The Particulate Nature of Matter — Free IB Physics SL Practice Questions

1FoundationMCQHeat and temperature1 markPaper 1~2 min

A digital thermometer displays a temperature of

20.0\ °\text{C}

. Using the conversion

F = \dfrac{9}{5}C + 32

, what is this temperature in degrees Fahrenheit?

Solutions

2MasteryMCQHeat and temperature1 markPaper 1~2 min

A mercury thermometer is calibrated so that the ice point corresponds to a column height of 0 cm and the steam point corresponds to a column height of 20 cm. The scale between these two fixed points is linear. When the mercury column stands 8 cm above the ice point, what is the temperature reading?

Solutions

3FoundationMCQHeat and temperature1 markPaper 1~2 min

A metal spoon is placed into a bowl of hot soup at

80\ \text{°C}

. The spoon handle is initially at

20\ \text{°C}

. After a few minutes, the handle becomes warm. Which statement correctly identifies both the direction of heat flow and the physical reason for it?

Solutions

4FoundationMCQHeat and temperature1 markPaper 1~2 min

A metal spoon is placed in a cup of hot tea. After a few minutes, the handle of the spoon, which remains above the tea, feels warm. Which statement best explains this observation?

Solutions

5MasteryMCQHeat and temperature1 markPaper 1~2 min

A thermometer reads

-10\ ^\circ\text{C}

at the ice point and

110\ ^\circ\text{C}

at the steam point. The thermometer responds linearly. When placed in a liquid, thermometer reads

37\ ^\circ\text{C}

. What is the actual temperature of the liquid?

Solutions

6FoundationMCQEarth's energy balance1 markPaper 1~2 min

A planet receives incoming solar radiation of

300 \text{ W m}^{-2}

and has an albedo of

0.20

. The planet emits outgoing terrestrial radiation of

240 \text{ W m}^{-2}

. Which statement correctly describes the planet's energy balance?

Solutions

7MasteryMCQImpact of human activity on the greenhouse effect1 markPaper 1~2 min

Two identical sealed transparent boxes are exposed to the same intensity of infrared radiation for 10 minutes. Box A contains air with a

\text{CO}_2

concentration of 0.04% by volume and Box B contains air with a

\text{CO}_2

concentration of 0.08% by volume. Both boxes start at the same temperature. Which statement describes the most likely temperature change after 10 minutes?

Solutions

8FoundationMCQEarth's energy balance1 markPaper 1~2 min

Incoming solar radiation at the top of Earth's atmosphere is

340 \text{ W m}^{-2}

. Clouds and the atmosphere reflect

77 \text{ W m}^{-2}

back to space, and Earth's surface reflects

23 \text{ W m}^{-2}

back to space. What is Earth's albedo?

Solutions

9FoundationMCQEarth's energy balance1 markPaper 1~2 min

The surface of Earth absorbs

161 \text{ W m}^{-2}

of incoming solar radiation and

333 \text{ W m}^{-2}

of downwelling longwave radiation from the atmosphere. The surface simultaneously emits

396 \text{ W m}^{-2}

of longwave terrestrial radiation upward. What is the net radiative flux at Earth's surface?

Solutions

10MasteryMCQEarth's energy balance1 markPaper 1~2 min

The shows Earth's energy balance in normalised units. Incoming solar radiation totals 100 units. Of this, 30 units are reflected by clouds and the surface back to space, 20 units are absorbed by the atmosphere, and 50 units are absorbed by the surface. The system is in radiative equilibrium, so the net radiation at the top of the atmosphere is zero. What is the total outgoing terrestrial (infrared) radiation leaving the Earth–atmosphere system to space?

Solutions

11FoundationMCQIdeal gas law (PV = nRT)1 markPaper 1~2 min

A weather balloon is filled with helium at ground level where the pressure is

1.00 \times 10^{5}

Pa and the temperature is

300

K. The balloon has a volume of

5.00 \text{ m}^3

. The balloon rises to an altitude where the pressure is

0.500 \times 10^{5}

Pa and the temperature is

250

K. Assuming the helium behaves an ideal gas, what is the volume of the balloon at this altitude?

Solutions

12MasteryMCQBoyle’s law, Charles’s law, Avogadro’s law1 markPaper 1~2 min

A capillary tube sealed at one end traps an air column of length

10.0 \text{ cm}

at a temperature of

20 \text{ °C}

. The tube is placed in a water bath at

80 \text{ °C}

. The pressure of the trapped air remains constant. What is the new length of the air column?

