Gas pressure, compression and expansion
Definition
Gas pressure
Gas pressure is caused by gas particles colliding with the walls of their container, or with any surface in the gas.
- Gas particles move randomly in all directions and collide with the walls, exerting a force on them.
- The combined effect of many collisions each second produces the pressure of the gas.
- The pressure produces a net force at right angles, that is perpendicular, to the wall or surface.
- A gas is compressed when its volume is decreased, and expanded when its volume is increased.
- For example, pushing in the plunger of a sealed syringe compresses the air inside, while pulling it out lets the gas expand.
Explaining pressure and volume with the particle model
- If the volume of a fixed mass of gas is increased at constant temperature, the same number of particles occupy a larger space.
- The particles keep the same average speed, because the temperature is unchanged.
- They travel further between collisions with the walls, so they hit the walls less often.
- So the pressure decreases.
- If instead the volume is decreased at constant temperature, the particles hit the walls more often, so the pressure increases.
Key Idea
For a fixed mass of gas at constant temperature, pressure and volume are inversely related: if one increases, the other decreases.
The pressure–volume equation
- For a fixed mass of gas held at constant temperature, pV=constantpV = \text{constant}pV=constant.
- ppp is the pressure in pascals, Pa\text{Pa}Pa; VVV is the volume in metres cubed, m3\text{m}^3m3.
- The product of pressure and volume is the same before and after a change, so p1V1=p2V2p_1 V_1 = p_2 V_2p1V1=p2V2.
- p1p_1p1 and V1V_1V1 are the initial pressure and volume; p2p_2p2 and V2V_2V2 are the final pressure and volume.
- If the volume halves, the pressure doubles; if the volume doubles, the pressure halves, as long as the mass of gas and the temperature are unchanged.
Example
- A fixed mass of gas has a volume of 0.020 m30.020\ \text{m}^30.020 m3 and a pressure of 120 000 Pa120\,000\ \text{Pa}120000 Pa. It is compressed at constant temperature until its volume is 0.015 m30.015\ \text{m}^30.015 m3. Calculate the new pressure.
- State the equation and rearrange for the new pressure:
- Calculate:
- This makes sense: the gas was compressed, so its volume decreased and its pressure increased.
Example
- A gas has a pressure of 100 000 Pa100\,000\ \text{Pa}100000 Pa and a volume of 0.030 m30.030\ \text{m}^30.030 m3. The pressure is increased to 150 000 Pa150\,000\ \text{Pa}150000 Pa at constant temperature. Calculate the new volume.
- State the equation and rearrange for the new volume:
- Calculate:
- The new volume is 0.020 m30.020\ \text{m}^30.020 m3: the pressure rose, so the volume fell.
Common Mistake
- Do not say that increasing the volume makes the particles move more slowly; at constant temperature their average speed does not change.
- The pressure falls because the particles collide with the walls less often, not because each particle has less energy.
Exam technique
- For an explanation, give a particle-model answer: particles move randomly, collide with the walls, and a larger volume means fewer collisions per second, so the pressure is lower.
- Mention constant temperature if the question states it.
- For a calculation, write p1V1=p2V2p_1 V_1 = p_2 V_2p1V1=p2V2 first, substitute the values with units, then rearrange.
Self review
- What causes the pressure of a gas, and in which direction does it act on a surface?
- What do compressing and expanding a gas do to its volume?
- Why does increasing the volume at constant temperature decrease the pressure?
- State the pressure–volume equation for a fixed mass of gas at constant temperature.
- If the volume of a gas is halved at constant temperature, what happens to its pressure?
