Calculating Gas Pressure
- Pressure is defined as
The force applied per unit area
- For example, when a drawing pin is pushed downwards:
- It is pushed into the surface, rather than up towards the finger
- This is because the sharp point is more concentrated (a small area) creating a larger pressure
When you push a drawing pin, it goes into the surface (rather than your finger)
- When an object is immersed in a liquid, the liquid will exert pressure, squeezing the object
- The pressure exerted on objects in fluids creates forces against surfaces
- These forces act at 90 degrees (at right angles) to the surface
The pressure of a fluid on an object creates a force normal (at right angles) to the surface
- The equation for pressure is:
- Where:
- P = pressure (Pa)
- F = force (N)
- A = cross-sectional area (m2)
- Pressure is measured in Pascals (Pa)
- This equation is only relevant when gas molecules exert a force perpendicular to the surface
Gas molecules bouncing off the walls of a container
- It is possible for someone to experience this force by closing their mouth and forcing air into their cheeks
- The strain on the cheeks is due to the force of the gas particles pushing at right angles to the cheeks
- This equation means:
- If a force is spread over a large area it will result in a small pressure
- If it is spread over a small area it will result in a large pressure
High heels produce a higher pressure on the ground because of their smaller area, compared to flat shoes
Worked example
The diagram below shows the parts of the lifting machine used to move a platform of cross-sectional area 2.73 × 10-2 m2 up and down.
The pump creates pressure in the liquid of 5.28 × 105 Pa to move the platform upwards.
Calculate the force that the liquid applies to the piston.
Answer:
Step 1: List the known quantities
- Cross-sectional area, A = 2.73 × 10-2 m2
- Pressure, P = 5.28 × 105 Pa
Step 2: Write down the relevant equation
Step 3: Rearrange for the force, F
F = p × A
Step 4: Substitute the values into the equation
F = (5.28 × 105) × (2.73 × 10-2) = 14 414.4
Step 5: Round to the appropriate number of significant figures and quote the correct unit
F = 14 400 N = 14.4 kN (3 s.f)
Examiner Tip
Make sure A is always the cross-sectional area of the surface that the force is being applied upon, especially if there are multiple areas given in the question.