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12.3States of Matter

Pressure in Fluids and the Gas Laws — American System Physics Revision Notes & Topical Questions

10 min read 7 parts Lesson 5 of 5 1 quiz

📚 American System Physics Hub / Topical Revision
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Lesson summary

Define pressure and use p = F/A.Pressure = force ÷ areap = F / A (Pa, N, m2).Change in liquid pressure = density × g × change in depth: Δp = ρgΔh (Pa, kg/m3, N/kg, m).What the symbols mean: p = pressure due to the liquid (Pa) · ρ = density of the liquid (kg m−3) · g = 9.81 N kg−1…

  • Boyle's law
  • Pressure law
  • Combined gas law (extension)
  • Hydraulics
  • Consequences
  • Gas pressure

Section 1 of 7Pressure in Fluids and the Gas Laws

1
12.3 Pressure in Fluids and the Gas Laws concept map: Pressure = force ÷ area, Boyle's law, Pressure law, Combined gas law (extension), Hydraulics
Visual guide to the key ideas explained in this lesson.
2
Pressure depends on both force and area. Spreading a force over a large area gives low pressure (snowshoes, wide tractor tyres, building foundations); concentrating it on a small area gives high pressure (knives, drawing pins, needles).
3
In a liquid, pressure increases with depth because there is more liquid above pushing down, and increases with the liquid's density. At a given depth it acts equally in all directions and does not depend on the shape of the container.
4
Consequences
Consequences dams are thicker at the base; water spurts furthest from the lowest hole in a can; divers feel greater pressure deeper down.
5
Gas pressure
Gas pressure gas particles move randomly at high speed. When they hit a wall they change momentum, exerting a force on it. The total force per unit area from many collisions is the pressure.
6
If a gas is compressed at constant temperature, the same number of particles hit a smaller wall area more often, so the pressure rises. Boyle's law: pV = constant.
7
If a gas in a sealed rigid container is heated, the particles move faster, hitting the walls more often and with greater force, so pressure rises. This is why aerosol cans must not be heated and tyre pressure rises after a long drive.
8
If a gas is heated at constant pressure (e.g. in a balloon or a syringe free to move), it expands: volume is proportional to kelvin temperature.
9
At absolute zero (0 K) the particles would have minimum kinetic energy and an ideal gas would exert no pressure; extrapolating a pressure–temperature graph for a gas to zero pressure gives about −273 °C.
10
Atmospheric pressure is about 100 000 Pa at sea level and decreases with altitude because there is less air above. It is measured with a barometer; gas pressure differences are measured with a manometer (Δp = ρgΔh using the height difference).
11
Hydraulic brakes and jacks work because liquids are almost incompressible and transmit pressure equally; a small force on a small piston gives a larger force on a larger piston.

Section 2 of 7Process & sequence

1
Boyle's law practical: connect a sealed syringe (or trapped air column) to a pressure gauge.
2
Record the initial volume and pressure of the trapped air.
3
Push the plunger in to a new volume, wait for the temperature to return to room temperature, then record pressure.
4
Repeat for at least 5 volumes, keeping temperature constant and the mass of gas fixed (no leaks).
5
Calculate pV for each reading, or plot p against 1/V.
6
Conclusion: pV is constant (p against 1/V is a straight line through the origin), confirming Boyle's law.

Why heating a sealed gas raises its pressurewrite these steps in this order; each step is a marking point.

1
Energy is transferred to the gas by heating.
2
The particles' average kinetic energy increases, so they move faster.
3
Particles collide with the walls more often.
4
Each collision exerts a greater force on the wall.
5
Greater total force per unit area means higher pressure (volume constant).

Section 3 of 7Compare

How a gas responds (fixed mass)
ChangeKept constantResultParticle explanation
Volume decreasedTemperaturePressure increases (pV = const)Particles hit walls more often (more frequent collisions per unit area)
Temperature increasedVolumePressure increases (p ∝ T)Particles move faster: more frequent and harder collisions
Temperature increasedPressureVolume increases (V ∝ T)Faster particles push walls out until collision rate per area is restored

Temperatures in gas law calculations must be in kelvin.

Section 4 of 7Worked examples

3000 Pa
A box of weight 600 N rests on a base of area 0.20 m2. Calculate the pressure on the floor.
  • p = F/A = 600 N ÷ 0.20 m2 = 3000 Pa (3.0 kPa).
    What the symbols mean: p = pressure (Pa = N m−2) · F = force acting at right angles to the surface (N) · A = area (m2)
Calculate the pressure due to seawater at a depth of 25 m (ρ = 1030 kg/m3, g = 9.8 N/kg) and the total pressure if atmospheric pressure is 1.0 × 105 Pa.
  • Δp = ρgΔh = 1030 × 9.8 × 25 = 252 350 Pa ≈ 2.5 × 105 Pa. Total = 2.52 × 105 + 1.0 × 105 ≈ 3.5 × 105 Pa.
300 kPa
A gas of volume 240 cm3 at 100 kPa is compressed at constant temperature to 80 cm3. Find the new pressure.
  • p1V1 = p2V2: p2 = 100 kPa × 240 ÷ 80 = 300 kPa.
    What the symbols mean: p1, V1 = pressure and volume before · p2, V2 = after; only for a fixed mass of gas at constant temperature

Section 5 of 7Key terms

Section 6 of 7Command terms

Command terms
Identify / Describe (FRQ)
A short, specific statement; describing requires relevant characteristics, not a single word.
Explain / Justify (FRQ)
Give the cause-and-effect reasoning or evidence; a restated fact does not score.
Calculate
Show setup, substitution and the answer with units.
Predict
State the expected outcome; add a reason only if asked to justify.
MCQ technique
Read every option; eliminate distractors that are true statements but do not answer the question; watch for NOT/EXCEPT.

Section 7 of 7Exam technique

Keywords the mark scheme looks for in this lesson

Keywords the mark scheme looks for in this lesson
Pressure (p) · Pascal (Pa) · Liquid pressure · Atmospheric pressure · Gas pressure · Boyle's law · Pressure law · Charles's law · Ideal gas · Manometer · Barometer · Hydraulic system
Learn each definition in the Key words tab exactly; a missing keyword in a definition usually loses the mark.

How to get full marks (examiner guidance)

1
Answer exactly what is asked; extra correct material does not earn credit, and contradictory statements can cancel credit (AP FRQ).
2
Use precise vocabulary, never “it/stuff/things”.
3
Show units and working in calculations.
4
In MCQs, predict the answer before reading the options, then eliminate.

Words to avoid

1
pressure = force × areapressure = force ÷ area (force per unit area).
2
gas particles hit the walls harder when compressedparticles hit the walls more frequently (temperature and speed unchanged).
3
gas particles expand when heatedparticles move faster, collide more often and with more force.
4
Don't use °C in p/T calculations — Write: convert to kelvin (add 273).
5
liquid pressure acts only downwardsliquid pressure acts equally in all directions at a given depth.
6
the particles collide with each other causing pressurepressure is caused by particles colliding with the container walls.

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