IB Physics SL B.3 Gas Laws

[Maximum number: 9]

A solid cylinder of height h and density $\rho$ rests on a flat surface.

(a)

Show that the pressure $p_{\mathrm{C}}$ exerted by the cylinder on the surface is given by $p_{\mathrm{C}}=\rho g h$ .

[ 2 ]

weight of cylinder $=A h g \rho$ $\text { pressure }=\frac{F}{A}=\frac{A h g \rho}{A}$

Marking guidance:

Allow use of $A=\pi r^{2}$ in MP1.

(b)

A tube of constant circular cross-section, sealed at one end, contains an ideal gas trapped by a cylinder of mercury of length 0.035 m . The whole arrangement is in the Earth's atmosphere. The density of mercury is $1.36 \times 10^{4} \mathrm{~kg} \mathrm{~m}^{-3}$ .

When the mercury is above the gas column the length of the gas column is 0.190 m .

[ 7 ]

(i)

Show that $\left(p_{\mathrm{o}}+p_{\mathrm{m}}\right) \times 0.190=\frac{n R T}{A}$ where
$p_{\mathrm{o}}=$ atmospheric pressure
$p_{\mathrm{m}}=$ pressure due to the mercury column
T= temperature of the trapped gas
n= number of moles of the trapped gas
A= cross-sectional area of the tube.

[ 2 ]

use of PV=nRT and V= Area × (0.190) seen substitution of $\mathrm{P}=p_{\mathrm{o}}+p_{\mathrm{m}}$ «re-arrangement to give answer»

(ii)

The tube is slowly rotated until the gas column is above the mercury.

Figure for Question (ii) — IB Physics SL

The length of the gas column is now 0.208 m . The temperature of the trapped gas does not change during the process.

Determine the atmospheric pressure. Give a suitable unit for your answer.

[ 4 ]

recognition that $\frac{\mathrm{nRT}}{\mathrm{A}}$ is constant $\boldsymbol{OR} 190 p_{\mathrm{o}}+190 p_{\mathrm{m}}=208 p_{0}-208 p_{\mathrm{m}}$ OR $p_{0}=\frac{398}{18} p_{\mathrm{m}}$

pressure due to mercury $p_{\mathrm{m}}=0.035 \times 1.36 \times 10^{4} \times 9.81\left(=4.67 \times 10^{3} \mathrm{~Pa}\right) 1.03 \times 10^{5}$ $\mathrm{Pa} \boldsymbol{O} \boldsymbol{R} \mathrm{Nm}^{-2} \boldsymbol{O} \boldsymbol{R} \mathrm{kgm}^{-1} \mathrm{~s}^{-2} \boldsymbol{}$

Marking guidance:

Do not award for a bald correct answer. Working must be shown to award MP3.

Award MP4 for any correct unit of pressure (eg "mm of mercury / Hg").

(iii)

Outline why the gas particles in the tube hit the mercury surface less often after the tube has been rotated.

[ 1 ]

[Maximum number: 6]

This question is in two parts. Part 1 is about ideal gases and specific heat capacity. Part 2 is about simple harmonic motion and waves.
Part 1 Ideal gases and specific heat capacity

(a)

State two assumptions of the kinetic model of an ideal gas.

[ 2 ]

(b)

Argon behaves as an ideal gas for a large range of temperatures and pressures. One mole of argon is confined in a cylinder by a freely moving piston.

[ 1 ]

(i)

Define what is meant by the term one mole of argon.

[ 1 ]

One mole of argon is the molecular weight of argon in grams, or $6.02\times10^{23}$ argon atoms, or the same number of particles as in 12 g of carbon-12.

Allow atoms or molecules for particles.

1\ \mathrm{mol}=6.02\times10^{23}\ \text{particles}

(c)

At the temperature of 350 K , the piston in (b) is now freed and the argon expands until its temperature reaches 300 K .
Explain, in terms of the molecular model of an ideal gas, why the temperature of argon decreases on expansion.

[ 3 ]

[Maximum number: 6]

The equipment shown in the diagram was used by a student to investigate the variation with volume, of the pressure p of air, at constant temperature. The air was trapped in a tube of constant cross-sectional area above a column of oil.

The pump forces oil to move up the tube decreasing the volume of the trapped air.

(a)

Outline how the results of this experiment are consistent with the ideal gas law at constant temperature.

[ 2 ]

$V \propto H$ thus ideal gas law gives $p \propto \frac{1}{H}$

so graph should be «a straight line through origin,» as observed

(b)

The cross-sectional area of the tube is $1.3 \times 10^{-3} \mathrm{~m}^{2}$ and the temperature of air is 300 K . Estimate the number of moles of air in the tube.

[ 2 ]

$n=\frac{b A}{R T} OR$ correct substitution of one point from the graph

$n=\frac{5 \times 10^{4} \times 1.3 \times 10^{-3}}{8.31 \times 300}=0.026 \approx 0.03$

Answer must be to 1 or 2 SF. Allow ECF from (b).

