IB Physics SL B 3 Gas Laws Questions

Practise IB Physics SL B.3 by modelling pressure, volume, amount and absolute temperature with ideal-gas equations and molecular explanations.

Exam points

Apply pressure definitions, pressure differences, hydrostatic pressure and enclosed-gas pressure to calculate forces in fluid and gas systems.
Convert between mass, moles and particles, then connect amount-of-substance data to pressure, volume, temperature and microscopic gas quantities.
Solve and compare multi-state gas problems with pV/T, PV=nRT and PV=NkBT, including connected containers, added or removed gas and graph data.
Explain gas pressure and ideal-gas internal energy from molecular momentum transfer, collision rate, mean kinetic energy and work during expansion.
Judge when the ideal-gas model is reliable using pressure, density, temperature and particle assumptions, and explain deviations at small volume or high pressure.

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

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Study B.3 Gas laws conceptsOpen the corresponding Concept lesson for explanations, examples and exam connections.

[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 ]

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Covered syllabus points

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Question 1

Question (a)

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Question (i)

Question (ii)

Question (iii)

Question 2

Question (a)

Question (b)

Question (i)

Question (c)