Solutions

13FoundationMCQIdeal gas law (PV = nRT)1 markPaper 1~2 min

A sealed syringe contains

30.0 \text{ cm}^3

of air at a pressure of

1.00 \times 10^5 \text{ Pa}

. The plunger is pushed in until the volume is

20.0 \text{ cm}^3

. The temperature of the air remains constant throughout. What is the new pressure of the air?

Solutions

14FoundationMCQIdeal gas law (PV = nRT)1 markPaper 1~2 min

A fixed mass of ideal gas is maintained at constant temperature. A student plots

P

on the vertical axis against

\dfrac{1}{V}

on the horizontal axis and obtains a straight line through the origin. Which quantity does the gradient of this line represent?

Solutions

15MasteryMCQBoyle’s law, Charles’s law, Avogadro’s law1 markPaper 1~2 min

A gas syringe contains

50.0 \text{ cm}^3

of gas at

20 \text{ °C}

. The gas is heated to

100 \text{ °C}

at constant pressure. What is the volume of the gas after heating?

Solutions

16FoundationMCQElectric charge and current1 markPaper 1~2 min

A student connects a

9.0\,\text{V}

battery to a small motor. The current in the circuit is

0.30\,\text{A}

. How much charge passes through the motor in

2.0

minutes?

Solutions

17MasteryMCQElectric charge and current1 markPaper 1~2 min

A negatively charged rod is brought close to, but not touching, the metal cap of an uncharged gold-leaf electroscope. The gold leaves diverge. Which row correctly describes the charge distribution the electroscope while the rod remains in place?

Solutions

18FoundationMCQElectric charge and current1 markPaper 1~2 min

A negatively charged rod is brought close to the metal cap of an uncharged gold-leaf electroscope, without touching it. The gold leaf diverges. The rod is then removed. What is the charge on the gold leaf immediately after the rod is removed?

Solutions

19FoundationMCQElectric charge and current1 markPaper 1~2 min

Two identical conducting spheres, P and Q, are mounted on insulating stands. Sphere P carries a charge of

+6.0 \times 10^{-9}

C and sphere Q carries a charge of

-2.0 \times 10^{-9}

C. The spheres are briefly brought into contact and then separated. What is the charge on sphere P after separation?

Solutions

20MasteryMCQOhm’s law and resistivity1 markPaper 1~2 min

A copper wire of length

2.0\text{ m}

and cross-sectional area

1.0 \times 10^{-6}\text{ m}^2

has resistivity

1.7 \times 10^{-8}\ \Omega\text{m}

. A potential difference of

0.34\text{ V}

is applied across its ends. What is the current in the wire?

Solutions

21MasterySAQ-SHeat and temperature5 marksPaper 2~8 min

The graph below shows the temperature of a pure substance as it is heated at a constant rate. The substance starts as a solid and is heated until it becomes a gas. The graph contains two horizontal sections.

(a)

State what is happening to the temperature of the substance during a horizontal section of the graph. [1 mark]

(b)

Explain, in terms of molecular energy, why the temperature does not change during a horizontal section even though heat is being added. [2 marks]

(c)

The specific latent heat of fusion of the substance is

3.34 \times 10^5 \ \text{J kg}^{-1}

and the specific latent heat of vaporisation is

7.54 \times 10^5 \ \text{J kg}^{-1}

. Calculate the ratio of the thermal energy required to completely vaporise

0.200 \ \text{kg}

of the substance (at its boiling point) to the thermal energy required to completely melt the same mass (at its melting point). [2 marks]

Solutions

22MasterySAQ-SHeat and temperature5 marksPaper 2~8 min

Two liquids, X and Y, of equal mass are heated by identical heaters for the same duration. The graph shows the temperature change of each liquid over time. Liquid X has a steeper gradient than liquid Y on the temperature–time graph.

