Ideal gases and the gas laws

This question is about pressure.

Small air bubbles form in a container of water.

The pressure of the water acts on these bubbles.

The diagrams show the forces that cause this pressure.

Which diagram correctly shows how the pressure of the water acts on a stationary air bubble?

The diagram shows the air bubbles rising to the surface of the water in a container.

Explain why the bubbles increase in volume as they get nearer to the surface of the water.

Assume that the temperature of the water is the same throughout the container.

The teacher pushes the balloon onto the board of nails. The balloon does not pop.

The teacher then pops the balloon using a single nail.

Explain why the balloon does not pop when pushed onto the board of nails.

The diagram shows a submarine at rest underwater.

There are two vertical forces acting on the submarine.

One of the forces is called upthrust.

Give the name of the other force.

Draw two arrows on the diagram to represent the vertical forces acting on the submarine.

State the formula linking pressure, density, gravitational field strength and height.

Calculate the pressure from the water at a point 38 m below the surface of the water.

[density of sea water = 1030 kg/m³]

To rise back to the surface, air is pumped into a storage tank inside the submarine.

Explain how the air exerts pressure on the walls of the storage tank.

The air in the storage tank starts at a pressure of 410 kPa.

As the submarine rises, the air in the storage tank increases in temperature from 2.5C to 18C. The volume of the storage tank remains constant.

Calculate the pressure of the air in the storage tank at 18C.

This question is about gas pressure.

Diagram 1 shows some of the molecules of a gas in a sealed container.

Diagram 1

The molecules collide with all the surfaces of the container. This exerts an outward force on the container and causes pressure.

Describe how the motion of the gas molecules causes an equal pressure on all the walls of the container.

You may add to diagram 1 to help your answer.

The width of the container is slowly decreased so that the volume of the container is smaller than before.

Diagram 2 shows the width of the container before and after this change. All other dimensions of the container remain the same.

Diagram 2

The initial volume of the gas is 130 cm³.

The initial pressure of the gas is 100 kPa.

Calculate the pressure of the gas after the width of the container is decreased.

Assume the temperature of the gas remains constant.

The photograph shows a water bath that a technician uses to heat some water.

The water bath is filled with water at an initial temperature of 15C.

Calculate the initial temperature of the water in kelvin.

The technician heats the water to a final temperature of 60C.

Describe how the energy of the water molecules changes as the temperature of the water increases.

The table shows some information about the heating element in the water bath and the heating process.

Calculate the energy transferred by the heating element in the water bath during the heating process.

Calculate the mass of water being heated.

Assume that all the energy is transferred to the thermal store of the water. [for water, specific heat capacity = 4200 J / kgC]

QUESTION CONTINUES ON THE NEXT PAGE

Some water evaporates as a gas from the water bath.

Describe the arrangement of particles in a gas.

Describe two differences between evaporation and boiling.

The diagram shows a simple barometer designed to measure atmospheric pressure.

State the formula linking pressure difference, height, density and gravitational field strength, g.

The total pressure at point X is 117 kPa.

The pressure of the trapped gas is 12 kPa.

Calculate the height of the liquid above point X.

[density of liquid = 1.36 × 10⁴kg/m³]

The Sun shines onto the barometer, increasing the temperature of the trapped gas.

The volume of the trapped gas remains constant.

Explain why the pressure of the trapped gas increases as its temperature increases.

The temperature of the trapped gas increases from 23 °C to 38 °C.

The pressure of the trapped gas is 12 kPa when its temperature is 23 °C.

Calculate the pressure of the trapped gas when its temperature is 38 °C.

A sample of steam (water in a gas state) is cooled using a very cold freezer.

The steam is cooled from an initial temperature of 150 °C.

Calculate the initial temperature of the steam in kelvin (K).

The temperature-time graph shows how the temperature of the steam changes during the cooling process.

The steam eventually becomes ice (water in a solid state).

The graph shows five stages, A, B, C, D and E, of the cooling process.

State which stages of the cooling process show a change of state.

Describe the differences in the arrangement of particles when the sample is in a gas state (steam) and a solid state (ice).

You may draw a diagram to help your answer.

Explain whether or not the energy in the kinetic store of the particles changes when the sample is changing state.

This question is about sound waves.

The table gives the frequencies of some different sound waves.

Place ticks () in the table to show which sound waves can be heard by humans.

The diagram shows the screen of an oscilloscope when a sound wave is detected.

Add to the diagram by drawing the trace of another sound wave that has a lower pitch and is quieter than the sound wave shown.

The speed of sound in air varies with temperature.

A student finds a formula in a textbook that links the speed of sound waves in air to the temperature of the air, measured in kelvin.

speed of sound in air = (0.606×temperature in kelvin) + 166

Calculate the speed of sound when the air temperature is 46 °C.

Calculate the wavelength of a sound wave with a frequency of 15 000 Hz when the air temperature is 46 °C.

The diagram shows a balloon with a mass attached held at rest just below the surface of a deep pool of water.

The balloon and mass are released.

The graph shows the velocity-time graph for the balloon and mass as they fall through the water.

