Revision Library

revisionlibrary.co.uk

GCSE · Physics

P3b Particle Motion, Gas Pressure and Temperature

AQA 8464 · Calculator allowed · about 75 minutes

Total Marks

Name: _______________________________ Date: ____ / ____ / ______

Answer ALL questions. Show all your working.

Describe the motion of the particles in a gas.

(Total for Question 1 is 2 marks)

A sealed container of gas is heated. State what happens to the average speed of the gas particles, and explain your answer in terms of kinetic energy.

(Total for Question 2 is 2 marks)

Use the particle model to explain why a gas exerts a pressure on the walls of its container.

(Total for Question 3 is 3 marks)

Convert the following temperatures to kelvin. Use: temperature in kelvin (K) = temperature in degrees Celsius (degC) + 273

(a)27 degC(1)

(b)-18 degC(1)

(Total for Question 4 is 3 marks)

State what is meant by 'absolute zero', and give its value in degrees Celsius.

(Total for Question 5 is 2 marks)

A rigid, sealed gas cylinder contains a fixed mass of gas at a fixed volume. The cylinder is placed near a heater and its temperature increases. Explain, using the particle model, why the pressure of the gas increases.

(Total for Question 6 is 4 marks)

Priya investigates how the pressure of a fixed mass of gas depends on its temperature, at constant volume. She uses a rigid, round-bottomed flask containing trapped air, sealed with a bung fitted with a pressure sensor connected to a data logger. The flask is fully submerged in a water bath, which is heated using an electric heater and stirred continuously. A thermometer measures the temperature of the water.

(a)Identify the independent variable and the dependent variable in this investigation.(2)

(b)State one variable that Priya must control during this investigation, and explain why.(2)

(c)Priya stirs the water continuously throughout the experiment. Give one reason why.(1)

(d)Give one safety precaution, other than wearing eye protection, that Priya should take when carrying out this experiment.(1)

(e)Priya's results are shown in the table below.
Temperature (degC): 20, 35, 50, 65, 80
Pressure (kPa): 105, 111, 116, 128, 127
Identify the anomalous result.(1)

(f)Suggest one possible reason for this anomalous result.(1)

(g)Describe the pattern shown by the rest of Priya's results (ignoring the anomalous result), and use the particle model to explain this pattern.(3)

(Total for Question 7 is 11 marks)

Zainab traps some air inside a sealed syringe. She pushes the plunger in, reducing the volume of the trapped gas at constant temperature. State and explain what happens to the pressure of the trapped gas.

(Total for Question 8 is 3 marks)

Higher tier. A sealed syringe contains 60 cm³ of gas at a pressure of 100 kPa. Aditi compresses the gas, at constant temperature, until its volume is 24 cm^3. Calculate the new pressure of the gas. Use p1V1 = p2V2.

(Total for Question 9 is 3 marks)

Higher tier. A gas syringe contains 45 cm³ of air at a pressure of 1.2 x 10⁵ Pa. Callum compresses the gas, at constant temperature, until its pressure is 3.0 x 10⁵ Pa.

(a)Calculate the new volume of the gas. Use p1V1 = p2V2.(3)

(b)State one assumption you have made in this calculation.(1)

(Total for Question 10 is 4 marks)

Higher tier. A fixed mass of gas is held at constant temperature in a cylinder fitted with a piston. Explain why decreasing the volume of the gas increases its pressure, and why pressure and volume are described as inversely proportional to each other in this case.

(Total for Question 11 is 3 marks)

A fixed mass of gas is held in a cylinder fitted with a piston. Explain, using the particle model of matter, how each of the following changes increases the pressure of the gas: (i) increasing the temperature of the gas while the piston is held in a fixed position (constant volume); (ii) pushing the piston further into the cylinder at constant temperature (decreasing the volume).

(Total for Question 12 is 6 marks)

Higher tier. A fixed mass of gas has a volume of 6.0 m³ at a pressure of 240 kPa. The gas expands at constant temperature until its volume is 16 m^3. Show that the new pressure of the gas is 90 kPa. Use p1V1 = p2V2.

(Total for Question 13 is 3 marks)

Triple science only. Ffion uses a hand pump to inflate a bicycle tyre. The piston of the pump exerts an average force of 45 N on the trapped air as it moves a distance of 0.12 m into the pump barrel.

