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B.3 Gas laws

Practice exam-style IB Physics questions for Gas laws, aligned with the syllabus and grouped by topic.

Verified by Kun
Verified by Kun
Paper
Difficulty
Status
Level
Question 1
SL • Paper 1A
Easy
Calculator Permitted

A sealed vessel contains 1.20Ɨ10221.20\times10^{22} helium atoms.

The amount of helium in the vessel is approximately

A.

5.0Ɨ10āˆ’2Ā mol5.0\times10^{-2}\ \text{mol}

B.

7.2Ɨ1045Ā mol7.2\times10^{45}\ \text{mol}

C.

2.0Ɨ10āˆ’2Ā mol2.0\times10^{-2}\ \text{mol}

D.

2.0Ɨ101Ā mol2.0\times10^{1}\ \text{mol}

Question 2
SL • Paper 1A
Easy
Calculator Permitted

A kinetic theory model is used to describe an ideal gas.

The statement that is an assumption of this model is

A.

The particles exert no intermolecular forces except during collisions.

B.

The particles move with the same velocity at all instants.

C.

The particles lose kinetic energy in collisions with the container walls.

D.

The particles occupy a volume comparable with the volume of the container.

Question 3
SL • Paper 1A
Easy
Calculator Permitted

A gas in a syringe exerts a normal force of 18Ā N18\ \text{N} on a piston of cross-sectional area 6.0Ā cm26.0\ \text{cm}^2.

The pressure exerted by the gas on the piston is

A.

3.0Ɨ104Ā Pa3.0\times10^4\ \text{Pa}

B.

3.0Ɨ105Ā Pa3.0\times10^5\ \text{Pa}

C.

1.1Ɨ105Ā Pa1.1\times10^5\ \text{Pa}

D.

3.0Ɨ103Ā Pa3.0\times10^3\ \text{Pa}

Question 4
SL • Paper 1A
Easy
Calculator Permitted

A fixed amount of ideal gas is kept at constant temperature.

The option that shows the graph of pressure PP against volume VV is

A.
B.
C.
D.
Question 5
SL • Paper 1A
Easy
Calculator Permitted

An ideal gas has amount 0.020Ā mol0.020\ \text{mol}, volume 5.0Ɨ10āˆ’4Ā m35.0\times10^{-4}\ \text{m}^3 and temperature 300Ā K300\ \text{K}.

The pressure of the gas is approximately

A.

1.0Ɨ105Ā Pa1.0\times10^5\ \text{Pa}

B.

1.0Ɨ104Ā Pa1.0\times10^4\ \text{Pa}

C.

2.5Ɨ105Ā Pa2.5\times10^5\ \text{Pa}

D.

1.2Ɨ106Ā Pa1.2\times10^6\ \text{Pa}

Question 6
HL • Paper 1A
Easy
Calculator Permitted

The temperature of 0.50Ā mol0.50\ \text{mol} of an ideal monatomic gas increases from 290Ā K290\ \text{K} to 350Ā K350\ \text{K}.

The increase in internal energy of the gas is approximately

A.

125Ā J125\ \text{J}

B.

2400Ā J2400\ \text{J}

C.

250Ā J250\ \text{J}

D.

370Ā J370\ \text{J}

Question 7
HL • Paper 1A
Easy
Calculator Permitted

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 PA/PBP_A/P_B is

A.

11

B.

1/21/2

C.

44

D.

22

Question 8
SL • Paper 2
Easy
Calculator Permitted

A sealed inspection hatch on a chamber has an area of 1.8Ɨ10āˆ’2Ā m21.8\times10^{-2}\ \text{m}^2. The gas pressure inside the chamber is greater than the pressure outside by 6.0Ā kPa6.0\ \text{kPa}.

A

State what is meant by pressure.

[1]
Write your answer here...
B

Calculate the resultant force on the hatch due to the pressure difference.

[2]
Write your answer here...

0

Question 9
SL • Paper 1A
Medium
Calculator Permitted

A fixed amount of ideal gas is held at constant volume. Its pressure is 100 kPa100\ \text{kPa} at 27 ∘C27\ ^\circ\text{C} and it is heated to 327 ∘C327\ ^\circ\text{C}.

The final pressure is

A.

400Ā kPa400\ \text{kPa}

B.

