What you'll learn
Pressure is a fundamental concept tested extensively in CIE IGCSE Physics papers, appearing in multiple-choice, structured and calculation questions. This topic examines how forces spread over areas, how liquids and gases exert pressure, and the behaviour of hydraulic systems. Understanding pressure is essential for questions worth 6-8 marks in Paper 2 and Paper 4, and regularly appears in practical contexts involving syringes, hydraulic brakes, and atmospheric phenomena.
Key terms and definitions
Pressure — the force acting per unit area, measured perpendicular to a surface (SI unit: pascal, Pa, or N/m²)
Pascal (Pa) — the SI unit of pressure, equivalent to one newton per square metre (1 Pa = 1 N/m²)
Hydraulic system — a mechanism that uses liquids to transmit pressure from one point to another, based on the principle that pressure in a liquid is transmitted equally in all directions
Atmospheric pressure — the pressure exerted by the weight of air molecules in the Earth's atmosphere, approximately 100 kPa or 1.0 × 10⁵ Pa at sea level
Barometer — an instrument used to measure atmospheric pressure, typically using a column of mercury
Manometer — a device used to measure gas pressure, consisting of a U-tube containing liquid
Density — mass per unit volume of a substance (kg/m³), directly related to pressure calculations in liquids
Core concepts
Pressure in solids
Pressure occurs when a force acts on a surface. The relationship is inversely proportional to area:
p = F/A
Where:
- p = pressure (Pa or N/m²)
- F = force (N)
- A = area (m²)
Key applications tested in CIE IGCSE Physics:
- Sharp objects concentrate force over small areas, producing high pressure (knives, needles, drawing pins)
- Broad surfaces spread force over large areas, producing low pressure (skis, snowshoes, caterpillar tracks on tanks)
- Foundations of buildings are wide to reduce pressure on ground and prevent sinking
- Studs on football boots increase pressure for better grip
When calculating pressure, ensure both force and area use correct SI units. Common exam questions provide force in newtons but area in cm² — conversion is essential: 1 m² = 10,000 cm².
Pressure in liquids
Liquids exert pressure due to their weight. Unlike solids, liquid pressure acts equally in all directions at a given depth. The pressure increases with depth according to:
p = ρgh
Where:
- p = pressure (Pa)
- ρ = density of liquid (kg/m³)
- g = gravitational field strength (N/kg), taken as 10 N/kg in CIE IGCSE
- h = depth below surface (m)
Critical characteristics of liquid pressure:
- Pressure increases linearly with depth
- Pressure is the same at equal depths regardless of container shape
- Pressure acts perpendicular to all surfaces in contact with liquid
- Pressure at a point acts equally in all directions
The total pressure at depth in a liquid exposed to atmosphere:
p(total) = p(atmospheric) + ρgh
CIE exam questions frequently test understanding that pressure differences drive liquid flow through holes at different depths in containers. Liquid flows faster from holes at greater depth due to higher pressure.
Demonstrating liquid pressure principles
Manometer demonstration: A U-tube manometer shows gas pressure by the difference in liquid levels. The pressure difference equals ρgh, where h is the vertical height difference between liquid columns.
Collapsing can experiment: When steam inside a sealed can condenses, internal pressure drops below atmospheric pressure. The greater external atmospheric pressure crushes the can inward — direct evidence that atmospheric pressure exists and is substantial.
Bourdon gauge: Used to measure gas pressure in cylinders. A curved metal tube straightens when internal pressure increases, moving a pointer on a dial.
Pressure in gases
Gases exert pressure through molecular collisions with container walls. Unlike liquids, gas pressure does not increase significantly with depth in small containers (gas density is much lower than liquids).
Molecular explanation of gas pressure:
- Gas molecules move randomly at high speeds
- Molecules collide with container walls
- Each collision exerts a tiny force on the wall
- Billions of collisions per second create measurable pressure
- More frequent or more forceful collisions increase pressure
Factors affecting gas pressure (at constant volume):
- Temperature increase → molecules move faster → more frequent and forceful collisions → pressure increases
- Adding more gas → more molecules → more collisions → pressure increases
Factors affecting gas pressure (at constant temperature):
- Volume decrease → molecules have less space → collisions more frequent → pressure increases
- This relationship is described by Boyle's Law: p₁V₁ = p₂V₂ (covered in kinetic theory)
Atmospheric pressure
The Earth's atmosphere creates pressure due to the weight of air molecules above any surface. Standard atmospheric pressure at sea level equals approximately:
- 100,000 Pa (1.0 × 10⁵ Pa)
- 100 kPa
- 1 bar (not SI, but commonly used)
Atmospheric pressure decreases with altitude because there is less air above. This explains why:
- Aircraft cabins must be pressurised
- Water boils at lower temperatures at high altitude
- Breathing becomes difficult on mountains
Mercury barometer: Measures atmospheric pressure using a sealed tube inverted in mercury reservoir. Atmospheric pressure supports a column of mercury approximately 760 mm (76 cm) high at sea level. The space above mercury is a vacuum (near zero pressure).
Calculation verification: p = ρgh = 13,600 kg/m³ × 10 N/kg × 0.76 m ≈ 103,000 Pa (close to standard atmospheric pressure, confirming the principle).
Hydraulic systems
Hydraulic systems multiply forces using Pascal's principle: pressure applied to an enclosed liquid is transmitted equally throughout the liquid in all directions.