(c)

The equation of the line of best fit is:

p=a+\frac{b}{H}

The equation above may be used to predict the pressure of the air at extremely large values of $\frac{1}{H}$ . Suggest why this will be an unreliable estimate of the pressure.

[ 2 ]

very large $\frac{1}{H}$ means very small volumes / very high pressures

at very small volumes the ideal gas does not apply

OR

at very small volumes some of the assumptions of the kinetic theory of gases do not hold

[Maximum number: 2]

A solid cylinder of height h and density $\rho$ rests on a flat surface.

Show that the pressure $p_{\mathrm{C}}$ exerted by the cylinder on the surface is given by $p_{\mathrm{C}}=\rho g h$ .

weight of cylinder $=A h g \rho$ $\text { pressure }=\frac{F}{A}=\frac{A h g \rho}{A}$

Marking guidance:

Allow use of $A=\pi r^{2}$ in MP1.

[Maximum number: 1]

This question is in two parts. Part 1 is about ideal gases and specific heat capacity. Part 2 is about simple harmonic motion and waves.
Part 1 Ideal gases and specific heat capacity

Argon behaves as an ideal gas for a large range of temperatures and pressures. One mole of argon is confined in a cylinder by a freely moving piston.

Define what is meant by the term one mole of argon.

One mole of argon is the molecular weight of argon in grams, or $6.02\times10^{23}$ argon atoms, or the same number of particles as in 12 g of carbon-12.

Allow atoms or molecules for particles.

1\ \mathrm{mol}=6.02\times10^{23}\ \text{particles}

[Maximum number: 2]

This question is in two parts. Part 1 is about ideal gases and specific heat capacity. Part 2 is about simple harmonic motion and waves.
Part 1 Ideal gases and specific heat capacity

State two assumptions of the kinetic model of an ideal gas.

[Maximum number: 2]

The equipment shown in the diagram was used by a student to investigate the variation with volume, of the pressure p of air, at constant temperature. The air was trapped in a tube of constant cross-sectional area above a column of oil.

The pump forces oil to move up the tube decreasing the volume of the trapped air.

Outline how the results of this experiment are consistent with the ideal gas law at constant temperature.

$V \propto H$ thus ideal gas law gives $p \propto \frac{1}{H}$

so graph should be «a straight line through origin,» as observed

[Maximum number: 2]

The equipment shown in the diagram was used by a student to investigate the variation with volume, of the pressure p of air, at constant temperature. The air was trapped in a tube of constant cross-sectional area above a column of oil.

The pump forces oil to move up the tube decreasing the volume of the trapped air.

The cross-sectional area of the tube is $1.3 \times 10^{-3} \mathrm{~m}^{2}$ and the temperature of air is 300 K . Estimate the number of moles of air in the tube.

$n=\frac{b A}{R T} OR$ correct substitution of one point from the graph

$n=\frac{5 \times 10^{4} \times 1.3 \times 10^{-3}}{8.31 \times 300}=0.026 \approx 0.03$

Answer must be to 1 or 2 SF. Allow ECF from (b).

[Maximum number: 1]

A solid cylinder of height h and density $\rho$ rests on a flat surface.

A tube of constant circular cross-section, sealed at one end, contains an ideal gas trapped by a cylinder of mercury of length 0.035 m . The whole arrangement is in the Earth's atmosphere. The density of mercury is $1.36 \times 10^{4} \mathrm{~kg} \mathrm{~m}^{-3}$ .

When the mercury is above the gas column the length of the gas column is 0.190 m .

Outline why the gas particles in the tube hit the mercury surface less often after the tube has been rotated.

[Maximum number: 3]

This question is in two parts. Part 1 is about ideal gases and specific heat capacity. Part 2 is about simple harmonic motion and waves.
Part 1 Ideal gases and specific heat capacity

At the temperature of 350 K , the piston in (b) is now freed and the argon expands until its temperature reaches 300 K .
Explain, in terms of the molecular model of an ideal gas, why the temperature of argon decreases on expansion.

[Maximum number: 2]

The equipment shown in the diagram was used by a student to investigate the variation with volume, of the pressure p of air, at constant temperature. The air was trapped in a tube of constant cross-sectional area above a column of oil.

The pump forces oil to move up the tube decreasing the volume of the trapped air.

The equation of the line of best fit is:

p=a+\frac{b}{H}

The equation above may be used to predict the pressure of the air at extremely large values of $\frac{1}{H}$ . Suggest why this will be an unreliable estimate of the pressure.

very large $\frac{1}{H}$ means very small volumes / very high pressures

at very small volumes the ideal gas does not apply

OR

at very small volumes some of the assumptions of the kinetic theory of gases do not hold

IB Physics SL B 3 Gas Laws Questions

Exam points

Covered syllabus points

Covered syllabus points

Question 1

Question (a)

Question (b)

Question (i)

Question (ii)

Question (iii)

Question 2

Question (a)

Question (b)

Question (i)

Question (c)

Question 3

Question (a)

Question (b)

Question (c)

Question 4

Question 5

Question 6

Question 7

Question 8

Question 9

Question 10

Question 11