1210Ā kPa1210\ \text{kPa}

C.

50Ā kPa50\ \text{kPa}

D.

200Ā kPa200\ \text{kPa}

Question 10
HL • Paper 1A
Medium
Calculator Permitted

An ideal gas has density 1.6Ā kgĀ māˆ’31.6\ \text{kg m}^{-3} and pressure 1.2Ɨ105Ā Pa1.2\times10^5\ \text{Pa}.

Using P=13ρv2P=\dfrac{1}{3}\rho v^2, the root mean square speed of the molecules is approximately

A.

270Ā mĀ sāˆ’1270\ \text{m s}^{-1}

B.

2300Ā mĀ sāˆ’12300\ \text{m s}^{-1}

C.

470Ā mĀ sāˆ’1470\ \text{m s}^{-1}

D.

150Ā mĀ sāˆ’1150\ \text{m s}^{-1}

Question 11
HL • Paper 1A
Medium
Calculator Permitted

An ideal gas expands from state X to state Y at constant temperature.

The pressure-volume diagram for this change is

A.
B.
C.
D.
Question 12
HL • Paper 1A
Medium
Calculator Permitted

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.

3/23/2

B.

2/32/3

C.

55

D.

66

Question 13
SL • Paper 2
Medium
Calculator Permitted

A rigid flask contains argon gas at a pressure of 1.20Ɨ105Ā Pa1.20\times10^5\ \text{Pa}, a volume of 2.40Ɨ10āˆ’3Ā m32.40\times10^{-3}\ \text{m}^3 and a temperature of 300Ā K300\ \text{K}.

A

Calculate the amount of argon in the flask.

[2]
Write your answer here...
B

Calculate the number of argon atoms in the flask.

[2]
Write your answer here...

0

Question 14
SL • Paper 2
Medium
Calculator Permitted

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^3Pressure / kPa
20300
25240
30200
40150
50120
60100
A

Explain how the data could be used to verify Boyle's law.

[3]
Write your answer here...

0

Question 15
SL • Paper 2
Medium
Calculator Permitted

A fixed amount of gas in a sealed syringe has an initial pressure of 100Ā kPa100\ \text{kPa}, volume of 32Ā cm332\ \text{cm}^3 and temperature of 290Ā K290\ \text{K}. It is compressed to 20Ā cm320\ \text{cm}^3 and its temperature becomes 330Ā K330\ \text{K}.

A

Determine the final pressure of the gas.

[3]
Write your answer here...

0

Question 16
SL • Paper 2
Medium
Calculator Permitted

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.

A

Suggest which situation is better approximated by an ideal gas model, giving reasons.

[3]
Write your answer here...

0

Question 17
SL • Paper 2
Medium
Calculator Permitted

A sample of helium may be treated as an ideal monatomic gas. The amount of helium is 0.080 mol0.080\ \text{mol}. Its temperature increases from 22 ∘C22\ ^\circ\text{C} to 82 ∘C82\ ^\circ\text{C}.

A

Calculate the increase in internal energy of the helium.

[3]
Write your answer here...

0

Question 18
HL • Paper 2
Medium
Calculator Permitted

A gas is contained in a cubical box. A molecule rebounds elastically from one wall of the box.

A simple diagram of a cubical container with one molecule approaching and rebounding from a wall. The velocity component perpendicular to the wall is indicated before and after collision, with the tangential component unchanged. The diagram labels the wall and the normal direction but does not include any derived pressure equation.
A

Outline how molecular collisions with the wall give rise to gas pressure.

[3]
Write your answer here...

0

Question 19
SL • Paper 1B
Medium
Calculator Permitted

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.

Force on piston plotted against absolute gas pressure.
A

Describe the relationship between the force exerted by the gas and the gas pressure.

[1]
Write your answer here...
B

Use the graph to determine the area of the piston.

[2]
Write your answer here...
C

Suggest one reason why the extrapolated force is not zero when the extrapolated pressure is zero.

[1]
Write your answer here...

0

Question 20
SL • Paper 1B
Medium
Calculator Permitted

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.

Pressure data plotted against reciprocal volume for a fixed gas sample.
A

Explain how the graph supports Boyle's law.

[1]
Write your answer here...
B

Use the graph to determine the value of PVPV for the gas sample.

