Particle motion and pressure in gases

Figure 14 is a graph of atmospheric pressure against height above the surface of the Earth.

height above the surface of the Earth in m

Figure 14

The atmospheric pressure at 3000 m above the surface of the Earth, as shown in Figure 14, is

Use Figure 14 to describe how the atmospheric pressure depends on the height above the surface of the earth.

Figure 15 shows an oxygen cylinder used to provide patients with oxygen in hospital.

The volume of the cylinder, V₁, is 2.3 litres.

The pressure of gas in the cylinder, P₁, is 15 MPa.

Oxygen is released from the cylinder to the patient at a pressure of P₂ = 0.35 MPa.

Show that the total volume, V₂, of oxygen that can be released to the patient is about 100 litres at this pressure.

Use the equation

The oxygen from the cylinder flows to the patient at 6 litres / minute.

Calculate the time taken for the 100 litres of oxygen to be used up at this rate.

time taken_........ minutes

A patient requires oxygen for a longer period of time.

Suggest what could be done to supply oxygen over this longer period of time.

*(c) Figure 16 shows a cylinder containing some gas.

A piston prevents the gas escaping.

In Figure 16x a small weight pushes down and the volume and pressure of the gas are measured.

Following this, in Figure 16y, a larger weight pushes down and the volume and pressure of the gas are measured again.

small weight larger weight

Explain why the pressure and volume of the gas in the cylinder change when the larger weight pushes down on the piston. The temperature of the gas does not change.

Your answer should include

• how the volume and pressure change

• how the gas particles exert a force on the piston

A technician is investigating the pressure and volume of some gas trapped in a container.

The table in Figure 16 shows the results from the investigation.

Figure 17 is a graph of the results.

One point has not been plotted on the graph in Figure 17.

The values for this point are shaded in the results table in Figure 16.

Plot the missing point on the graph in Figure 17.

Draw a smooth curve through the points on the graph in Figure 17.

Use the graph in Figure 17 to estimate the volume at a pressure of 120 kPa.

volume =_........

The temperature of the gas in the container is 293 K.

Which of these is the same temperature as 293 K?

Figure 18 shows a cylinder containing some gas.

The cylinder of gas warms up and the temperature of the gas increases.

Complete the following sentence to describe what happens as the gas warms up.

Thermal energy transfers to_........ energy of the gas particles.

Figure 19a shows a container of gas.

The gas has a pressure of P₁ and volume V₁.

Figure 19b shows the same container after the gas has been compressed.

The pressure is now P₂ and the volume is V₂.

The temperature of the gas does not change.

Use data from Figure 19a and Figure 19b to calculate the pressure P₂ of the gas in Figure 19b.

Use the equation

* (c) Some gas is trapped in a container similar to the container in Figure 19a. The gas is compressed at a constant temperature.

Explain, in terms of gas particles, why the pressure of the gas increases when the volume decreases.

Your answer should refer to

• how the gas particles exert a pressure

• why the pressure increases when the volume decreases.

Which of these changes of state describes sublimation?

Figure 21 shows a sealed aerosol can.

The sealed can is taken from a cold room into a warm room.

If the volume of the can remains the same, which of these does not change?

Figure 22 shows a storage heater.

The storage heater contains bricks.

The bricks are heated electrically.

The electrical heater supplies 210 kJ of energy to each brick in the storage heater.

One brick has a mass of 5.8 kg.

The specific heat capacity for the brick is 860 J/kg K.

Use this data to calculate the increase in temperature of the brick.

temperature increase =_........

The actual temperature increase will be smaller than you calculated in (i).

Explain why the actual temperature increase will be smaller than the value in (i).

* (d) Describe an investigation to determine the value for the specific heat capacity of water.

Your answer should include details of

• the apparatus needed

• the experimental procedure

• how the value may be calculated from the measurements taken.

You may draw a diagram to help your answer.

Figure 5 shows the apparatus used to investigate the melting of some crushed ice.

Suggest one safety precaution needed when using the electrical heater.

