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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.

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Question 1
SL • Paper 1A
Easy
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SL • Paper 1A
Easy
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A sealed vessel contains 1.20×10221.20\times10^{22} helium atoms.

The amount of helium in the vessel is approximately

A.

5.0×10−2 mol5.0\times10^{-2}\ \text{mol}

B.

7.2×1045 mol7.2\times10^{45}\ \text{mol}

C.

2.0×10−2 mol2.0\times10^{-2}\ \text{mol}

D.

2.0×101 mol2.0\times10^{1}\ \text{mol}

Question 2
SL • Paper 1A
Easy
Calculator Permitted
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
SL • Paper 1A
Easy
Calculator Permitted

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

The pressure exerted by the gas on the piston is

A.

3.0×104 Pa3.0\times10^4\ \text{Pa}

B.

3.0×105 Pa3.0\times10^5\ \text{Pa}

C.

1.1×105 Pa1.1\times10^5\ \text{Pa}

D.

3.0×103 Pa3.0\times10^3\ \text{Pa}

Question 4
SL • Paper 1A
Easy
Calculator Permitted
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.
A simple Cartesian graph with vertical axis labelled pressure P and horizontal axis labelled volume V. The plotted curve is a horizontal straight line across the graph at constant pressure. No numerical scale is shown.
B.
A simple Cartesian graph with vertical axis labelled pressure P and horizontal axis labelled volume V. The plotted curve is a vertical straight line at one fixed value of volume. No numerical scale is shown.
C.
A simple Cartesian graph with vertical axis labelled pressure P and horizontal axis labelled volume V. The plotted curve is a straight line rising from the origin to the upper right. No numerical scale is shown.
D.
A simple Cartesian graph with vertical axis labelled pressure P and horizontal axis labelled volume V. The plotted curve is a smooth decreasing hyperbola, steep at small V and flattening at larger V, staying above both axes. No numerical scale is shown.

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Question 5
SL • Paper 1A
Easy
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SL • Paper 1A
Easy
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An ideal gas has amount 0.020 mol0.020\ \text{mol}, volume 5.0×10−4 m35.0\times10^{-4}\ \text{m}^3 and temperature 300 K300\ \text{K}.

The pressure of the gas is approximately

A.

1.0×105 Pa1.0\times10^5\ \text{Pa}

B.

1.0×104 Pa1.0\times10^4\ \text{Pa}

C.

2.5×105 Pa2.5\times10^5\ \text{Pa}

D.

1.2×106 Pa1.2\times10^6\ \text{Pa}

Question 6
HL • Paper 1A
Easy
Calculator Permitted
HL • Paper 1A
Easy
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The temperature of 0.50 mol0.50\ \text{mol} of an ideal monatomic gas increases from 290 K290\ \text{K} to 350 K350\ \text{K}.

The increase in internal energy of the gas is approximately

A.

125 J125\ \text{J}

B.

2400 J2400\ \text{J}

C.

250 J250\ \text{J}

D.

370 J370\ \text{J}

Question 7
HL • Paper 1A
Easy
Calculator Permitted
HL • Paper 1A
Easy
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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
SL • Paper 2
Easy
Calculator Permitted

A sealed inspection hatch on a chamber has an area of 1.8×10−2 m21.8\times10^{-2}\ \text{m}^2. The gas pressure inside the chamber is greater than the pressure outside by 6.0 kPa6.0\ \text{kPa}.

A

State what is meant by pressure.

[1]
B

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

[2]

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Question 9
SL • Paper 1A
Medium
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SL • Paper 1A
Medium
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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.

400 kPa400\ \text{kPa}

B.

1210 kPa1210\ \text{kPa}

C.

50 kPa50\ \text{kPa}

D.

200 kPa200\ \text{kPa}

Question 10
HL • Paper 1A
Medium
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HL • Paper 1A
Medium
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An ideal gas has density 1.6 kg m−31.6\ \text{kg m}^{-3} and pressure 1.2×105 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.

270 m s−1270\ \text{m s}^{-1}

B.

2300 m s−12300\ \text{m s}^{-1}

C.

470 m s−1470\ \text{m s}^{-1}

D.

150 m s−1150\ \text{m s}^{-1}

Question 11
HL • Paper 1A
Medium
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HL • Paper 1A
Medium
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An ideal gas expands from state X to state Y at constant temperature.

