Surface Pressure

When one object exerts a Force on another object, this force is spread out across the entire surface area of contact.

The video below demonstrates the "Bed of Nails" pressure trick:-

An example of pressure:-

This difference in pressure is why the point of the pin is pushed into the wood, but the flat head (which is applying the same Force) does not enter your finger.

The amount of Force exerted over a unit area is defined as:-

Where :-

P = Pressure (Pa)

F = Force (N)

A = Area (m2)

The unit of pressure is the Pascal. A pressure of one Pascal is experienced when a Force of 1 Newton is applied to 1 m2 of area.

Example 1 -

If an elephant with a mass of 5500 kg has a single foot surface area of 0.18m2, what is the pressure the Elephant exerts on the ground?

P = ?

F = mg = 5500 x 9.8 = 53900N

A = 0.18 x 4 = 0.72 m2

P = 53900 / 0.72 = 74861 Pa

P = 74.8 kPa

Example 2 -

An ice skater has a mass of 75 kg stands on one leg, with a skate surface area of 0.5 cm2. What is the pressure exerted by the skater on the ice?

P = ?

F = mg = 75 x 9.8 = 735 N

A = 0.5 cm2 = 5x10-5 m2

P = 735 / ( 5x10-5 ) = 14700000 Pa

P = 14.7 MPa

Notice in the above examples, even though the skater weighs much less than the Elephant, the actual applied Pressure by the skater is much greater.

Kinetic Model

In order to fully understand how Pressure acts upon a gas we must look at the gas at a particle level.

The above diagram shows a simplified model of the particles of gas within a sealed container.

In a gas, the particles are:-

Far apart (~ 10 times the separation of a liquid / solid)

Low Density (~ 1000 times less than that of a liquid / solid)

Moving at a High Speed (~ 500 ms-1 for Oxygen at room temperature)

In the above container, the gas particles are moving randomly around the container, colliding with each other and importantly in this case, the container walls.

Each time a particle collides with the walls of the container, it exerts a force on the wall. As particles are continuously colliding with the walls, the gas exerts a pressure onto the container.

The Kelvin Temperature Scale

When working with gases under pressure, we find that using the traditional Celsius temperature scale does not work. Instead we have to use the Kelvin Temperature scale. This scale for measuring temperature was developed by the scientist William Thomson (the Lord Kelvin) at the University of Glasgow.

During experimentation, Lord Kelvin discovered that matter could not be cooled indefinitely, but had a lowest possible value, at which all particle motion stops.

This value, knows as Absolute Zero, has a value of -273 °C on the Celsius scale.

In order to take this finding into account, Lord Kelvin "reset" the Celsius scale so that the zero was at absolute zero and not the freezing point of water. This means that to convert between Celsius and Kelvin we must simply add 273 to the traditional temperature measurement.

TK = TC + 273


TK = Temperature in Kelvin ( K )

TC = Temperature in Celsius (°C )

It is important to note also that as the above formula shows only a numerical addition meaning that a change in temperature of 1°C is the equivalent of a change of 1 K.

Example 3 -

The temperature in the classroom today is 20 °C, what is the room temperature in Kelvin?

TK = 20 + 273

TK = 293 K