In a hydraulic system with two pistons:
p₁ = p₂
F₁/A₁ = F₂/A₂
Therefore:
F₂/F₁ = A₂/A₁
The force multiplication equals the ratio of piston areas. A small force on a small piston produces a large force on a large piston, provided the pressure remains constant.
Real-world applications tested in CIE IGCSE:
- Hydraulic brakes: Small force on brake pedal creates large force at wheel cylinders
- Hydraulic car jacks: Small input force lifts heavy vehicles
- Hydraulic presses: Shape metal using enormous forces from small inputs
- Dentist chairs: Smooth height adjustment using incompressible liquid
Advantages of hydraulic systems:
- Force multiplication without complex gears
- Smooth operation
- Forces transmitted around corners through pipes
- Liquids are incompressible, providing immediate response
Worked examples
Example 1: Pressure calculation for a block
Question: A rectangular concrete block has dimensions 2.0 m × 1.5 m × 0.5 m and mass 3000 kg. Calculate the minimum and maximum pressure the block can exert on horizontal ground.
Solution:
Weight of block: F = mg = 3000 kg × 10 N/kg = 30,000 N
Maximum pressure occurs with smallest contact area:
Smallest face area: A = 1.5 m × 0.5 m = 0.75 m²
p(max) = F/A = 30,000 N / 0.75 m² = 40,000 Pa or 40 kPa ✓
Minimum pressure occurs with largest contact area:
Largest face area: A = 2.0 m × 1.5 m = 3.0 m²
p(min) = F/A = 30,000 N / 3.0 m² = 10,000 Pa or 10 kPa ✓
Exam tip: Always identify which surface gives maximum/minimum area before calculating.
Example 2: Pressure in a liquid
Question: A submarine is at a depth of 250 m below the sea surface. The density of seawater is 1030 kg/m³ and atmospheric pressure is 1.0 × 10⁵ Pa. Calculate:
(a) The pressure due to the seawater at this depth [2 marks]
(b) The total pressure acting on the submarine [2 marks]
Solution:
(a) Using p = ρgh:
p = 1030 kg/m³ × 10 N/kg × 250 m
p = 2,575,000 Pa or 2.58 × 10⁶ Pa or 2580 kPa ✓✓
(b) Total pressure = atmospheric pressure + water pressure:
p(total) = 1.0 × 10⁵ Pa + 2.58 × 10⁶ Pa
p(total) = 2.68 × 10⁶ Pa or 2680 kPa ✓✓
Note: Many students forget to add atmospheric pressure in part (b) — always check what the question asks for.
Example 3: Hydraulic system
Question: A hydraulic jack has a small piston of area 0.002 m² and a large piston of area 0.08 m². A force of 150 N is applied to the small piston. Calculate the force exerted by the large piston. [3 marks]
Solution:
Pressure is transmitted equally: p₁ = p₂
Therefore: F₁/A₁ = F₂/A₂ ✓
Rearranging: F₂ = F₁ × (A₂/A₁) ✓
F₂ = 150 N × (0.08 m² / 0.002 m²)
F₂ = 150 N × 40
F₂ = 6000 N ✓
The force is multiplied by 40, equal to the ratio of the areas.
Common mistakes and how to avoid them
Using incorrect units for area: Converting cm² to m² incorrectly (remember: 1 m² = 10,000 cm², not 100 cm²). Always convert to SI units before calculation: divide cm² by 10,000.
Confusing force and pressure: Writing that "sharp objects have more force" when they actually have greater pressure due to smaller area. Force remains the same; pressure changes with area.
Forgetting atmospheric pressure: In liquid pressure questions asking for total pressure, students often calculate only ρgh and omit the atmospheric pressure contribution. Read questions carefully for "total" or "absolute" pressure.
Assuming pressure depends on liquid volume or container shape: Pressure at a given depth depends only on ρ, g, and h — not on the width of the container or total volume. Pressure is the same at equal depths in a narrow tube or wide tank.
Reversing the hydraulic ratio: Writing F₂/F₁ = A₁/A₂ instead of F₂/F₁ = A₂/A₁. The larger area produces the larger force — check your ratio direction makes physical sense.
Incorrect density values: Using density of water (1000 kg/m³) when the question specifies seawater, oil, or other liquids with different densities. Always use the density value given in the question.
Exam technique for Pressure
Command word "Calculate": Show formula, substitution with units, and final answer with correct units. Marks are typically 1 for formula/method, 1 for substitution, 1 for answer. Never skip working.
"Explain" questions on pressure applications: Use the pressure formula to support your answer. For example: "Skis have large area, so for the same force (weight), pressure = F/A is smaller, preventing sinking into snow." Link design feature → area change → pressure change → practical consequence.
Describing hydraulic systems: Examiners expect: (1) pressure transmitted through liquid, (2) pressure equal throughout, (3) small force on small area produces large force on large area. Mentioning "incompressible liquid" gains marks.
Extended calculation questions: These often combine pressure concepts with other topics (moments, energy, forces). Read carefully to identify all steps required. Show each stage clearly — partial marks are available even if final answer is wrong.
Quick revision summary
Pressure (p = F/A) increases when force increases or area decreases, measured in pascals (N/m²). In liquids, pressure increases with depth (p = ρgh) and acts equally in all directions. Atmospheric pressure (≈100 kPa) results from air weight and decreases with altitude. Gases exert pressure through molecular collisions with surfaces. Hydraulic systems transmit pressure through liquids to multiply forces (F₂/F₁ = A₂/A₁). Always use SI units, show calculation steps clearly, and remember to add atmospheric pressure when calculating total pressure in liquids.