Mean free path, average distance an object will move between collisions. The constant μ is the mean free path and is the average (mean) distance traveled by a molecule between collisions. The mean free path of an oxygen gas molecule under a pressure of 1 atmosphere at 0° C is about 6 × 10-6 cm (2 × 10−6 inch).

tau

The mean free path is the average distance that a particle can travel between two successive collisions with other particles.

where ℓ is the mean free path, n is the number of target particles per unit volume, and σ is the effective cross-sectional area for collision.

λ is the mean free path expressed in the length units, T is the temperature of the gas, p is the pressure of the gas, d is the diameter of a particle, k is the Boltzmann constant k = 1.380649 * 10^(−23) J / K .

Factors affecting mean free path Density: As gas density increases, the molecules become closer to each other. Increasing the number of molecules or decreasing the volume causes density to increase.

If the temperature is increased at constant pressure, the gas expands, the average distance between molecules increases, and the mean free path increases. If the pressure is increased at constant temperature, the gas compresses and the mean free path decreases.

Which of the following has longest mean free path under identical conditions of temperature and pressure ? Under identical conditions of T and P,n is same, As σ is lower for H2, l will be largest. Step by step solution by experts to help you in doubt clearance & scoring excellent marks in exams.

Gas molecules travel at a range of speeds—some molecules move much faster than others. The average speed of a gas depends on its molar mass—the lighter the mass, the faster the average speed.

most probable speed, vmp:

• vmp=√2RTM,
• vave=√8RTπM,
• vrms=√3RTM,

With an increase in temperature, the particles gain kinetic energy and move faster. The actual average speed of the particles depends on their mass as well as the temperature – heavier particles move more slowly than lighter ones at the same temperature.

The root-mean-square speed is the measure of the speed of particles in a gas, defined as the square root of the average velocity-squared of the molecules in a gas. The root-mean-square speed takes into account both molecular weight and temperature, two factors that directly affect the kinetic energy of a material.

The rms speed is not the average or the most likely speed of molecules, as we will see in Distribution of Molecular Speeds, but it provides an easily calculated estimate of the molecules’ speed that is related to their kinetic energy.

In mathematics and its applications, the root mean square (RMS or rms) is defined as the square root of the mean square (the arithmetic mean of the squares of a set of numbers). The RMS is also known as the quadratic mean and is a particular case of the generalized mean with exponent 2.

The root mean square velocity is the square root of the average of the square of the velocity. The reason we use the rms velocity instead of the average is that for a typical gas sample the net velocity is zero since the particles are moving in all directions.

For any list of numbers holds: The root mean square (rms) is always equal or higher than the average (avg). The reason is that higher values in the list have a higher weight (because you average the squares) in the calculation of a rms compared to the calculation of the avg.

A simple explanation of why the RMS value is higher than the average, is that the power climbs more rapidly because of this multiplication than just the simple waveform climbs. For example, when you double the voltage the power goes to four times. This is because when you double the voltage the current also doubles.

RMS gives you the equivalent DC voltage for the same power. If you would measure the resistor’s temperature as a measure of dissipated energy you’ll see that it’s the same as for a DC voltage of 0.71 V, not 0.64 V. Measuring average voltage is cheaper than measuring RMS voltage however, and that’s what cheaper DMMs do.

The RMS value is the square root of the mean (average) value of the squared function of the instantaneous values. Since an AC voltage rises and falls with time, it takes more AC voltage to produce a given RMS voltage than it would for DC. For example, it would take 169 volts peak AC to achieve 120 volts RMS (.