(a)Calculate the work done on the gas as the piston moves through this distance. Use: work done = force x distance moved in the direction of the force (W = F x d).(2)

(b)State which energy store of the gas increases as a result of this work being done on it.(1)

(Total for Question 14 is 3 marks)

Triple science only. When Ffion pumps up the tyre quickly, she notices that the barrel of the pump becomes warm. Explain, in terms of energy transfers, why the temperature of the air inside the pump increases as it is compressed.

(Total for Question 15 is 3 marks)

Triple science only. A piston of cross-sectional area 0.0025 m² is used to compress gas in a sealed cylinder. The pressure of the gas is 2.0 x 10⁵ Pa. The piston moves a distance of 0.080 m while compressing the gas. Use p = F / A and W = F x d.

(a)Calculate the force exerted by the gas on the piston.(2)

(b)Calculate the work done on the gas as the piston moves through 0.080 m. Use your answer to part (a).(2)

(Total for Question 16 is 4 marks)

Triple science only. Ffion also notices that the pump barrel only becomes slightly warm if she inflates the same tyre slowly, using the same total number of pump strokes. Explain this difference.

(Total for Question 17 is 3 marks)

Higher tier. For a fixed mass of gas at constant temperature, p1V1 = p2V2. Describe the shape of a graph of pressure (y-axis) plotted against 1/volume (x-axis) for this gas, and explain why it has this shape.

(Total for Question 18 is 3 marks)

Higher tier. A weather balloon is released from the ground carrying a sealed container of 8.0 m³ of helium gas. At ground level, the atmospheric pressure is 1.0 x 10⁵ Pa. As the balloon rises, the falling atmospheric pressure allows the gas inside to expand. Assume the temperature of the gas remains constant.

(a)Calculate the volume of the gas when the atmospheric pressure has fallen to 2.5 x 10⁴ Pa. Use p1V1 = p2V2.(3)

(b)In reality, the temperature of the atmosphere (and of the gas in the balloon) falls as the balloon rises. Explain whether the actual volume of the gas at this altitude would be greater than, less than, or equal to your answer to part (a).(3)

(Total for Question 19 is 6 marks)

Mark scheme · P3b Particle Motion, Gas Pressure and Temperature

Question 1

B1 particles move randomly, in random directions, oe
B1 particles move in straight lines, at high (constantly changing) speed, until they collide with each other or the walls of their container, oe
Answer: Gas particles move randomly, in straight lines, at high and constantly changing speed, until they collide with each other or the container walls.

Question 2

B1 the average speed of the particles increases, oe
B1 because the average kinetic energy of the particles increases as the temperature increases, oe
Answer: The average speed increases, because the average kinetic energy of the particles increases as the temperature rises.

Question 3

B1 the gas particles move randomly and continuously, colliding with the walls of the container, oe
B1 each collision exerts a (tiny) force on the wall, acting at right angles (normal) to the surface, oe
B1 the total force from the very large number of collisions, acting over the surface area of the walls, causes the pressure of the gas, oe
Answer: Gas particles move randomly and collide with the container walls; each collision exerts a force at right angles to the surface, and the total force per unit area from many collisions causes the gas pressure.

Question 4

(a) B1 300 K cao
(a) Answer: 300 K
(b) B1 255 K cao
(b) Answer: 255 K
(c) B1 373 K cao
(c) Answer: 373 K

Question 5

B1 the (theoretical) minimum possible temperature, at which particles have the minimum possible kinetic energy, oe
B1 -273 degC (accept 0 K) cao
Answer: Absolute zero is the lowest possible temperature, at which particles have minimum kinetic energy. It is equal to -273 degC (0 K).

Question 6

B1 as temperature increases, the average kinetic energy of the gas particles increases, so they move faster, oe
B1 the particles collide with the walls of the cylinder more frequently, oe
B1 the particles also collide with the walls with greater force (more energetic collisions), oe
B1 since the volume (and wall area) is constant, this greater and more frequent force increases the force per unit area, so the pressure increases, oe
Answer: Heating increases the particles' average kinetic energy, so they move faster and collide with the walls more often and with more force; since the volume is constant, this increases the pressure.

