A sealed vessel contains helium atoms.
The amount of helium in the vessel is approximately
A kinetic theory model is used to describe an ideal gas.
The statement that is an assumption of this model is
The particles exert no intermolecular forces except during collisions.
The particles move with the same velocity at all instants.
The particles lose kinetic energy in collisions with the container walls.
The particles occupy a volume comparable with the volume of the container.
A gas in a syringe exerts a normal force of on a piston of cross-sectional area .
The pressure exerted by the gas on the piston is
A fixed amount of ideal gas is kept at constant temperature.
The option that shows the graph of pressure against volume is
An ideal gas has amount , volume and temperature .
The pressure of the gas is approximately
The temperature of of an ideal monatomic gas increases from to .
The increase in internal energy of the gas is approximately
Two rigid containers have the same volume and are at the same temperature. Container A contains twice as many molecules of an ideal gas as container B.
The ratio is
A sealed inspection hatch on a chamber has an area of . The gas pressure inside the chamber is greater than the pressure outside by .
State what is meant by pressure.
Calculate the resultant force on the hatch due to the pressure difference.
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A fixed amount of ideal gas is held at constant volume. Its pressure is at and it is heated to .
The final pressure is
An ideal gas has density and pressure .
Using , the root mean square speed of the molecules is approximately
An ideal gas expands from state X to state Y at constant temperature.
The pressure-volume diagram for this change is
A fixed amount of ideal gas changes state. Its absolute temperature becomes three times larger and its pressure becomes two times larger.
The final volume divided by the initial volume is
A rigid flask contains argon gas at a pressure of , a volume of and a temperature of .
Calculate the amount of argon in the flask.
Calculate the number of argon atoms in the flask.
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A student investigates a fixed mass of gas in a syringe. The temperature is kept constant. The student records the pressure for different volumes.
| Volume / cm^3 | Pressure / kPa |
|---|---|
| 20 | 300 |
| 25 | 240 |
| 30 | 200 |
| 40 | 150 |
| 50 | 120 |
| 60 | 100 |
Explain how the data could be used to verify Boyle's law.
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A fixed amount of gas in a sealed syringe has an initial pressure of , volume of and temperature of . It is compressed to and its temperature becomes .
Determine the final pressure of the gas.
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The same sample of carbon dioxide is tested in two different situations: situation X is at low pressure and high temperature, and situation Y is at high pressure and low temperature.
Suggest which situation is better approximated by an ideal gas model, giving reasons.
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A sample of helium may be treated as an ideal monatomic gas. The amount of helium is . Its temperature increases from to .
Calculate the increase in internal energy of the helium.
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A gas is contained in a cubical box. A molecule rebounds elastically from one wall of the box.

Outline how molecular collisions with the wall give rise to gas pressure.
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A sealed cylinder contains air beneath a movable piston. A force sensor measures the normal force exerted by the gas on the piston while the gas pressure is varied slowly at constant temperature.

Describe the relationship between the force exerted by the gas and the gas pressure.
Use the graph to determine the area of the piston.
Suggest one reason why the extrapolated force is not zero when the extrapolated pressure is zero.
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A fixed mass of air is compressed slowly in a syringe. The temperature of the air is kept constant by allowing time for thermal equilibrium after each change of volume.

Explain how the graph supports Boyle's law.
Use the graph to determine the value of for the gas sample.
Outline why the compression should be carried out slowly.
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A fixed amount of gas in a flexible sealed container changes from state 1 to state 2. The gas is allowed to reach thermal equilibrium in each state.
| State | Pressure / kPa | Volume / m^3 | Temperature / K |
|---|---|---|---|
| 1 | 100 | 2.40 Ć 10^-3 | 300 |
| 2 | 160 | ? | 360 |
State the quantity that remains constant for this fixed amount of gas if it behaves ideally.
In state 1, , and . In state 2, and . Calculate .
Explain why temperature values in the combined gas law must be in kelvin.
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An ideal gas has initial pressure , density and root mean square molecular speed . The gas is changed to a state in which the density is and the root mean square speed is .
The new pressure is
Air in a room is modelled as an ideal gas. The pressure is and the density is .
Calculate the root mean square speed of the air molecules using .
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An ideal monatomic gas in a cylinder has pressure and volume .
Determine the internal energy of the gas.
The gas then expands isothermally. State and explain the change, if any, in its internal energy.
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The pressure-volume diagram shows a cycle for a fixed mass of ideal gas. During the process A to B, the gas expands at a constant pressure of from to . During B to C the volume is constant and the pressure decreases. The cycle is completed by C to A.

Identify the type of change represented by B to C.
Determine the work done by the gas during A to B.
State what the area enclosed by the cycle represents.
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Nitrogen gas is stored in two containers. Container A is at and . Container B is at and .
Evaluate which container is more likely to contain nitrogen that behaves as an ideal gas.
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A student adds measured amounts of helium to a rigid flask of known volume. The flask is kept in a water bath at constant temperature. The pressure is recorded after each addition.