Use information from the graph to determine the terminal velocity of the balloon and mass.

Explain how the balloon reaches terminal velocity.

You should use ideas about forces acting on the balloon in your answer.

State the formula linking pressure difference, height, density and gravitational field strength.

Calculate the increase in pressure on the balloon when it has reached a depth of 25 m in the water.

[for water, density = 1000 kg/m³]

At the surface, the atmospheric pressure on the balloon is 1.010⁵Pa.

Show that the total pressure on the balloon at a depth of 25 m is 3.510⁵Pa.

At the surface, where the pressure is 1.010⁵Pa, the balloon has a volume of 0.46 m³.

Calculate the volume of the balloon at a depth of 25 m.

Diagram 1 represents the atoms of a gas inside a container.

Diagram 1

Explain how the atoms exert a pressure on the walls of the container.

Explain why the pressure of the gas in the container decreases as its temperature decreases.

The volume of the container does not change.

Diagram 2 shows a device called a magneto-optical trap (MOT).

Physicists use the device to cool gases to extremely low temperatures.

The MOT uses laser beams and magnetic fields to trap a small collection of atoms with extremely small kinetic energies.

Each trapped atom has a mass of 5.0 × 10^–27kg and a mean speed of 73 m / s.

Calculate the temperature of the trapped atoms.

[mean kinetic energy of an atom = 2.1 × 10^–23 × temperature in kelvin]

The diagram shows an empty metal container that has a hole in the top.

Describe how the air molecules in the container exert a pressure on its inner walls.

The container is heated for a long time.

Explain what happens to the number of air molecules in the container.

A lid is placed on the hot container.

The lid seals the hole and the container is allowed to cool.

As the container cools, it collapses.

Explain why the container collapses.

Scientific balloons are tested in a laboratory before they are used.

In the first test the pressure of the air inside the balloon is 120 kPa.

The balloon is sealed and has a volume of 92 m³.

The pressure of the air inside the balloon is reduced to 64 kPa by reducing the external air pressure.

Calculate the new volume of the balloon.

volume =_........ ³

Give an assumption that is made in the calculation.

The pressure of the air in the balloon is returned to 120 kPa.

The temperature of the air inside the balloon is 290 K.

The balloon is tested again, changing the temperature of the air and keeping the volume of the balloon constant.

Explain why the pressure of the air in the balloon decreases when the temperature of the air decreases.

Calculate the temperature of the air when the pressure of the air in the balloon is 64 kPa.

Give your answer in kelvin.

The photograph shows a mechanic pumping air into a car tyre.

Before being pumped into the tyre, some air has a volume of 0.0043 m³ at a pressure of 100 kPa.

The pressure of this air inside the tyre is 270 kPa.

Calculate the volume of this air inside the tyre, assuming the temperature of the air does not change.

Give your answer in standard form.

volume =_........ ³

The car is fitted with a tyre pressure monitoring system.

A warning light will show in the car if the air pressure in the tyre falls below 250 kPa.

Using ideas about particles, explain why the air pressure inside the tyre is lower on a cold winter day than on a warm summer day.

The air pressure in the tyre is 270 kPa when the air temperature is 20 °C.

On a cold winter day, the temperature is 2 °C.

Determine whether the tyre pressure warning light will show in the car on the cold winter day.

[assume tyre volume does not change]

This question is about gas pressure.

The diagram shows a cylinder containing propane gas.

The propane gas is stored in the cylinder at a pressure of 1.03 × 10⁶Pa.

State the formula linking pressure, force and area.

The cylinder has an internal surface area of 1.13 m².

Calculate the force exerted on the walls of the cylinder by the propane gas.

Explain why the pressure exerted by the propane gas acts equally in all directions.

The graph shows how the pressure of a gas varies with its temperature.

Describe how the graph can be used to show that there is a minimum value of temperature, known as absolute zero.

Give the value of absolute zero in °C.

Temperature can also be measured in kelvin.

On the axes below, sketch a graph to show how the pressure of a gas varies with its kelvin temperature.

This question is about solids, liquids and gases.

Melting is the process that occurs when a solid changes into a liquid.

Using ideas about particles, describe the process of melting.

A sealed metal flask contains air at room temperature.

The flask is then heated.

The graph shows how the pressure of the air increases as its temperature increases.

Explain how heating the flask increases the temperature of the air inside the flask.

Explain why the pressure of the air increases as its temperature increases.

Using the graph, determine the pressure of the air when its temperature is 400 K.

The air in the flask is now cooled to a temperature of 230 K.

Calculate the new pressure of the air.

pressure =_........

The diagram shows apparatus used to investigate how the pressure of a gas varies with temperature.

The volume of the gas is kept constant by the flask.

The volume of the gas is a control variable.

State why it is important to keep a control variable constant throughout the investigation.

The pressure of the gas changes as its temperature increases.

The graph shows the results.

– 400 – 300 – 200 – 100 0 100 200

Explain how these results show that there is a linear, but not proportional, relationship between the pressure of the gas and its temperature in °C.

Use the graph to determine the value for absolute zero.