Question 7

(a) B1 independent variable: temperature of the water/gas
(a) B1 dependent variable: pressure of the gas
(a) Answer: Independent variable: temperature of the gas/water. Dependent variable: pressure of the gas.
(b) B1 the volume of the gas must be kept constant, e.g. by using a rigid, sealed flask, oe
(b) B1 so that any change in pressure recorded is caused only by the change in temperature, making it a fair test, oe
(b) Answer: Volume must be kept constant (rigid, sealed flask), so any pressure change recorded is caused only by the change in temperature, making it a fair test.
(c) B1 to ensure the temperature is the same (evenly distributed) throughout the water bath, so the thermometer reading represents the temperature of the gas, oe
(c) Answer: To keep the water at a uniform temperature, so the thermometer reading represents the gas temperature accurately.
(d) B1 any sensible precaution, e.g. do not exceed the maximum working pressure/temperature rating of the flask and sensor, to prevent it cracking or the bung being forced out, oe
(d) Answer: For example: do not exceed the maximum pressure/temperature rating of the flask, to prevent it cracking or the bung being forced out.
(e) B1 the result at 65 degC (128 kPa) is anomalous
(e) Answer: The pressure of 128 kPa recorded at 65 degC is anomalous.
(f) B1 any sensible suggestion, e.g. the reading may have been taken before the gas had reached the same temperature as the water (not enough time to reach thermal equilibrium), or a random error in reading the pressure sensor/data logger, oe
(f) Answer: For example: the reading may have been taken before the gas had fully reached the water's temperature, or there was a random error in the sensor reading.
(g) B1 as the temperature of the gas increases, the pressure increases (roughly steadily), oe
(g) B1 increasing temperature increases the average kinetic energy (speed) of the gas particles, so they collide with the walls of the flask more frequently and with greater force, oe
(g) B1 since the volume (and wall area) is constant, this greater and more frequent force increases the pressure, oe
(g) Answer: Pressure increases roughly steadily as temperature increases; higher temperature gives the particles more kinetic energy, so they hit the walls more often and harder, and since volume is fixed this raises the pressure.

Question 8

B1 the pressure increases, oe
B1 the particles now have less space (volume) to move in, so they travel a shorter distance between collisions with the walls of the syringe, oe
B1 so the particles collide with the walls more often (in a given time), increasing the force per unit area (pressure), oe
Answer: Pressure increases: with less volume, particles travel a shorter distance between wall collisions, so they collide with the walls more often, increasing the pressure.

Question 9

M1 correct substitution: 100 * 60 = p2 * 24, oe
M1 correct rearrangement: p2 = (100 * 60) / 24, oe
A1 250 kPa cao
Answer: 250 kPa

Question 10

(a) M1 correct rearrangement: V2 = p1V1 / p2, oe
(a) M1 correct substitution: (1.2 x 10⁵ * 45) / (3.0 x 10⁵), oe
(a) A1 18 cm³ cao
(a) Answer: 18 cm³
(b) B1 the temperature (and mass/amount) of the gas stays constant during the compression, oe
(b) Answer: That the temperature of the gas stays constant during the compression.

Question 11

B1 at constant temperature, the average kinetic energy (and average speed) of the gas particles stays the same, oe
B1 in a smaller volume, particles have less distance to travel between collisions with the container walls, so they collide with the walls more frequently, oe
B1 since the number of particles and their average speed are unchanged, this increased collision frequency alone increases the pressure, so p x V remains constant (p is inversely proportional to V), oe
Answer: At constant temperature the particles' average speed is unchanged; in a smaller volume they travel less distance between wall collisions, so they collide more often, increasing pressure while p x V stays constant.