[2]
Write your answer here...
C

Outline why the compression should be carried out slowly.

[1]
Write your answer here...

0

Question 21
SL • Paper 1B
Medium
Calculator Permitted

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.

StatePressure / kPaVolume / m^3Temperature / K
11002.40 Ɨ 10^-3300
2160?360
A

State the quantity that remains constant for this fixed amount of gas if it behaves ideally.

[1]
Write your answer here...
B

In state 1, P1=100Ā kPaP_1=100\ \text{kPa}, V1=2.40Ɨ10āˆ’3Ā m3V_1=2.40\times10^{-3}\ \text{m}^3 and T1=300Ā KT_1=300\ \text{K}. In state 2, P2=160Ā kPaP_2=160\ \text{kPa} and T2=360Ā KT_2=360\ \text{K}. Calculate V2V_2.

[2]
Write your answer here...
C

Explain why temperature values in the combined gas law must be in kelvin.

[1]
Write your answer here...

0

Question 22
HL • Paper 1A
Medium
Calculator Permitted

An ideal gas has initial pressure PP, density ρ\rho and root mean square molecular speed vv. The gas is changed to a state in which the density is 4ρ4\rho and the root mean square speed is v/2v/2.

The new pressure is

A.

2P2P

B.

P/4P/4

C.

PP

D.

P/2P/2

Question 23
HL • Paper 2
Medium
Calculator Permitted

Air in a room is modelled as an ideal gas. The pressure is 1.01Ɨ105Ā Pa1.01\times10^5\ \text{Pa} and the density is 1.15Ā kgĀ māˆ’31.15\ \text{kg m}^{-3}.

A

Calculate the root mean square speed of the air molecules using P=13ρv2P=\dfrac{1}{3}\rho v^2.

[3]
Write your answer here...

0

Question 24
HL • Paper 2
Medium
Calculator Permitted

An ideal monatomic gas in a cylinder has pressure 2.0Ɨ105Ā Pa2.0\times10^5\ \text{Pa} and volume 1.5Ɨ10āˆ’3Ā m31.5\times10^{-3}\ \text{m}^3.

A

Determine the internal energy of the gas.

[2]
Write your answer here...
B

The gas then expands isothermally. State and explain the change, if any, in its internal energy.

[1]
Write your answer here...

0

Question 25
HL • Paper 2
Medium
Calculator Permitted

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 1.2Ɨ105Ā Pa1.2\times10^5\ \text{Pa} from 2.0Ɨ10āˆ’3Ā m32.0\times10^{-3}\ \text{m}^3 to 5.0Ɨ10āˆ’3Ā m35.0\times10^{-3}\ \text{m}^3. During B to C the volume is constant and the pressure decreases. The cycle is completed by C to A.

Pressure-volume cycle of a gas with three states.
A

Identify the type of change represented by B to C.

[1]
Write your answer here...
B

Determine the work done by the gas during A to B.

[2]
Write your answer here...
C

State what the area enclosed by the cycle represents.

[1]
Write your answer here...

0

Question 26
HL • Paper 2
Medium
Calculator Permitted

Nitrogen gas is stored in two containers. Container A is at 8.0Ā MPa8.0\ \text{MPa} and 290Ā K290\ \text{K}. Container B is at 100Ā kPa100\ \text{kPa} and 500Ā K500\ \text{K}.

A

Evaluate which container is more likely to contain nitrogen that behaves as an ideal gas.

[3]
Write your answer here...

0

Question 27
SL • Paper 1B
Medium
Calculator Permitted

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.

Absolute pressure increases in direct proportion to the amount of helium added at constant temperature.
A

State the relationship shown between pressure and the amount of helium in the flask.

[1]
Write your answer here...
B

For the final trial, the absolute pressure is 166Ā kPa166\ \text{kPa}, the volume is 2.00Ɨ10āˆ’3Ā m32.00\times10^{-3}\ \text{m}^3 and the temperature is 300Ā K300\ \text{K}. Calculate the number of helium atoms in the flask.

[2]
Write your answer here...
C

Suggest why helium is a suitable gas for this investigation at room temperature and low pressure.

[1]
Write your answer here...

0

Question 28
SL • Paper 1B
Medium
Calculator Permitted

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.

