IB Physics SL B.3 Gas Laws Question Bank

Practise modelling ideal gases with pressure, volume, amount and absolute temperature, then explain molecular pressure, internal energy and model limitations.

Exam points

calculate pressure from perpendicular force and area or convert mass and particles to amount
apply PV/T or PV=nRT with absolute temperature to compare states or solve an unknown quantity
explain gas pressure through molecular momentum changes and collisions with container walls
calculate ideal monatomic internal energy and relate temperature to mean kinetic energy
state ideal-gas assumptions and identify low-density, low-pressure, high-temperature validity

Covered syllabus points

B.3.1—Pressure B.3.2—Amount of substance B.3.3—Ideal gas model B.3.4—Empirical gas laws B.3.5—Ideal gas equations B.3.6—Molecular pressure model B.3.7—Ideal gas internal energy B.3.8—Ideal gas approximation limits

[Maximum number: 9]

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

Figure for Question B.3 Gas laws question 1 — IB Physics SL

(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 ]

All question bank results loaded

Covered syllabus points

B.3 Gas laws question 1

Question (a)

Question (b)

Question (i)

Question (ii)

Question (iii)

B.3 Gas laws question 2

Question (a)

Question (b)

Question (i)

Question (c)