Suggest one way of heating the crushed ice without using electricity.

Figure 6 shows a graph produced from the data collected by the data logger in Figure 5.

Labels P, Q, R and S have been added.

At the start, P, the beaker contains crushed ice at –8C.

Describe what happens to the crushed ice during the next 15 minutes.

You may use labels P, Q, R and S to help your answer.

Figure 7 shows bubbles of air that a diver breathes out.

The bubbles rise towards the surface.

Which row of the table is correct as one bubble rises?

Which of these is a unit of pressure?

The diver measures air pressure in atmospheres.

A bubble has an initial volume, V₁, of 0.50 litres, at a pressure, P₁, of 3.30 atmospheres.

The bubble rises towards the surface of the water, where the pressure, P₂, is 1.07 atmospheres.

Calculate the volume, V₂, of the bubble near the surface.

Use the equation

volume, V₂, of the bubble =_........

Which of these means changing state from solid directly to gas?

An object has a mass of 7.22×10^–2kg and a volume of 2.69×10^–5m³.

Calculate the density, ρ, of the object.

Use the equation

State the unit.

Aluminium has a melting point of 660C.

The absolute zero of temperature is –273C.

Calculate the melting point of aluminium in kelvin.

melting point of aluminium =_........

Describe the motion of particles in liquid aluminium (above 660C).

*(d) The table shows some properties of two materials used as thermal insulation.

The higher the R‑value, the better the thermal insulating properties of the material.

Assess which of these materials may be the more suitable to use as thermal insulation in a building.

Your answer should compare the properties of fibreglass and polystyrene given in the table.

Which of these means changing state from solid directly to gas?

An object has a mass of 7.22×10^–2kg and a volume of 2.69×10^–5m³.

Calculate the density, ρ, of the object.

Use the equation

State the unit.

Aluminium has a melting point of 660C.

The absolute zero of temperature is –273C.

Calculate the melting point of aluminium in kelvin.

melting point of aluminium =_........

Describe the motion of particles in liquid aluminium (above 660C).

A student determines the volume of a piece of metal by measuring the volume of water that it displaces.

The student wrote the following in his notebook.

The student’s description is incomplete.

Suggest two sentences that the student could have included to provide a more complete description of the correct procedure.

Figure 6 shows helium gas inside a container.

Draw an arrow on Figure 6 to show the direction of the force due to the helium gas, at the point labelled X.

Explain, in terms of particles, why the helium gas exerts a force on the sides of the container.

The container of helium is moved from a cold room to a warmer room.

State the effect of an increase in temperature on the helium gas particles inside the container.

A fixed mass of helium gas is compressed into a container, with no change in temperature.

The table in Figure 7 shows the pressure P₁ and volume V₁ before the gas is compressed, and the volume V₂ after the gas is compressed.

Calculate the pressure P₂ after the gas is compressed.

Use the equation

pressure P₂ =_........

A shop sells the container of helium gas shown in Figure 8.

The container of helium gas can be used to fill party balloons.

A filled party balloon has a volume of 0.07 m³ at a pressure of 105 kPa.

The shop claims that you can fill at least 30 party balloons using the gas from the container.

Comment on the shop’s claim.

Use information about the volume of the gas at a pressure of 105 kPa as shown in the table in Figure 7.

Explain the difference between the term ‘specific heat capacity’ and the term ‘specific latent heat’ when applied to heating substances.

Figure 19 shows some apparatus that may be used to determine the specific heat capacity of water.

A student measures the initial temperature of the water.

The power supply is switched on for 10 minutes and then switched off.

Explain how the student should then obtain an accurate reading for the final temperature of the water, to be used in the calculation of the specific heat capacity.

*(c) A container of gas is at room temperature.

The gas is then heated.

The volume of the container remains the same.

By considering changes in velocities of the gas particles, explain how the temperature increase affects

• the average kinetic energy of the particles

• the pressure the particles exert on the walls of the container.