Gas column length at different temperatures.
A

Use the extrapolated line to estimate the Celsius temperature corresponding to zero volume.

[2]
Write your answer here...
B

State why the length of the trapped gas column is proportional to its volume.

[1]
Write your answer here...
C

Evaluate the reliability of using this experiment to determine absolute zero.

[2]
Write your answer here...

0

Question 29
SL • Paper 1B
Medium
Calculator Permitted

A fixed amount of ideal gas undergoes the changes shown on a pressure-volume diagram.

Pressure-volume diagram for an ideal gas process.
A

State the type of change represented by the path from A to B.

[1]
Write your answer here...
B

Compare the temperature of the gas at B with the temperature at C.

[1]
Write your answer here...
C

The path from B to C is at a pressure of 2.0Ɨ105Ā Pa2.0\times10^5\ \text{Pa} and the volume increases by 3.0Ɨ10āˆ’3Ā m33.0\times10^{-3}\ \text{m}^3. Determine the work done by the gas from B to C.

[2]
Write your answer here...

0

Question 30
HL • Paper 1B
Medium
Calculator Permitted

The internal energy of a sample of ideal monatomic gas is measured at different temperatures. The amount of gas is constant.

Internal energy of an ideal monatomic gas against temperature.
A

Explain why the graph is expected to be linear for an ideal monatomic gas.

[1]
Write your answer here...
B

The gradient of the best-fit line is 12.5Ā JĀ Kāˆ’112.5\ \text{J K}^{-1}. Determine the amount of gas in the sample.

[2]
Write your answer here...
C

Determine the increase in internal energy when the temperature increases by 80Ā K80\ \text{K}.

[1]
Write your answer here...

0

Question 31
HL • Paper 1B
Medium
Calculator Permitted

A molecular simulation of an ideal gas records the number of particles, pressure, volume and temperature for several equilibrium states.

StateHighlightPressure / PaVolume / m^3Number of particles, NTemperature / K
18.28Ɨ10^21.00Ɨ10^-182.00Ɨ10^5300
21.38Ɨ10^31.00Ɨ10^-182.50Ɨ10^5400
3ā˜…1.10Ɨ10^31.00Ɨ10^-182.50Ɨ10^5320
46.90Ɨ10^21.20Ɨ10^-181.50Ɨ10^5400
A

For the highlighted row, P=1.10Ɨ103Ā PaP=1.10\times10^3\ \text{Pa}, V=1.00Ɨ10āˆ’18Ā m3V=1.00\times10^{-18}\ \text{m}^3, N=2.50Ɨ105N=2.50\times10^5 and T=320Ā KT=320\ \text{K}. Calculate the value of the Boltzmann constant from these data.

[2]
Write your answer here...
B

Use NA=6.02Ɨ1023Ā molāˆ’1N_A=6.02\times10^{23}\ \text{mol}^{-1} to calculate RR from the value of kBk_B.

[1]
Write your answer here...
C

State the effect on pressure of doubling NN while keeping VV and TT constant.

[1]
Write your answer here...

0

Question 32
HL • Paper 2
Medium
Calculator Permitted

Neon atoms in an ideal gas sample have mass 3.35Ɨ10āˆ’26Ā kg3.35\times10^{-26}\ \text{kg} per atom. The thermodynamic temperature of the gas is 400Ā K400\ \text{K}.

A

Calculate the average translational kinetic energy of one neon atom.

[1]
Write your answer here...
B

Calculate the root mean square speed of the neon atoms.

[2]
Write your answer here...
C

Explain why the mean velocity of the atoms may be zero while the root mean square speed is not zero.

[1]
Write your answer here...

0

Question 33
HL • Paper 1B
Hard
Calculator Permitted

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.

StateDensity / kg m^-3rms speed / m s^-1
11.20500
21.20550
A

For one state, ρ=1.20Ā kgĀ māˆ’3\rho=1.20\ \text{kg m}^{-3} and v=500Ā mĀ sāˆ’1v=500\ \text{m s}^{-1}. Calculate the pressure predicted by the kinetic model.

[2]
Write your answer here...
B

At constant density, the root mean square speed increases from 500Ā mĀ sāˆ’1500\ \text{m s}^{-1} to 550Ā mĀ sāˆ’1550\ \text{m s}^{-1}. Determine the percentage increase in pressure.