(a)

Deduce which liquid has the higher specific heat capacity. Use the graph and the equation

Q = mc\Delta T

to justify your answer. [2 marks]

(b)

The temperature of liquid X rises by

15.0 \text{ °C}

when

5000 \text{ J}

of energy is supplied to a sample of liquid X. The specific heat capacity of liquid X is

2500 \text{ J kg}^{-1} \text{ K}^{-1}

. Calculate the mass of the sample. [3 marks]

Solutions

23ChallengeSAQ-LHeat and temperature7 marksPaper 2~11 min

Data

P = \dfrac{W}{t}

,

\quad Q = mc\Delta T

,

\quad \Delta T(\text{K}) = \Delta T(°\text{C})

A student investigates the thermal properties of an unknown liquid. A 0.500 kg sample is heated using an electric heater rated at 120 W, fully immersed in the liquid, which is stirred continuously. The initial temperature is 20.0 °C. After 150 s the temperature reaches 68.0 °C.

(a)

Determine the specific heat capacity of the liquid, assuming all electrical energy is absorbed by the liquid. [3 marks]

(b)

The student repeats the experiment with the heater only partially immersed and without stirring. The temperature after 150 s is 55.0 °C. Explain, in terms of thermal energy transfer, why the measured temperature rise is smaller. [2 marks]

(c)

The accepted specific heat capacity of water is 4180 J kg

^{-1}

K

^{-1}

. The student claims the unknown liquid could be water, and that any discrepancy is due to random measurement error. Evaluate this claim. [2 marks]

Solutions

24MasterySAQ-SHeat and temperature7 marksPaper 2~11 min

A student uses a temperature probe connected to a data logger to record the cooling of a hot metal cylinder in air. The graph shows temperature decreasing non-linearly with time, approaching room temperature of 20 °C.

(a)

Explain why the rate of cooling decreases as the metal cylinder approaches room temperature. [2 marks]

(b)

The cylinder has a mass of 0.200 kg and specific heat capacity of 500 J kg⁻¹ K⁻¹. It cools from 80 °C to 50 °C. Calculate the thermal energy lost by the cylinder. [2 marks]

(c)

The student claims that, because the rate of cooling decreases over time, the cylinder will never actually reach room temperature. Evaluate this claim. [3 marks]

Solutions

25MasterySAQ-SHeat and temperature8 marksPaper 2~12 min

A student uses an electric heater to heat

0.200 \text{ kg}

of a liquid. The heater supplies thermal energy at a constant rate of

50.0 \text{ W}

. The temperature of the liquid is recorded every

30 \text{ s}

, and the data is plotted on a graph of temperature (y-axis) against time (x-axis). The graph shows a straight line with a gradient of

0.600 \text{ °C s}^{-1}

.

(a)

State the feature of the graph that indicates the liquid is not changing state. [1 mark]

(b)

Explain why a straight line on this graph confirms that no phase change is occurring. [2 marks]

(c)

Calculate the specific heat capacity of the liquid. [3 marks]

(d)

The student suggests that the calculated value of specific heat capacity will be an overestimate of the true value. Evaluate this claim. Useful equations:

P = \dfrac{Q}{t}

,

\quad Q = mc\Delta T

[2 marks]

Solutions

26ChallengeSAQ-LImpact of human activity on the greenhouse effect7 marksPaper 2~11 min

The burning of fossil fuels releases both

\text{CO}_2

and sulfur dioxide (

\text{SO}_2

).

\text{SO}_2

forms sulfate aerosols in the atmosphere, which have a cooling effect by reflecting sunlight back to space. The radiative forcing from

\text{SO}_2

aerosols in 2020 was estimated to be

-0.4 \text{ W m}^{-2}

, while the forcing from

\text{CO}_2

was

+2.2 \text{ W m}^{-2}

.

(a)

Using

\Delta F_{\text{net}} = \Delta F_{\text{CO}_2} + \Delta F_{\text{SO}_2}

, determine the net radiative forcing from these two sources and the percentage of the

\text{CO}_2

warming that is offset by

\text{SO}_2

cooling. [3 marks]

(b)

Explain why reducing

\text{SO}_2

emissions through clean air legislation can paradoxically accelerate global warming. [2 marks]

(c)

A government proposes immediately eliminating all

\text{SO}_2

emissions to maximise public health benefits. Evaluate whether this policy is justified, considering both the short-term and long-term consequences. [2 marks]