Question 12

Level 1 (1-2): Basic, isolated statement(s) that pressure increases in one or both situations, with little or no reference to the particle model or reasoning linking cause to effect.
Level 2 (3-4): Some correct use of the particle model to explain the pressure increase in at least one of the two situations. Reasoning about the frequency and/or force of particle collisions is present but may be incomplete or only partly linked to pressure.
Level 3 (5-6): A clear, logically linked explanation of both situations using the particle model, correctly relating the increase in pressure to the frequency and/or force of particle collisions with the container walls in each case.
Indicative content:
- Gas particles are in continuous, random motion and collide with the walls of the container.
- Pressure is caused by the total force from these many collisions acting on a given area of the walls.
- (i) Increasing temperature at constant volume: the average kinetic energy of the particles increases, so they move faster.
- (i) Faster particles collide with the walls of the cylinder more frequently.
- (i) Faster particles also collide with the walls with greater force (more energetic collisions).
- (i) Both the increased frequency and increased force of collisions increase the pressure.
- (ii) Decreasing volume at constant temperature: the average kinetic energy (and speed) of the particles is unchanged.
- (ii) In a smaller volume, particles travel a shorter distance between collisions with the walls, so they collide with the walls more frequently.
- (ii) The force of each individual collision is unchanged (temperature is constant), but the increased frequency of collisions increases the pressure.
- A strong answer distinguishes that in (i) both the frequency and force of collisions increase, whereas in (ii) only the frequency increases.

Question 13

M1 correct substitution shown: 240 * 6.0 = p2 * 16, oe
M1 correct rearrangement/calculation: p2 = (240 * 6.0) / 16 (= 1440 / 16), oe
A1 working correctly leads to p2 = 90 kPa cao
Answer: 90 kPa (shown)

Question 14

(a) M1 correct substitution: W = 45 * 0.12, oe
(a) A1 5.4 J cao
(a) Answer: 5.4 J
(b) B1 the internal energy (store) of the gas, oe (accept thermal energy store)
(b) Answer: The internal energy store of the gas.

Question 15

B1 work is done on the trapped gas by the piston as it compresses the gas, oe
B1 this work done transfers energy to the gas, increasing its internal energy (energy store), oe
B1 as the internal energy of the gas increases, the average kinetic energy of its particles increases, so the temperature of the gas rises, oe
Answer: Work done on the gas by the piston transfers energy to it, increasing its internal energy; this raises the particles' average kinetic energy, so the temperature rises.

Question 16

(a) M1 correct rearrangement and substitution: F = p * A = 2.0 x 10⁵ * 0.0025, oe
(a) A1 500 N cao
(a) Answer: 500 N
(b) M1 correct substitution: W = (their answer to a) * 0.080, ft from candidate's part (a) answer, oe
(b) A1 40 J cao (or correct ft value from candidate's F)
(b) Answer: 40 J

Question 17

B1 the same total amount of work is done on the gas whether pumping quickly or slowly, so the same total energy is transferred to the gas overall, oe
B1 pumping quickly transfers this energy in a shorter time, so the rate of energy transfer (power) is much greater, causing a bigger rise in temperature, oe
B1 pumping slowly gives more time for the transferred energy to be transferred away to the surroundings (e.g. through the metal barrel) as it is produced, so the temperature rise is smaller/less noticeable, oe
Answer: The same total work is done either way, but pumping quickly transfers it in less time (higher power), causing a bigger temperature rise; pumping slowly allows more time for energy to spread to the surroundings.

Question 18

B1 a straight line through the origin, oe (i.e. pressure is directly proportional to 1/volume)
B1 because, at constant temperature, p x V = constant for a fixed mass of gas, so p = constant x (1/V), oe
B1 the gradient of the line is equal to this constant (equal to p1V1, or p2V2, etc. for the gas), oe
Answer: A straight line through the origin, because p x V is constant at fixed temperature, so p is directly proportional to 1/V; the gradient equals that constant.

Question 19

(a) M1 correct rearrangement: V2 = p1V1 / p2, oe
(a) M1 correct substitution: (1.0 x 10⁵ * 8.0) / (2.5 x 10⁴), oe
(a) A1 32 m³ cao
(a) Answer: 32 m³
(b) B1 the actual volume would be less than the calculated value, oe
(b) B1 because a lower temperature means the gas particles have less kinetic energy (move slower), oe
(b) B1 so the fall in temperature partly offsets the volume increase caused by the drop in pressure, meaning the constant-temperature assumption over-estimates the true increase in volume, oe
(b) Answer: Less than 32 m³, because the fall in temperature reduces the particles' kinetic energy, partly offsetting the volume increase caused by the drop in pressure.

Particle Motion, Gas Pressure and Temperature - Worksheets, Questions and Revision