[2]
Write your answer here...
C

Explain, in terms of molecular collisions, why increasing the root mean square speed increases the pressure.

[1]
Write your answer here...

0

Question 34
HL • Paper 1B
Hard
Calculator Permitted

The graph shows how the compressibility factor ZZ varies with pressure for a real gas at two different temperatures. For one mole of gas, Z=PVRTZ=\dfrac{PV}{RT}.

Compressibility factor of a real gas vs pressure at two temperatures, with an ideal-gas reference line.
A

State the value of ZZ for an ideal gas.

[1]
Write your answer here...
B

Identify the conditions in the graph under which the real gas most closely approximates ideal behaviour.

[1]
Write your answer here...
C

Explain why the lower-temperature curve deviates more from ideal behaviour at high pressure.

[2]
Write your answer here...
D

Suggest why liquefaction is not predicted by the ideal gas model.

[1]
Write your answer here...

0

Question 35
HL • Paper 1B
Hard
Calculator Permitted

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 101Ā kPa101\ \text{kPa}.

Gauge pressure of a fixed-volume gas at different temperatures.
A

At one temperature the gauge pressure is 48Ā kPa48\ \text{kPa}. Determine the absolute pressure of the gas.

[1]
Write your answer here...
B

Using the absolute pressure scale, the extrapolated temperature-axis intercept is āˆ’275 ∘C-275\ ^\circ\text{C}. Compare this with the accepted value of absolute zero.

[2]
Write your answer here...
C

Explain why the gauge pressure readings alone should not be used to test the pressure law.

[2]
Write your answer here...

0

Question 36
SL • Paper 2
Hard
Calculator Permitted

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.

A labelled diagram of a sealed syringe connected to a pressure sensor and placed in a water bath. The syringe contains trapped air, has a movable plunger with a scale for volume, and the water bath has a thermometer. Labels should include trapped air, pressure sensor, water bath, thermometer, and plunger.
A

The initial volume of the trapped air is 46.0Ā cm346.0\ \text{cm}^3 at a pressure of 1.05Ɨ105Ā Pa1.05\times10^5\ \text{Pa} and a temperature of 22.0∘C22.0^\circ\text{C}.

I.

Determine the amount of air in the syringe.

[3]
Write your answer here...
II.

The plunger is moved until the volume is 31.0 cm331.0\ \text{cm}^3 while the temperature remains 22.0∘C22.0^\circ\text{C}. Calculate the new pressure.

[2]
Write your answer here...
B

Explain, using the kinetic model, why the pressure increases when the volume is reduced at constant temperature.

[3]
Write your answer here...

0

Question 37
SL • Paper 2
Hard
Calculator Permitted

A student investigates the pressure law using a fixed mass of gas in a rigid flask of volume 2.40Ɨ10āˆ’3Ā m32.40\times10^{-3}\ \text{m}^3. The flask is placed in water baths at different temperatures. The measured pressure of the gas is plotted against temperature in degrees Celsius.

Pressure-temperature data for a fixed gas volume.
A

The gradient of the best-fit line is 0.335Ā kPaĀ Kāˆ’10.335\ \text{kPa K}^{-1}. The volume of the flask is 2.40Ɨ10āˆ’3Ā m32.40\times10^{-3}\ \text{m}^3.

I.

Show that the amount of gas in the flask is about 0.097Ā mol0.097\ \text{mol}.

[3]
Write your answer here...
II.

Determine the number of molecules in the flask.

[2]
Write your answer here...
B

Evaluate two limitations of using this experiment to estimate absolute zero by extrapolating the graph.

[3]
Write your answer here...

0

Question 38
SL • Paper 2
Hard
Calculator Permitted

A sample of neon gas contains 0.150Ā mol0.150\ \text{mol} of atoms. Neon may be treated as an ideal monatomic gas. The temperature of the gas is increased from 290Ā K290\ \text{K} to 410Ā K410\ \text{K}.

A

Consider the internal energy of the gas.

I.

Calculate the initial internal energy of the gas.

[2]
Write your answer here...
II.

Calculate the change in internal energy of the gas.

[2]
Write your answer here...
III.

State why no intermolecular potential energy term is included in this calculation.

[1]
Write your answer here...
B

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.

[2]
Write your answer here...

