Press the plunger of a syringe with its tip sealed and the air inside squeezes easily, because unlike liquids and solids, a gas has wide spaces between its particles, so its volume changes a lot with pressure and temperature.
At constant temperature, doubling the pressure halves the volume; this inverse relationship between pressure and volume is Boyle's law.
At constant pressure, raising the temperature makes the particles move faster and push harder on the walls, so the volume grows; this is Charles's law.
Raise the pressure in the syringe picture and the point on the P-V graph slides along the curve; raise the temperature in the balloon picture and the balloon grows past its 0 °C size (dashed).
①At constant temperature, a gas gets smaller when the pressure on it increases.
②Pressure and volume are inversely proportional: double the pressure and the volume halves, triple it and the volume drops to a third.
③So P × V stays the same. The syringe in the picture holds 100 mL at 1 atm, so P × V = 100 throughout.
④Under more pressure the same number of particles is packed into a smaller space and hits the walls more often.
Temperature and Volume (Charles's Law)
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Warming a balloon: higher temperature, larger volume (constant pressure)
20°C
🔍 Charles's Law
①At constant pressure, a gas gets larger as its temperature rises.
②A higher temperature makes the particles move faster and push the walls harder and more often; to keep the pressure the same, the volume has to grow.
③For every 1 °C rise the volume grows by about 1/273 of its volume at 0 °C, so heating from 0 °C to 100 °C makes it about 1.37 times as large.
④A dented table tennis ball pops back out in hot water because the air inside warms up and expands.
Reading Boyle's Law on a Graph
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Pressure and volume of the gas in the syringe: the current state on the inverse curve
Boyle's law
P₁V₁ = P₂V₂ (constant temperature)
Pressure times volume stays the same; pressure and volume are inversely proportional.
Charles's law
V₁T₁ = V₂T₂
Volume is proportional to the absolute temperature T (K), which is the Celsius temperature plus 273.
📐 The Two Laws Together
①Boyle's law: at constant temperature, the higher the pressure, the smaller the volume (inverse).
②Charles's law: at constant pressure, the higher the temperature, the larger the volume.
③Both are explained by gas particles moving nonstop and hitting the walls.
④Absolute temperature K = °C + 273, and the graph heads toward zero volume at 0 K (−273 °C).
Exam Key Points
Summary
Boyle: P × V = constant · Charles: V ÷ T = constant
Change one of a gas's pressure, volume or temperature and the others change with it.
🎯 Exam Points
①Boyle's law: at constant temperature, pressure and volume are inversely proportional.
②Charles's law: at constant pressure, the higher the temperature, the larger the volume.
③The P-V graph is an inverse curve, and every point on it has the same P × V.
④The V-T graph is a straight line that passes through the origin when drawn against absolute temperature.
⑤Everyday examples: a snack bag puffing up on a mountain and a diver's bubbles growing as they rise (Boyle); hot-air balloons and a dented table tennis ball popping out (Charles).
Examples and Unit Test
Example 1
At constant temperature, a gas has a volume of 6 L at 1 atm. What is its volume when compressed to 2 atm? (Boyle's law)
1
The temperature is constant, so use Boyle's law, P₁V₁ = P₂V₂.
2
1 × 6 = 2 × V₂, so V₂ = 6 ÷ 2 = 3 L; doubling the pressure halved the volume.
▸ 3 L
See how many times the pressure grew, and divide the volume by that number.
Example 2
At constant pressure, what happens to a balloon's volume in a warm place, and why? (Charles's law)
1
At constant pressure, a gas gets larger as its temperature rises (Charles's law).
2
As the temperature rises, the gas particles in the balloon move faster and push harder on its inner wall, so the balloon swells.
▸ It gets larger (the particles move faster)
The balloon in the picture is also larger than its 0 °C size (dashed) when the temperature goes up.
Unit-test style
Which statement about the properties of gases is correct?
②At constant temperature, pressure and volume are inversely proportional
③At constant pressure, a higher temperature gives a smaller volume
④Boyle law states that pressure and volume are proportional
⑤A gas keeps the same volume even when temperature changes
▸ ② At constant temperature, pressure and volume are inversely proportional
1
By Boyle's law, at constant temperature volume shrinks as pressure grows, an inverse relationship, so ② is correct.
2
Volume shrinks as pressure grows (①), at constant pressure volume grows with temperature (③), Boyle's law is an inverse relationship (④), and a gas expands when its temperature rises (⑤).