Solutions

27MasterySAQ-SEarth's energy balance5 marksPaper 2~8 min

The below shows the Earth's energy balance in arbitrary units. - Incoming solar radiation: 100 units - Reflected solar radiation (by surface and atmosphere): 20 units - Absorbed by Earth's surface: 50 units - Absorbed by atmosphere: 30 units - Outgoing terrestrial (infrared) radiation to space: 70 units

(a)

State the condition required for the Earth's energy balance to be maintained. [1 mark]

(b)

Calculate the net energy gained or lost by the Earth system per unit time, using the values given. [2 marks]

(c)

Deduce whether the Earth is warming or cooling. [2 marks]

Solutions

28ChallengeSAQ-LImpact of human activity on the greenhouse effect7 marksPaper 2~11 min

Data

1 tonne

= 1000\ \text{kg}

A power plant produces 1000 MW of electrical power and emits

\text{CO}_2

at a rate of 500 tonnes per hour. A carbon capture and storage (CCS) system is installed that captures 90% of the emitted

\text{CO}_2

but requires 30% of the plant's original electrical output to operate.

(a)

Calculate the net electrical power output of the plant after CCS is installed. [1 mark]

(b)

Determine the mass of

\text{CO}_2

emitted per hour after the CCS system operates. [1 mark]

(c)

Explain why the effective reduction in

\text{CO}_2

emitted per megawatt-hour of useful energy delivered is less than 90%. [2 marks]

(d)

Evaluate whether CCS represents a viable long-term strategy for mitigating climate change, with reference to both technical limitations and economic considerations. [3 marks]

Solutions

29MasterySAQ-SEarth's energy balance7 marksPaper 2~11 min

A graph shows the variation of incoming solar radiation

S

and outgoing terrestrial radiation

L

with latitude for a hypothetical planet. - At the equator:

S = 400 \ \text{W m}^{-2}

,

L = 350 \ \text{W m}^{-2}

- At the poles:

S = 100 \ \text{W m}^{-2}

,

L = 150 \ \text{W m}^{-2}

Use:

\text{Net radiation} = S - L

(a)

State whether the equator and the poles each experience a net energy gain or loss. [2 marks]

(b)

Calculate the net radiation balance at the equator and at the poles. [2 marks]

(c)

Explain why the existence of these two opposing net radiation balances does not result in the equator continuously warming and the poles continuously cooling. [3 marks]

Solutions

30MasterySAQ-SEarth's energy balance5 marksPaper 2~8 min

A region of Earth's surface receives incoming solar radiation of

250 \text{ W m}^{-2}

. Of this,

50 \text{ W m}^{-2}

is reflected back to space and

20 \text{ W m}^{-2}

is absorbed by the atmosphere. The surface emits infrared radiation of

150 \text{ W m}^{-2}

and outgoing infrared radiation to space is

180 \text{ W m}^{-2}

.

(a)

Explain why reflected solar radiation does not contribute to the energy balance of the Earth–atmosphere system, whereas outgoing infrared radiation does. [2 marks]

(b)

Calculate the net energy flux at Earth's surface. [2 marks]

(c)

The outgoing infrared radiation to space is

180 \text{ W m}^{-2}

, yet the surface emits

150 \text{ W m}^{-2}

. Deduce what this implies about the role of the atmosphere in the energy budget. [1 mark]

Solutions

31ChallengeSAQ-LBoyle’s law, Charles’s law, Avogadro’s law7 marksPaper 2~11 min

A student performs an experiment to verify Boyle's law using a gas syringe. The following data are recorded for a fixed mass of gas at constant temperature

T_1 = 300\,\text{K}

:

P\,/\,10^5\,\text{Pa}

—

V\,/\,\text{cm}^3

1.00

—

20.0

2.00

—

9.6

4.00

—

5.0

(a)

Calculate the product

PV

for each data point and identify which measurement is inconsistent with Boyle's law (

PV = k

). State the value of

k

that the consistent data support. [2 marks]

(b)

The student heats the gas at constant volume from

T_1 = 300\,\text{K}

until the pressure doubles. Determine the new temperature

T_2

. [2 marks]

(c)

Explain, using kinetic molecular theory, why the product

PV

remains constant when temperature is constant. [2 marks]

(d)

Evaluate one source of systematic error in this syringe experiment that could cause a data point to deviate from

PV = k

. [1 mark]

Solutions

32MasterySAQ-SReal gases and deviations from ideal gas behaviour5 marksPaper 2~8 min

Data

Z = \frac{PV}{nRT}, \quad R = 0.08206\,\text{L\,atm\,mol}^{-1}\text{K}^{-1}

The graph below shows the isotherms (

PV

curves) for a real gas at three different temperatures

T_1 < T_2 < T_3

, compared to the ideal gas isotherm (dashed line).