0

Question 39
HL • Paper 1B
Hard
Calculator Permitted

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.

Two molecular speed distributions with rms speed markers.
A

Identify which curve represents the higher temperature.

[1]
Write your answer here...
B

The root mean square speeds indicated on the graph are 420Ā mĀ sāˆ’1420\ \text{m s}^{-1} and 600Ā mĀ sāˆ’1600\ \text{m s}^{-1}. Determine the ratio of the higher temperature to the lower temperature.

[2]
Write your answer here...
C

Explain why a gas at rest can have zero mean velocity but a non-zero root mean square speed.

[1]
Write your answer here...

0

Question 40
SL • Paper 2
Hard
Calculator Permitted

A container of helium is at room temperature. Helium may be modelled as an ideal monatomic gas. The density of the helium is 0.164Ā kgĀ māˆ’30.164\ \text{kg m}^{-3} and the pressure is 1.00Ɨ105Ā Pa1.00\times10^5\ \text{Pa}.

A

Use the kinetic theory equation P=13ρv2P=\dfrac{1}{3}\rho v^2, where vv is the root mean square speed.

I.

Calculate the root mean square speed of the helium atoms.

[2]
Write your answer here...
II.

Explain why the mean velocity of the atoms is zero even though the root mean square speed is not zero.

[2]
Write your answer here...
B

Discuss how molecular collisions with the walls give rise to the macroscopic pressure of the gas.

[3]
Write your answer here...

0

Question 41
SL • Paper 2
Hard
Calculator Permitted

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.

P-V paths from a common initial state.
A

Identify the graphical features expected for the three processes on a pressure-volume diagram.

[3]
Write your answer here...
B

One process doubles the volume of the gas from its initial state.

I.

For the constant-temperature process, state and explain the change in pressure.

[2]
Write your answer here...
II.

For the constant-pressure process, state and explain the change in thermodynamic temperature.

[1]
Write your answer here...
C

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.

[2]
Write your answer here...

0

Question 42
SL • Paper 2
Hard
Calculator Permitted

A diver releases a small bubble of air at a depth where the absolute pressure is 3.2Ɨ105Ā Pa3.2\times10^5\ \text{Pa} and the water temperature is 6∘C6^\circ\text{C}. Near the surface the absolute pressure is 1.0Ɨ105Ā Pa1.0\times10^5\ \text{Pa} and the water temperature is 20∘C20^\circ\text{C}. The initial bubble volume is 1.6Ā cm31.6\ \text{cm}^3. Assume the amount of gas in the bubble is constant.

A vertical cross-section of water showing a small air bubble at depth and a larger bubble near the surface. Labels show depth region with higher absolute pressure and lower temperature, and surface region with lower absolute pressure and higher temperature. The diagram must not include calculated volumes.
A

Use the combined gas law to model the change in volume of the bubble.

I.

Calculate the volume of the bubble near the surface.

[3]
Write your answer here...
II.

State which change, pressure or temperature, has the larger effect on the change in volume.

[1]
Write your answer here...
III.

Explain why the pressure used in this calculation must be absolute pressure rather than gauge pressure.

[1]
Write your answer here...
B

Evaluate whether the ideal gas model is likely to be reliable for the bubble during its rise.

[3]
Write your answer here...

0

Question 43
HL • Paper 2
Hard
Calculator Permitted

A cubic container of side 0.250Ā m0.250\ \text{m} contains nitrogen gas at 300Ā K300\ \text{K} and pressure 1.20Ɨ105Ā Pa1.20\times10^5\ \text{Pa}. Nitrogen may be treated as an ideal gas with molar mass 2.80Ɨ10āˆ’2Ā kgĀ molāˆ’12.80\times10^{-2}\ \text{kg mol}^{-1}.

A cube containing gas molecules moving randomly. One molecule is shown approaching and rebounding from a wall, with velocity components normal to the wall indicated before and after collision. Labels should include side length, wall, molecule, and normal component of velocity.
A

Consider the molecular speed of the nitrogen molecules.

I.

Calculate the density of the nitrogen gas.

[2]
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II.

Use P=13ρv2P=\dfrac{1}{3}\rho v^2 to calculate the root mean square speed.

[2]
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III.

Show that this speed is consistent with 12mv2=32kBT\dfrac{1}{2}mv^2=\dfrac{3}{2}k_BT for one molecule.