The pressure-volume diagram for this change is

A.
A pressure-volume graph with vertical axis labelled P and horizontal axis labelled V. State X is at lower pressure and smaller volume. A straight diagonal line slopes upward to the right to state Y at higher pressure and larger volume.
B.
A pressure-volume graph with vertical axis labelled P and horizontal axis labelled V. State X and state Y are joined by a horizontal straight line directed to the right, showing increasing volume at unchanged pressure.
C.
A pressure-volume graph with vertical axis labelled P and horizontal axis labelled V. State X and state Y are joined by a vertical straight line with no change in volume. The pressure changes between the two states.
D.
A pressure-volume graph with vertical axis labelled P and horizontal axis labelled V. State X is at relatively high pressure and small volume. A smooth decreasing curve leads down and to the right to state Y at lower pressure and larger volume. The curve stays above both axes and has the shape of an isotherm.
Question 12
HL • Paper 1A
Medium
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HL • Paper 1A
Medium
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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

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Question 13
SL • Paper 2
Medium
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SL • Paper 2
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A rigid flask contains argon gas at a pressure of 1.20×105 Pa1.20\times10^5\ \text{Pa}, a volume of 2.40×10−3 m32.40\times10^{-3}\ \text{m}^3 and a temperature of 300 K300\ \text{K}.

A

Calculate the amount of argon in the flask.

[2]
B

Calculate the number of argon atoms in the flask.

[2]
Question 14
SL • Paper 2
Medium
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SL • Paper 2
Medium
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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 / cm3^3

Pressure / kPa

20

300

25

240

30

200

40

150

50

120

60

100

A

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

[3]
Question 15
SL • Paper 2
Medium
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SL • Paper 2
Medium
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A fixed amount of gas in a sealed syringe has an initial pressure of 100 kPa100\ \text{kPa}, volume of 32 cm332\ \text{cm}^3 and temperature of 290 K290\ \text{K}. It is compressed to 20 cm320\ \text{cm}^3 and its temperature becomes 330 K330\ \text{K}.

A

Determine the final pressure of the gas.

[3]
Question 16
SL • Paper 2
Medium
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SL • Paper 2
Medium
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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.

A

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

[3]

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Question 17
SL • Paper 2
Medium
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SL • Paper 2
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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]
Question 18
HL • Paper 2
Medium
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HL • Paper 2
Medium
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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]
Question 19
SL • Paper 1B
Medium
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SL • Paper 1B
Medium
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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.

Force on piston plotted against absolute gas pressure.
A

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

[1]
B

Use the graph to determine the area of the piston.

[2]
C

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

[1]
Question 20
SL • Paper 1B
Medium
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SL • Paper 1B
Medium
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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.

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

Explain how the graph supports Boyle's law.

[1]
B

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

[2]
C

Outline why the compression should be carried out slowly.

[1]

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Question 21
SL • Paper 1B
Medium
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SL • Paper 1B
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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 / m3\text{m}^{3}

Temperature / K

1

100

2.40×10−32.40 \times 10^{-3}

300

2

160

?

360

A

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

[1]
B

In state 1, P1=100 kPaP_1=100\ \text{kPa}, V1=2.40×10−3 m3V_1=2.40\times10^{-3}\ \text{m}^3 and T1=300 KT_1=300\ \text{K}. In state 2, P2=160 kPaP_2=160\ \text{kPa} and T2=360 KT_2=360\ \text{K}. Calculate V2V_2.

[2]
C

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

[1]
Question 22
HL • Paper 1A
Medium
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HL • Paper 1A
Medium
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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
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HL • Paper 2
Medium
Calculator Permitted

Air in a room is modelled as an ideal gas. The pressure is 1.01×105 Pa1.01\times10^5\ \text{Pa} and the density is 1.15 kg m−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]
Question 24
HL • Paper 2
Medium
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HL • Paper 2
Medium
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An ideal monatomic gas in a cylinder has pressure 2.0×105 Pa2.0\times10^5\ \text{Pa} and volume 1.5×10−3 m31.5\times10^{-3}\ \text{m}^3.

A

Determine the internal energy of the gas.

