Gases, Pressure and Fluids
Gas Pressure and the Particle Model
A gas exerts gas pressure on any surface it is in contact with. The particle model explains why: gas particles are in constant, rapid, random motion. When they collide with the walls of a container, each collision exerts a tiny force on the wall. The total pressure is the combined effect of billions of these collisions per second.
If the volume of the container is reduced at constant temperature, the particles are confined to a smaller space. They travel shorter distances between collisions with the walls, so they hit the walls more frequently. More collisions per second means a greater pressure. Conversely, increasing the volume at constant temperature reduces the collision frequency and lowers the pressure.
Gas pressure is caused by particle collisions with container walls. Decreasing the volume (at constant temperature) increases the frequency of collisions and therefore increases the pressure. Increasing the volume decreases pressure.
Boyle’s Law
Robert Boyle, working in the 1660s, measured the relationship between pressure and volume for a trapped gas at constant temperature. He found that pressure and volume are inversely proportional: as one doubles, the other halves. This is now known as Boyle’s law.
The mathematical form is:
$$p_1 V_1 = p_2 V_2$$
Where \(p_1\) and \(V_1\) are the initial pressure and volume, and \(p_2\) and \(V_2\) are the final pressure and volume. Pressure is measured in pascals (Pa) and volume in cubic metres (m³). Boyle’s law applies only when temperature and the amount of gas are kept constant.
A gas occupies 0.60 m³ at a pressure of 200 kPa. The gas is compressed at constant temperature until its volume is 0.20 m³. Calculate the new pressure.
Using \(p_1 V_1 = p_2 V_2\):
\(p_2 = \frac{p_1 V_1}{V_2} = \frac{200 \times 0.60}{0.20} = \frac{120}{0.20} = 600\) kPa
Always check units are consistent before substituting. Pressure can be in Pa or kPa as long as both \(p_1\) and \(p_2\) use the same unit.
Absolute Zero
Scope note: absolute zero and the kelvin scale are not on this specification. They are here as background. What is assessed is the particle explanation of why heating a gas at constant volume raises its pressure, and that treatment is qualitative only.
Temperature affects gas pressure too. Raising the temperature of a gas at constant volume gives the particles more kinetic energy — they move faster and collide with the walls more forcefully and more frequently, so pressure increases. Cooling the gas has the opposite effect. Scientists found that extrapolating the pressure–temperature relationship for any gas reaches zero pressure at the same temperature: −273°C. This is called absolute zero.
The Kelvin scale uses absolute zero as its starting point (0 K). To convert: \(T(K) = T(°C) + 273\). The Kelvin scale is important for gas law calculations because pressure and volume are proportional to temperature in kelvin, not in Celsius.
Absolute zero = −273°C = 0 K. At absolute zero, particles would have minimum possible kinetic energy. To convert to kelvin: add 273. Gas pressure and volume are proportional to temperature in kelvin.
Pressure in Fluids
A fluid (liquid or gas) exerts pressure at right angles (normal) to any surface it is in contact with. This pressure acts equally in all directions at a given depth. The equation for pressure on a solid surface is:
$$P = \frac{F}{A}$$
Where \(P\) is pressure in pascals (Pa), \(F\) is the force in newtons (N), and \(A\) is the area in square metres (m²). One pascal equals one newton per square metre.
Pressure in a liquid increases with depth because there is a greater weight of liquid above. The pressure also depends on the density of the liquid. The equation for pressure due to a column of liquid is:
$$P = \rho g h$$
Where \(\rho\) (rho) is the density of the liquid in kg/m³, \(g\) is gravitational field strength (approximately 10 N/kg near Earth’s surface), and \(h\) is the depth in metres.
Because pressure increases with depth, the upward force on the bottom surface of a submerged object is greater than the downward force on its top surface. This net upward force is called upthrust. An object floats when the upthrust equals its weight. An object sinks when its weight exceeds the upthrust. Whether an object floats or sinks depends on the relationship between its density and the density of the fluid: an object denser than the fluid sinks; one less dense than the fluid floats.
Worked example: Calculate the pressure at 5.0 m depth in sea water (density 1025 kg/m³). \(P = 1025 \times 10 \times 5.0 = 51\,250\) Pa ≈ 51 kPa (plus atmospheric pressure above the water surface).
Atmospheric Pressure
Earth’s atmosphere is a layer of gas held around the planet by gravity. The atmospheric pressure at sea level is approximately 100 000 Pa (100 kPa). Atmospheric pressure decreases with altitude because there is less air above — fewer particle collisions occur from the thinner air overhead.
Atmospheric pressure decreases with altitude because the column of air above is shorter and less dense, so fewer particle collisions occur per unit area. (Higher tier) Pressure at depth \(h\) in a fluid: \(P = \rho g h\).