(a)

Describe how temperature affects the deviation from ideal gas behaviour, as shown by the graph. [2 marks]

(b)

At temperature

T_2 = 300\,\text{K}

, a

1.00\,\text{mol}

sample of the gas occupies

V = 0.500\,\text{L}

at a measured pressure of

P = 40.0\,\text{atm}

. (i) Calculate the compressibility factor

Z

for the gas under these conditions. [2]
(ii) State and explain whether attractive or repulsive intermolecular forces dominate at this state. [1 mark]

Solutions

33ChallengeSAQ-LBoyle’s law, Charles’s law, Avogadro’s law7 marksPaper 2~11 min

Data

Volume /

10^{-6}\ \text{m}^3

— 200 — 250 — 333 — 400 — 500 Pressure /

10^{5}\ \text{Pa}

— 5.00 — 4.00 — 3.00 — 2.50 — 2.00

pV = nRT

,

R = 8.31\ \text{J mol}^{-1}\text{K}^{-1}

A student investigates the relationship between pressure and volume for a fixed mass of an ideal gas at a constant temperature of 300 K. The student records the following

(a)

The student plots pressure

p

against

\dfrac{1}{V}

and obtains a straight line through the origin. (i) State what this graph demonstrates about the relationship between

p

and

V

. [1]
(ii) Calculate the gradient of the graph and hence determine the value of the constant

k

in Boyle's law,

pV = k

. [2 marks]

(b)

Explain, using the kinetic molecular model, why

pV

remains constant for an ideal gas at constant temperature. [2 marks]

(c)

The student repeats the experiment at 350 K with the same fixed mass of gas. Deduce whether

k

changes and determine its new value. [2 marks]

Solutions

34MasterySAQ-SIdeal gas law (PV = nRT)5 marksPaper 2~8 min

Data

PV = nRT

,

R = 8.31 \text{ J mol}^{-1} \text{ K}^{-1}

The graph shows the relationship between pressure and volume for a fixed mass of an ideal gas at two different temperatures,

T_1

and

T_2

.

T_1 = 300 \text{ K}

. The curve for

T_1

passes through point A at

V = 0.020 \text{ m}^3

,

P = 1.2 \times 10^5 \text{ Pa}

. The curve for

T_2

passes through point B at

V = 0.020 \text{ m}^3

,

P = 1.8 \times 10^5 \text{ Pa}

.

(a)

State how the curve for

T_1

would change if the number of moles of gas were increased while keeping temperature constant. [1 mark]

(b)

Calculate

T_2

. [2 marks]

(c)

The gas is taken from state B and compressed isothermally to

V = 0.010 \text{ m}^3

. Deduce whether the internal energy of the gas increases, decreases, or remains the same during this process. [2 marks]

Solutions

35MasterySAQ-SBoyle’s law, Charles’s law, Avogadro’s law5 marksPaper 2~8 min

Data

P_1V_1 = P_2V_2

A student investigates Boyle's law using a gas syringe sealed with a plunger. The initial volume of the gas is

30.0 \text{ cm}^3

at atmospheric pressure

1.01 \times 10^5 \text{ Pa}

. The student pushes the plunger slowly, reducing the volume to

12.0 \text{ cm}^3

.

(a)

State Boyle's law, including both conditions required for it to apply. [2 marks]

(b)

Calculate the new pressure of the gas in the syringe. [3 marks]

Solutions

36ChallengeSAQ-LElectric charge and current7 marksPaper 2~11 min

Data

F = k\frac{q_1 q_2}{r^2}, \quad F = \frac{mv^2}{r}, \quad k = 8.99 \times 10^{9}\,\text{N\,m}^2\,\text{C}^{-2}

e = 1.60 \times 10^{-19}\,\text{C}, \quad m_e = 9.11 \times 10^{-31}\,\text{kg}

A simple model of a hydrogen atom treats the electron as orbiting the proton in a circular path at a radius of

r = 5.3 \times 10^{-11}\,\text{m}

.