When the pressure in a container of gas increases, the particles of the gas

A student investigates the pressure and volume of some trapped gas. Figure 4 shows the apparatus used.

Figure 5 shows the student’s table of results.

Suggest what the student should add to the headings of the table in Figure 5.

Use Figure 5 to estimate the volume of gas for a pressure reading of ‘170’.

volume of gas =_........

Suggest two ways the student could improve the investigation.

Explain whether the values, in the column headed ‘ p × V ’ in Figure 5, fit the equation

Describe, in terms of particles, two differences between a solid and a liquid of the same substance.

Figure 6 shows the dimensions of a solid block of concrete.

Density of concrete, ρ, = 2100 kg / m³.

Calculate the mass of the concrete block.

Use the equation

m = ρ × V

Figure 7 shows a shed made mostly of concrete blocks.

State two practical ways to reduce heat loss from this shed.

On a very cold day, the temperature of the air is −4 °C.

Calculate the value of this temperature on the kelvin scale.

Figure 16 shows a metal container with a movable piston.

Point X is on the inner surface of the container.

The gas in the container is at a higher pressure than the air outside the container.

Which of these shows the direction of the force, due to the gas, on the container at point X?

The pressure of the gas in Figure 16 (P₁) is 120 kPa.

The volume of the gas in Figure 16 (V₁) is 2500 cm³.

The piston is pushed up slowly so that the temperature of the gas does not change.

The new volume of the gas (V₂) is 1600 cm³.

Calculate the new pressure of the gas, P₂.

Use the equation

new pressure, P₂ =_........

Figure 17 shows a bicycle pump with a closed end.

The area of the piston is 2 cm².

A force of 28 N is applied to the piston.

Calculate the pressure, in N/cm², of the piston on the air in the bicycle pump.

*(d) A container is sealed so that the mass of the gas inside cannot change.

The volume of the gas is changed and the pressure is measured at different volumes.

The temperature of the gas does not change.

Figure 18 is a graph of the results.

Explain, in terms of the movement of particles, why there is a pressure on the container and why the pressure changes as shown in Figure 18.

The particles of a gas exert a pressure on the walls of a container.

Which row of the table is correct when the pressure of the gas changes?

A digital thermometer gives a temperature reading of 23 °C.

Calculate the value of this temperature in kelvin.

A student changes the volume of gas in a container and notes the pressure for different values of the volume. The results are shown in Figure 6 and plotted on the graph in Figure 7.

Identify the anomalous result plotted on Figure 7 by drawing a circle on Figure 7 around the anomalous point.

Draw the curve of best fit on Figure 7.

Describe how the graph in Figure 7 would change if the student repeated the experiment with the same mass of gas, at a higher constant temperature.

Figure 8 shows a small container of carbon dioxide at high pressure.

The pressure, P₁, in the container is 8.00 MPa.

The volume, V₁, of the container is 14.5 cm³.

The container is pierced and all of the carbon dioxide goes into a large balloon.

The volume of gas, V₂, in the large balloon is 1160 cm³.

Calculate the pressure, P₂, in the large balloon.

Use the equation

Figure 1 shows air inside a cylinder with a movable piston.

The piston is pulled a little way in the direction of the arrow, but stays inside the cylinder.

Which of these increases?

Figure 2 shows a rubber tube that can be used inside a bicycle tyre.

The tube is inflated with a bicycle pump.

The air inside the tube exerts an outward force on the wall of the tube.

State the angle that this outward force makes with the wall of the tube.

It takes 4.8 litres of air from the atmosphere to inflate the empty tube to a pressure of 400 000 Pa.

Atmospheric pressure is 100 000 Pa.

Calculate the volume of air inside the tube.

Assume the temperature of the air inside the tube is the same as the temperature of the air outside the tube.

Use an equation selected from the list of equations at the end of this paper.

When a bicycle pump is used to inflate the tube, the air in the bicycle pump gets warm.

You should ignore any effects of friction in the pump.

Explain why the air in the bicycle pump gets warm.