State the relationship shown between pressure and the amount of helium in the flask.
For the final trial, the absolute pressure is , the volume is and the temperature is . Calculate the number of helium atoms in the flask.
Suggest why helium is a suitable gas for this investigation at room temperature and low pressure.
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A gas column is trapped in a narrow capillary tube by a small drop of oil. The capillary is placed in a water bath. The pressure of the trapped gas is constant and the length of the gas column is measured at different temperatures.

Use the extrapolated line to estimate the Celsius temperature corresponding to zero volume.
State why the length of the trapped gas column is proportional to its volume.
Evaluate the reliability of using this experiment to determine absolute zero.
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A fixed amount of ideal gas undergoes the changes shown on a pressure-volume diagram.

State the type of change represented by the path from A to B.
Compare the temperature of the gas at B with the temperature at C.
The path from B to C is at a pressure of and the volume increases by . Determine the work done by the gas from B to C.
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The internal energy of a sample of ideal monatomic gas is measured at different temperatures. The amount of gas is constant.

Explain why the graph is expected to be linear for an ideal monatomic gas.
The gradient of the best-fit line is . Determine the amount of gas in the sample.
Determine the increase in internal energy when the temperature increases by .
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A molecular simulation of an ideal gas records the number of particles, pressure, volume and temperature for several equilibrium states.
| State | Highlight | Pressure / Pa | Volume / m^3 | Number of particles, N | Temperature / K |
|---|---|---|---|---|---|
| 1 | 8.28Ć10^2 | 1.00Ć10^-18 | 2.00Ć10^5 | 300 | |
| 2 | 1.38Ć10^3 | 1.00Ć10^-18 | 2.50Ć10^5 | 400 | |
| 3 | ā | 1.10Ć10^3 | 1.00Ć10^-18 | 2.50Ć10^5 | 320 |
| 4 | 6.90Ć10^2 | 1.20Ć10^-18 | 1.50Ć10^5 | 400 |
For the highlighted row, , , and . Calculate the value of the Boltzmann constant from these data.
Use to calculate from the value of .
State the effect on pressure of doubling while keeping and constant.
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Neon atoms in an ideal gas sample have mass per atom. The thermodynamic temperature of the gas is .
Calculate the average translational kinetic energy of one neon atom.
Calculate the root mean square speed of the neon atoms.
Explain why the mean velocity of the atoms may be zero while the root mean square speed is not zero.
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A computer model represents an ideal gas in a cubic container. The density and root mean square speed of the molecules are recorded for different states of the gas.
| State | Density / kg m^-3 | rms speed / m s^-1 |
|---|---|---|
| 1 | 1.20 | 500 |
| 2 | 1.20 | 550 |
For one state, and . Calculate the pressure predicted by the kinetic model.
At constant density, the root mean square speed increases from to . Determine the percentage increase in pressure.
Explain, in terms of molecular collisions, why increasing the root mean square speed increases the pressure.
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The graph shows how the compressibility factor varies with pressure for a real gas at two different temperatures. For one mole of gas, .

State the value of for an ideal gas.
Identify the conditions in the graph under which the real gas most closely approximates ideal behaviour.
Explain why the lower-temperature curve deviates more from ideal behaviour at high pressure.
Suggest why liquefaction is not predicted by the ideal gas model.
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A fixed volume of gas is heated in a water bath. A pressure sensor records gauge pressure, which is the pressure above atmospheric pressure. Atmospheric pressure is .

At one temperature the gauge pressure is . Determine the absolute pressure of the gas.
Using the absolute pressure scale, the extrapolated temperature-axis intercept is . Compare this with the accepted value of absolute zero.
Explain why the gauge pressure readings alone should not be used to test the pressure law.
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A sealed syringe contains air that may be modelled as an ideal gas. The syringe is placed in a water bath and the plunger is slowly moved so that the air remains in thermal equilibrium with the bath.

The initial volume of the trapped air is at a pressure of and a temperature of .
Determine the amount of air in the syringe.
The plunger is moved until the volume is while the temperature remains . Calculate the new pressure.
Explain, using the kinetic model, why the pressure increases when the volume is reduced at constant temperature.
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A student investigates the pressure law using a fixed mass of gas in a rigid flask of volume . The flask is placed in water baths at different temperatures. The measured pressure of the gas is plotted against temperature in degrees Celsius.

