Paper 4

Physics9702

Paper 4

Physics9702

Boyle's Law and Charles's Law

A gas law compares two states of the same fixed amount of gas. First identify which quantity stays constant. Then use thermodynamic temperature in kelvin.

Keep the stated quantity constant

Boyle's law

Keep temperature and the amount of gas constant.
Pressure is inversely proportional to volume.
$p$ against $1/V$ is a straight line through the origin.

Charles's law

Keep pressure and the amount of gas constant.
Volume is proportional to thermodynamic temperature.
$V$ against $T/\mathrm{K}$ is a straight line through the origin.

Swipe left or right to see the whole diagram →

The fixed conditions are part of each law. Boyle's law gives an inverse curve; Charles's law is linear only when temperature is measured in kelvin.

Common mistake

The curved Boyle's-law graph is

p

against

V

. The straight graph is

p

against

1/V

. Do not describe both graphs as linear.

Use Boyle's law at constant temperature

p_1V_1=p_2V_2

Symbols

$p_1,p_2$ = gas pressures in the two states (Pa)
$V_1,V_2$ = gas volumes in the two states (m³)

Worked example

Compress a gas at constant temperature

A gas has volume 120 cm³ at pressure $1.00\times10^5\ \mathrm{Pa}$ . It is compressed at constant temperature to 80.0 cm³. Find the new pressure.

The same volume unit is used on both sides, so it cancels in the ratio.
Substitute into Boyle's law.
$p_2=\dfrac{p_1V_1}{V_2}$
$p_2=\dfrac{1.00\times10^5\times120}{80.0}$

Answer

p_2=1.50\times10^5\ \mathrm{Pa}

Use Charles's law at constant pressure

\frac{V_1}{T_1}=\frac{V_2}{T_2}

Symbols

$V_1,V_2$ = gas volumes in the two states (m³)
$T_1,T_2$ = thermodynamic temperatures (K)

Worked example

Heat a gas at constant pressure

A gas has volume 300 cm³ at 300 K. It is heated at constant pressure to 360 K. Find the new volume.

Substitute into Charles's law.
$V_2=V_1\dfrac{T_2}{T_1}=300\times\dfrac{360}{300}$

Answer

V_2=360\ \mathrm{cm^3}

State the fixed condition before using a gas law. Use kelvin for every temperature ratio.

PreviousAmount of Substance and the Mole NextThe Equation of State

Boyle's Law and Charles's Law

A gas law compares two states of the same fixed amount of gas. First identify which quantity stays constant. Then use thermodynamic temperature in kelvin.

Keep the stated quantity constant

Boyle's law

Keep temperature and the amount of gas constant.
Pressure is inversely proportional to volume.
$p$ against $1/V$ is a straight line through the origin.

Charles's law

Keep pressure and the amount of gas constant.
Volume is proportional to thermodynamic temperature.
$V$ against $T/\mathrm{K}$ is a straight line through the origin.

Swipe left or right to see the whole diagram →

The fixed conditions are part of each law. Boyle's law gives an inverse curve; Charles's law is linear only when temperature is measured in kelvin.

Common mistake

The curved Boyle's-law graph is

p

against

V

. The straight graph is

p

against

1/V

. Do not describe both graphs as linear.

Use Boyle's law at constant temperature

p_1V_1=p_2V_2

Symbols

$p_1,p_2$ = gas pressures in the two states (Pa)
$V_1,V_2$ = gas volumes in the two states (m³)

Worked example

Compress a gas at constant temperature

A gas has volume 120 cm³ at pressure $1.00\times10^5\ \mathrm{Pa}$ . It is compressed at constant temperature to 80.0 cm³. Find the new pressure.

The same volume unit is used on both sides, so it cancels in the ratio.
Substitute into Boyle's law.
$p_2=\dfrac{p_1V_1}{V_2}$
$p_2=\dfrac{1.00\times10^5\times120}{80.0}$

Answer

p_2=1.50\times10^5\ \mathrm{Pa}

Use Charles's law at constant pressure

\frac{V_1}{T_1}=\frac{V_2}{T_2}

Symbols

$V_1,V_2$ = gas volumes in the two states (m³)
$T_1,T_2$ = thermodynamic temperatures (K)

Worked example

Heat a gas at constant pressure

A gas has volume 300 cm³ at 300 K. It is heated at constant pressure to 360 K. Find the new volume.

Substitute into Charles's law.
$V_2=V_1\dfrac{T_2}{T_1}=300\times\dfrac{360}{300}$

Answer

V_2=360\ \mathrm{cm^3}

State the fixed condition before using a gas law. Use kelvin for every temperature ratio.

PreviousAmount of Substance and the Mole NextThe Equation of State