[1]
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B

Discuss the origin of the factor 13\dfrac{1}{3} in P=13ρv2P=\dfrac{1}{3}\rho v^2.

[3]
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Question 44
HL • Paper 2
Hard
Calculator Permitted

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.

A

Compare the microscopic models for the gases in the two containers.

I.

State two assumptions of the ideal gas model that are most likely to fail for the gas in container B.

[2]
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II.

Explain why these assumptions fail near condensation.

[2]
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B

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.

[4]
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0

Question 45
HL • Paper 2
Hard
Calculator Permitted

A steel cylinder of volume 12.0Ā L12.0\ \text{L} contains oxygen gas at 18.0∘C18.0^\circ\text{C} and a pressure of 8.00Ɨ105Ā Pa8.00\times10^5\ \text{Pa}. Oxygen has molar mass 3.20Ɨ10āˆ’2Ā kgĀ molāˆ’13.20\times10^{-2}\ \text{kg mol}^{-1}.

A labelled steel gas cylinder connected to a pressure gauge and thermometer. The cylinder label indicates oxygen, fixed volume, and no visible leaks. The diagram should show the gas cylinder as rigid and closed.
A

Estimate the quantity of oxygen in the cylinder.

I.

Calculate the amount of oxygen in moles.

[2]
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II.

Determine the number of oxygen molecules in the cylinder.

[2]
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III.

Calculate the mass of oxygen in the cylinder.

[1]
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B

Evaluate whether using the ideal gas equation is appropriate for the oxygen in this cylinder.

[2]
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0

Question 46
HL • Paper 2
Hard
Calculator Permitted

A research balloon is filled with helium before launch. At launch the helium volume is 4.8Ā m34.8\ \text{m}^3, the temperature is 288Ā K288\ \text{K} and the pressure is 1.01Ɨ105Ā Pa1.01\times10^5\ \text{Pa}. At high altitude the pressure is 2.5Ɨ104Ā Pa2.5\times10^4\ \text{Pa} and the temperature is 235Ā K235\ \text{K}. The balloon material allows the helium to expand without significant leakage until this altitude.

A two-stage diagram of a weather balloon at launch and at high altitude. The launch balloon is smaller and labelled with sea-level pressure and temperature; the high-altitude balloon is larger and labelled with lower pressure and lower temperature. No calculated volume should be shown.
A

Model the helium as an ideal gas.

I.

Calculate the amount of helium in the balloon at launch.

[2]
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II.

Calculate the volume of the helium at high altitude.

[2]
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III.

Explain why the volume increases even though the temperature decreases.

[1]
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B

Evaluate the assumptions involved in applying the ideal gas law to the helium in the balloon at high altitude.

[3]
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0

Question 47
HL • Paper 2
Hard
Calculator Permitted

A cylinder contains an ideal monatomic gas fitted with a frictionless piston. The gas is heated slowly at constant pressure and expands from 2.0Ɨ10āˆ’3Ā m32.0\times10^{-3}\ \text{m}^3 to 5.0Ɨ10āˆ’3Ā m35.0\times10^{-3}\ \text{m}^3. The pressure is 1.5Ɨ105Ā Pa1.5\times10^5\ \text{Pa} throughout the expansion.

P-V graph for a constant-pressure gas expansion.
A

Analyse the energy changes of the gas during the expansion.

I.

Calculate the work done by the gas.

[2]
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II.

Determine the change in internal energy of the gas.

[2]
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III.

Calculate the energy transferred to the gas by heating.

[1]
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B

Discuss, in molecular terms, how gas particles of high kinetic energy can be used to perform mechanical work on the piston.

[2]
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0

Question 48
HL • Paper 2
Hard
Calculator Permitted

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.

Schematic P–V cycle of a gas.
A

Interpret the cycle using gas laws.

I.

Explain why the temperature increases during the constant-volume step from A to B.

[2]
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II.

Explain why the temperature increases during the constant-pressure expansion from B to C.

[2]
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III.

State what happens to the thermodynamic temperature during the compression from C to A.

[1]
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B

Discuss the significance of the enclosed area of the cycle and relate it to molecular behaviour.

[3]
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B.2 Greenhouse effect

B.4 Thermodynamics