Law?

For a fixed mass of gas at constant temperature, pressure is inversely proportional to volume. This means p1V1 = p2V2.

What are the key assumptions when using p1V1 = p2V2?

The mass (and number) of gas particles remains constant, and the temperature remains constant.

What is absolute zero?

Absolute zero is the temperature at which the molecules in a substance have zero kinetic energy. It is equal to -273 °C or 0 K.

Convert 300 K to degrees Celsius.

θ/°C = T/K − 273, so 300 − 273 = 27 °C.

Convert 27 °C to kelvin.

T/K = θ/°C + 273, so 27 + 273 = 300 K.

Why is it not possible to have a temperature below 0 K?

At 0 K (absolute zero), particles have zero kinetic energy. It is not possible to remove any more energy from the system, so a lower temperature cannot exist.

What happens to the temperature of a gas when work is done on it by compression?

The temperature increases. The work done transfers energy to the gas, increasing its internal energy and the kinetic energy of its molecules.

Explain why a bicycle pump gets warm when used to inflate a tyre.

Compressing the air does work on the gas, transferring energy to it. This increases the internal energy and the kinetic energy of the molecules, so the temperature rises.

What happens to the temperature of a gas when it expands and does work?

The temperature decreases. The gas does work, losing energy, which reduces the kinetic energy of its molecules.

Give an example of a gas doing work and cooling down.

When pressurised carbon dioxide is released from a cylinder, it expands and does work. This causes it to cool rapidly and can form dry ice (solid CO2).

A gas occupies 0.70 m³ at 200 Pa. It is compressed to 0.15 m³ at constant temperature. Calculate the new pressure.

Using p1V1 = p2V2: 200 × 0.70 = p2 × 0.15, so p2 = (200 × 0.70) / 0.15 = 933 Pa (to 3 s.f.).

Sketch the graph of pressure against temperature (in °C) for a gas at constant volume. What is the significance of the x-intercept?

The graph is a straight line that intercepts the temperature axis at -273 °C. This point is absolute zero, where the pressure would be zero.

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