Question

If the pressure of a gas is really due to the random collisions of molecules with the walls of the container, why do pressure gauges – even very sensitive ones – give perfectly steady readings? Shouldn't the gauge be continually jiggling and fluctuating? Explain.

Answer 1

The pressure gauge gives steady readings because the large number of gas molecules colliding with the container walls averages out the fluctuations. It can be compared to a casino's takings, which fluctuate by the minute and hour, but averages out over a longer period of time. Similarly, a tank of gas has a huge number of molecules that collide in a second, resulting in steady pressure readings.

Step-by-step explanation:

The pressure gauge gives steady readings because even though individual gas molecule collisions with the container walls are random and fluctuate, the large number of molecules colliding with the walls on a scale of time and space we measure results in only a tiny, usually unobservable fraction of fluctuation from the average. It can be compared to a casino's takings which fluctuate by the minute and hour, but over long times they are very close to the averages expected from the odds. Similarly, a tank of gas has a huge number of molecules that make enormous collisions in a second, resulting in steady pressure readings on the pressure gauge.

Answer 2

there is no fluctuation in the measurement because the quantity of molecule is too large and a quantity of some molecules is imperceptible.

Step-by-step explanation:

The pressure measurement is carried out by calibrating the force exerted by the air on a surface of known area, suppose a small area 1 mm² = 0.01 cm²

To find out if the random movement of air molecules affects the pressure reading, let's calculate the number of molecules that reaches the pressure gauge.

In a system at atmospheric pressure and in a volume of 1 m³ (walls of 1 m each) there is one mole of air molecules, this mole is evenly distributed, so how many molecules fall on our surface

# _molecule = 6.02 10²³ 0.01 10⁻⁴ / 1

#_molecular = 6.02 10¹⁷ molecules per second

therefore the variation of the number of molecules is not very important

Consequently there is no fluctuation in the measurement because the quantity of molecule is too large and a quantity of some molecules is imperceptible.