(a)

Determine the electrostatic force between the electron and the proton. [2 marks]

(b)

Determine the orbital speed of the electron, assuming the electrostatic force provides the centripetal force. [2 marks]

(c)

Determine the period of the electron's orbit. [1 mark]

(d)

The speed of light is

c = 3.00 \times 10^{8}\,\text{m s}^{-1}

. Calculate the ratio

v/c

for the orbiting electron and hence evaluate whether a classical (non-relativistic) treatment is valid for this model. [2 marks]

Solutions

37MasterySAQ-SElectric charge and current5 marksPaper 2~8 min

Data

k = 8.99 \times 10^{9}\,\text{N\,m}^{2}\,\text{C}^{-2}

,

E = \dfrac{kQ}{r^{2}}

*

Figure 1 shows two point charges fixed in position. Charge

X = +3.0\,\mu\text{C}

and charge

Y = -3.0\,\mu\text{C}

are separated by a distance of

0.40\,\text{m}

. Point M is the midpoint of the line joining X and Y. *

(a)

State the direction of the net electric field at M and explain why the contributions from X and Y do not cancel. [2 marks]

(b)

Calculate the magnitude of the net electric field at M. [3 marks]

Solutions

38ChallengeSAQ-LElectric charge and current7 marksPaper 2~11 min

Two small charged spheres, X and Y, are placed

0.30\,\text{m}

apart in a vacuum. Sphere X carries a charge of

+4.0 \times 10^{-6}\,\text{C}

and sphere Y carries a charge of

-2.0 \times 10^{-6}\,\text{C}

. Each sphere has a radius of

1.5 \times 10^{-2}\,\text{m}

.

(a)

Determine the magnitude and direction of the electrostatic force exerted on sphere Y by sphere X. [3 marks]

(b)

Explain, using the concept of electric field, how sphere X exerts a force on sphere Y without the two spheres being in contact. [2 marks]

(c)

Evaluate whether modelling the two spheres as point charges is valid for this calculation. Support your answer with a quantitative comparison. [2 marks]

Solutions

39ChallengeSAQ-LElectric charge and current7 marksPaper 2~11 min

A copper wire of length

2.0\,\text{m}

and uniform cross-sectional area

1.0 \times 10^{-6}\,\text{m}^2

carries a steady current of

5.0\,\text{A}

. The number density of free electrons in copper is

8.5 \times 10^{28}\,\text{m}^{-3}

.

(a)

Determine the drift velocity of the electrons in the wire. [3 marks]

(b)

Explain why the drift velocity is much smaller than the random thermal speed of electrons, yet the current is established almost instaneously when the circuit is closed. [2 marks]

(c)

A second copper wire carries the same current but has a cross-sectional area of

2.0 \times 10^{-6}\,\text{m}^2

. Determine the drift velocity in this wire and hence evaluate whether the assumption of a constant electron number density

n

is sufficient to predict how drift velocity changes with wire geometry. [2 marks]

Solutions

40MasterySAQ-SOhm’s law and resistivity6 marksPaper 2~9 min

Data

R = \frac{\rho L}{A}

A student investigates the electrical behaviour of a cylindrical wire made of an unknown metal. The wire has a length of

2.5\,\text{m}

and a cross-sectional area of

1.2 \times 10^{-6}\,\text{m}^2

. The student measures the potential difference across the wire for different currents and obtains a constant resistance of

0.36\,\Omega

.

(a)

State how the resistance of a metallic wire depends on its length and on its cross-sectional area. [2 marks]

(b)

Calculate the resistivity of the metal. [2 marks]

(c)

The student claims the wire is made of nichrome (resistivity

\approx 1.1 \times 10^{-6}\,\Omega\,\text{m}

) or aluminium (resistivity

\approx 2.8 \times 10^{-8}\,\Omega\,\text{m}

). Using your answer to (b), identify which metal is more consistent with the data and suggest one reason why the calculated value may differ from the accepted value. [2 marks]

Solutions

The Particulate Nature of Matter — Free Physics SL Practice Questions