The gradient of the best-fit line is . The volume of the flask is .
Show that the amount of gas in the flask is about .
Determine the number of molecules in the flask.
Evaluate two limitations of using this experiment to estimate absolute zero by extrapolating the graph.
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A sample of neon gas contains of atoms. Neon may be treated as an ideal monatomic gas. The temperature of the gas is increased from to .
Consider the internal energy of the gas.
Calculate the initial internal energy of the gas.
Calculate the change in internal energy of the gas.
State why no intermolecular potential energy term is included in this calculation.
Explain why a temperature change in kelvin has the same numerical value as a temperature change in degrees Celsius, but the temperature in the gas-law equation must be in kelvin.
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A simulation gives the distribution of molecular speeds for the same ideal gas at two different temperatures. Vertical markers indicate the root mean square speed for each distribution.

Identify which curve represents the higher temperature.
The root mean square speeds indicated on the graph are and . Determine the ratio of the higher temperature to the lower temperature.
Explain why a gas at rest can have zero mean velocity but a non-zero root mean square speed.
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A container of helium is at room temperature. Helium may be modelled as an ideal monatomic gas. The density of the helium is and the pressure is .
Use the kinetic theory equation , where is the root mean square speed.
Calculate the root mean square speed of the helium atoms.
Explain why the mean velocity of the atoms is zero even though the root mean square speed is not zero.
Discuss how molecular collisions with the walls give rise to the macroscopic pressure of the gas.
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The same fixed amount of an ideal gas is taken through three separate processes starting from the same initial state. Process X is at constant temperature, process Y is at constant pressure, and process Z is at constant volume.

Identify the graphical features expected for the three processes on a pressure-volume diagram.
One process doubles the volume of the gas from its initial state.
For the constant-temperature process, state and explain the change in pressure.
For the constant-pressure process, state and explain the change in thermodynamic temperature.
Compare the work done by the gas in an expansion at constant pressure with an expansion between the same initial and final volumes along an isothermal path below it on the pressure-volume diagram.
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A diver releases a small bubble of air at a depth where the absolute pressure is and the water temperature is . Near the surface the absolute pressure is and the water temperature is . The initial bubble volume is . Assume the amount of gas in the bubble is constant.

Use the combined gas law to model the change in volume of the bubble.
Calculate the volume of the bubble near the surface.
State which change, pressure or temperature, has the larger effect on the change in volume.
Explain why the pressure used in this calculation must be absolute pressure rather than gauge pressure.
Evaluate whether the ideal gas model is likely to be reliable for the bubble during its rise.
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A cubic container of side contains nitrogen gas at and pressure . Nitrogen may be treated as an ideal gas with molar mass .

Consider the molecular speed of the nitrogen molecules.
Calculate the density of the nitrogen gas.
Use to calculate the root mean square speed.
Show that this speed is consistent with for one molecule.
Discuss the origin of the factor in .
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Two sealed containers have the same volume and are at the same temperature. Container A holds an ideal gas. Container B holds a real gas close to condensation.
Compare the microscopic models for the gases in the two containers.
State two assumptions of the ideal gas model that are most likely to fail for the gas in container B.
Explain why these assumptions fail near condensation.
At a particular instant the two gases have the same temperature and contain the same number of particles. Discuss whether their internal energies must be the same.
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A steel cylinder of volume contains oxygen gas at and a pressure of . Oxygen has molar mass .

Estimate the quantity of oxygen in the cylinder.
Calculate the amount of oxygen in moles.
Determine the number of oxygen molecules in the cylinder.
Calculate the mass of oxygen in the cylinder.
Evaluate whether using the ideal gas equation is appropriate for the oxygen in this cylinder.
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A research balloon is filled with helium before launch. At launch the helium volume is , the temperature is and the pressure is . At high altitude the pressure is and the temperature is . The balloon material allows the helium to expand without significant leakage until this altitude.

Model the helium as an ideal gas.
Calculate the amount of helium in the balloon at launch.
Calculate the volume of the helium at high altitude.
Explain why the volume increases even though the temperature decreases.
Evaluate the assumptions involved in applying the ideal gas law to the helium in the balloon at high altitude.
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A cylinder contains an ideal monatomic gas fitted with a frictionless piston. The gas is heated slowly at constant pressure and expands from to . The pressure is throughout the expansion.

Analyse the energy changes of the gas during the expansion.
Calculate the work done by the gas.
Determine the change in internal energy of the gas.
Calculate the energy transferred to the gas by heating.
Discuss, in molecular terms, how gas particles of high kinetic energy can be used to perform mechanical work on the piston.
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A fixed amount of ideal gas is taken through a cyclic process represented on a pressure-volume diagram. The cycle consists of a constant-volume pressure increase, a constant-pressure expansion, and a compression back to the starting state.

Interpret the cycle using gas laws.
Explain why the temperature increases during the constant-volume step from A to B.
Explain why the temperature increases during the constant-pressure expansion from B to C.
State what happens to the thermodynamic temperature during the compression from C to A.
Discuss the significance of the enclosed area of the cycle and relate it to molecular behaviour.
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