Explain how the pressure of the gas changes as its temperature increases.

Include ideas about particles in your answer.

The pressure of the gas is 112 kPa when its temperature is 35 °C.

The gas is heated to 340 °C using some different apparatus.

Calculate the pressure of the gas when its temperature is 340 °C.

Assume the gas has a constant volume.

The volume of the gas is constant in the investigation.

Give the name of the other quantity that must be constant for the calculation to be correct.

A glass contains fizzy water.

Bubbles of carbon dioxide form at the bottom of the glass and rise to the surface.

The graph shows the relationship between the volume of a bubble and the pressure of the gas in the bubble.

Describe the relationship shown by the graph.

State the formula linking pressure difference, height, gravitational field strength and density.

The depth of the fizzy water in the glass is 22 cm.

The density of the fizzy water is 1080 kg/m³.

Calculate the pressure difference at the bottom of the glass due to the fizzy water.

Calculate the pressure of the gas in the bubble when the bubble is at the bottom of the glass.

[atmospheric pressure = 101 000 Pa]

When a bubble is at the top of the glass, the pressure of the gas in the bubble is equal to 101 000 Pa and the bubble has a volume of 0.084 cm³.

Calculate the volume of the gas in the bubble when the bubble is at the bottom of the glass.

Assume the temperature of the gas remains constant.

volume =_........ ³

A force called upthrust acts vertically upwards on the bubble.

When the bubble is released, it accelerates vertically upwards.

Draw two labelled arrows on the diagram to show the forces on the bubble as it is released.

A student uses a computer simulation to investigate the motion of particles in a gas.

He records the pressure of the gas and the mean speed of the particles in the gas at different temperatures.

The graphs show his results.

Give a reason why the student does not start the y-axis scale from zero on either of his graphs.

Describe the relationships shown by the graphs.

Explain why the value of temperature chosen in the simulation should not decrease below – 273 °C.

The student then calculates the kinetic energy of a single gas particle at each temperature.

Using the curve of best fit on graph 2, determine the mean speed of a gas particle when the gas temperature is 100 °C.

The mass of a single gas particle is 5.3 × 10^–26 kg.

Calculate the average kinetic energy of a gas particle when the temperature of the gas is 100 °C.

Calculate the temperature of the gas in kelvin when its temperature is 100 °C.

On the axes, sketch a graph of the average kinetic energy of the gas particles against temperature in kelvin.

This is a question about Io, a moon of Jupiter.

The diagram shows two jets of gas from volcanoes on Io.

One jet of gas is from the volcano Prometheus and the other is from the volcano Tvashtar.

Gas particles in the Prometheus jet leave the surface of Io and move vertically upwards.

The particles reach their maximum height when their speed is zero.

Some particles in the Prometheus jet reach a maximum height of 92 km.

Calculate the initial speed of these particles as they leave the surface of Io.

[acceleration due to gravity on Io 1.8 m/s²]

Before the gas particles leave the surface of Io, they are trapped in a chamber.

Explain how the gas particles exert a pressure on the walls of the chamber.

The Tvashtar chamber has the same volume as the Prometheus chamber and contains the same number of molecules of the same type of gas.

The temperature of the gas in the Prometheus chamber is 1200 K.

The temperature of the gas in the Tvashtar chamber is 1600 K.

The pressure of the gas in the Prometheus chamber is 8.2 kPa.

Calculate the pressure of the gas in the Tvashtar chamber.

Explain why the pressure inside the chambers increases when the temperature increases.

Use ideas about particles in your answer.

Explain why the particles from the Tvashtar chamber reach a greater maximum height than the particles from the Prometheus chamber.

This question is about pressure in gases.

Photograph 1 shows an open conical flask containing air.

The air in the flask is heated to a temperature of 85 °C.

Calculate the temperature of the air in the flask in kelvin.

Describe how the motion of the molecules in the flask changes when the temperature of the air inside the flask increases.

The pressure of the air in the flask does not change when the temperature of the air increases.

State what happens to the number of air molecules in the flask when the temperature of the air inside the flask increases.

Photograph 2 shows a boiled egg, without its shell, placed in the top of the conical flask containing hot air.

The flask is no longer being heated.

The egg seals the flask so that no air escapes.

Photograph 3 shows the egg and the flask a short time later.

Explain why the egg moves down into the flask and then stops moving.

Refer to ideas about pressure in your answer.

A student uses a syringe containing trapped air to investigate pressure.

Diagram 1 shows the apparatus he uses.

Diagram 2 shows the pressure gauge when the piston is at its initial position.

Determine the reading on the pressure gauge.

The piston is pushed in so that the volume of trapped air in the syringe is halved. The temperature of the trapped air remains constant.

Explain how the reading on the pressure gauge will change when the piston is pushed in.

The position of the piston is then fixed so that the volume of trapped air in the syringe is now constant.

The air in the syringe is then cooled.

State how the motion of air particles inside the syringe changes when the air is cooled.

Explain how the pressure of the trapped air inside the syringe changes when the air is cooled.

Refer to particles in your answer.

The density of the liquid is 1.3 x