[2]
B

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

[1]

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Question 25
HL • Paper 2
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HL • Paper 2
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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 1.2×105 Pa1.2\times10^5\ \text{Pa} from 2.0×10−3 m32.0\times10^{-3}\ \text{m}^3 to 5.0×10−3 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]
B

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

[2]
C

State what the area enclosed by the cycle represents.

[1]
Question 26
HL • Paper 2
Medium
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HL • Paper 2
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Nitrogen gas is stored in two containers. Container A is at 8.0 MPa8.0\ \text{MPa} and 290 K290\ \text{K}. Container B is at 100 kPa100\ \text{kPa} and 500 K500\ \text{K}.

A

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

[3]
Question 27
SL • Paper 1B
Medium
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SL • Paper 1B
Medium
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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.

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]
B

For the final trial, the absolute pressure is 166 kPa166\ \text{kPa}, the volume is 2.00×10−3 m32.00\times10^{-3}\ \text{m}^3 and the temperature is 300 K300\ \text{K}. Calculate the number of helium atoms in the flask.

[2]
C

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

[1]
Question 28
SL • Paper 1B
Medium
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SL • Paper 1B
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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.

Gas column length at different temperatures.
A

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

[2]
B

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

[1]
C

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

[2]

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Question 29
SL • Paper 1B
Medium
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SL • Paper 1B
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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]
B

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

[1]
C

The path from B to C is at a pressure of 2.0×105 Pa2.0\times10^5\ \text{Pa} and the volume increases by 3.0×10−3 m33.0\times10^{-3}\ \text{m}^3. Determine the work done by the gas from B to C.

[2]
Question 30
HL • Paper 1B
Medium
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HL • Paper 1B
Medium
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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.

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]
B

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

[2]
C

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

[1]
Question 31
HL • Paper 1B
Medium
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HL • Paper 1B
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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 / m3\text{m}^{3}

Number of particles, N

Temperature / K

1

8.28×1028.28 \times 10^{2}

1.00×10−181.00 \times 10^{-18}

2.00×1052.00 \times 10^{5}

300

2

1.38×1031.38 \times 10^{3}

1.00×10−181.00 \times 10^{-18}

2.50×1052.50 \times 10^{5}

400

3

★

1.10×1031.10 \times 10^{3}

1.00×10−181.00 \times 10^{-18}

2.50×1052.50 \times 10^{5}

320

4

6.90×1026.90 \times 10^{2}

1.20×10−181.20 \times 10^{-18}

1.50×1051.50 \times 10^{5}

400

A

For the highlighted row, P=1.10×103 PaP=1.10\times10^3\ \text{Pa}, V=1.00×10−18 m3V=1.00\times10^{-18}\ \text{m}^3, N=2.50×105N=2.50\times10^5 and T=320 KT=320\ \text{K}. Calculate the value of the Boltzmann constant from these data.

[2]
B

Use NA=6.02×1023 mol−1N_A=6.02\times10^{23}\ \text{mol}^{-1} to calculate RR from the value of kBk_B.

[1]
C

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

[1]
Question 32
HL • Paper 2
Medium
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HL • Paper 2
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Neon atoms in an ideal gas sample have mass 3.35×10−26 kg3.35\times10^{-26}\ \text{kg} per atom. The thermodynamic temperature of the gas is 400 K400\ \text{K}.

A

Calculate the average translational kinetic energy of one neon atom.

[1]
B

Calculate the root mean square speed of the neon atoms.

[2]
C

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

[1]

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Question 33
HL • Paper 1B
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HL • Paper 1B
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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^{-3}

rms speed / m s−1^{-1}

1

1.20

500

2

1.20

550

A

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

[2]
B

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

[2]
C

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

[1]
Question 34
HL • Paper 1B
Hard
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HL • Paper 1B
Hard
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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]
B

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

[1]
C

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

[2]
D

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

[1]
Question 35
HL • Paper 1B
Hard
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HL • Paper 1B
Hard
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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 101 kPa101\ \text{kPa}.

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

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

[1]
B

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

[2]
C

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

[2]
Question 36
SL • Paper 2
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SL • Paper 2
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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.

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 46.0 cm346.0\ \text{cm}^3 at a pressure of 1.05×105 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]
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]
B

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

[3]

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Question 37
SL • Paper 2
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SL • Paper 2
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A student investigates the pressure law using a fixed mass of gas in a rigid flask of volume 2.40×10−3 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 0.335 kPa K−10.335\ \text{kPa K}^{-1}. The volume of the flask is 2.40×10−3 m32.40\times10^{-3}\ \text{m}^3.

I.

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

[3]
II.

Determine the number of molecules in the flask.

[2]
B

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

[3]
Question 38
SL • Paper 2
Hard
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SL • Paper 2
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A sample of neon gas contains 0.150 mol0.150\ \text{mol} of atoms. Neon may be treated as an ideal monatomic gas. The temperature of the gas is increased from 290 K290\ \text{K} to 410 K410\ \text{K}.

A

Consider the internal energy of the gas.

I.

Calculate the initial internal energy of the gas.

[2]
II.

Calculate the change in internal energy of the gas.

[2]
III.

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

[1]
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]
Question 39
HL • Paper 1B
Hard
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HL • Paper 1B
Hard
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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.

Two molecular speed distributions with rms speed markers.
A

Identify which curve represents the higher temperature.

[1]
B

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

[2]
C

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

[1]
Question 40
SL • Paper 2
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SL • Paper 2
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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 0.164 kg m−30.164\ \text{kg m}^{-3} and the pressure is 1.00×105 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]
II.

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

[2]
B

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

[3]

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Question 41
SL • Paper 2
Hard
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SL • Paper 2
Hard
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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.

P-V paths from a common initial state.
A

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

[3]
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]
II.

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

[1]
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]
Question 42
SL • Paper 2
Hard
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SL • Paper 2
Hard
Calculator Permitted

A diver releases a small bubble of air at a depth where the absolute pressure is 3.2×105 Pa3.2\times10^5\ \text{Pa} and the water temperature is 6∘C6^\circ\text{C}. Near the surface the absolute pressure is 1.0×105 Pa1.0\times10^5\ \text{Pa} and the water temperature is 20∘C20^\circ\text{C}. The initial bubble volume is 1.6 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]
II.

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

[1]
III.

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

[1]
B

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

[3]
Question 43
HL • Paper 2
Hard
Calculator Permitted
HL • Paper 2
Hard
Calculator Permitted

A cubic container of side 0.250 m0.250\ \text{m} contains nitrogen gas at 300 K300\ \text{K} and pressure 1.20×105 Pa1.20\times10^5\ \text{Pa}. Nitrogen may be treated as an ideal gas with molar mass 2.80×10−2 kg mol−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]
II.

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

[2]
III.

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

[1]
B

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

[3]
Question 44
HL • Paper 2
Hard
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HL • Paper 2
Hard
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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.

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]
II.

Explain why these assumptions fail near condensation.

[2]
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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Question 45
HL • Paper 2
Hard
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HL • Paper 2
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A steel cylinder of volume 12.0 L12.0\ \text{L} contains oxygen gas at 18.0∘C18.0^\circ\text{C} and a pressure of 8.00×105 Pa8.00\times10^5\ \text{Pa}. Oxygen has molar mass 3.20×10−2 kg mol−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]
II.

Determine the number of oxygen molecules in the cylinder.

[2]
III.

Calculate the mass of oxygen in the cylinder.

[1]
B

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

[2]
Question 46
HL • Paper 2
Hard
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HL • Paper 2
Hard
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A research balloon is filled with helium before launch. At launch the helium volume is 4.8 m34.8\ \text{m}^3, the temperature is 288 K288\ \text{K} and the pressure is 1.01×105 Pa1.01\times10^5\ \text{Pa}. At high altitude the pressure is 2.5×104 Pa2.5\times10^4\ \text{Pa} and the temperature is 235 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]
II.

Calculate the volume of the helium at high altitude.

[2]
III.

Explain why the volume increases even though the temperature decreases.

[1]
B

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

[3]
Question 47
HL • Paper 2
Hard
Calculator Permitted
HL • Paper 2
Hard
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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 2.0×10−3 m32.0\times10^{-3}\ \text{m}^3 to 5.0×10−3 m35.0\times10^{-3}\ \text{m}^3. The pressure is 1.5×105 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]
II.

Determine the change in internal energy of the gas.

[2]
III.

Calculate the energy transferred to the gas by heating.

[1]
B

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

[2]
Question 48
HL • Paper 2
Hard
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HL • Paper 2
Hard
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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.

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]
II.

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

[2]
III.

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

[1]
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