Can we use molecular speed of gas formula also for the air?

In summary, the molecular speed of gas is given by the formula $$v=\sqrt{\frac{3RT}{M}},$$ where R is the gas constant and M is the molecular mass. This formula can be used for the air, which is a mixture of different gases, by modeling it as a diatomic ideal gas. The computed RMS velocity also gives the speed of sound, which is proportional to the molecular speed in an ideal gas with a diatomic ratio of ##C_p/C_v## = 7/5.
  • #1
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Can we use molecular speed of gas formula also for the air? I mean if we can use molecular mass of the air.
Molecular speed of gas is generally $$v=\sqrt{\frac{3RT}{M}},$$where R is gas constant and M is molecular mass. Can we use this formula for the air as well, when the air is a mixture of different gasses?
 
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  • #2
You can use the molecular speed of gas for air.
I believe the computed RMS velocity gives you the speed of sound.

The molecular weight of air is close to 28.96 g/mole.
Given single percentages and integer atomic weights.
N2 + O2 + Ar = (14*2)*0.78 + (16*2)*0.21 + (40)*0.01 = 28.96 g/mole.
 
  • #3
You can model the air as a diatomic ideal gas and get some good results. Air is made mostly of nitrogen and oxygen, both of which are diatomic gasses.
 
  • #4
Baluncore said:
I believe the computed RMS velocity gives you the speed of sound.
For a given gas, the two are proportional.
https://physics.stackexchange.com/questions/78879/simple-explanation-of-relation-between-speed-of-sound-and-r-m-s-speed said:
In an ideal gas, the speed of sound ##v_s## is related to the r.m.s. molecular speed ##v_m## by $$\frac{v_s}{v_m}=\sqrt{\frac{\gamma}{3}}$$where ##\gamma## = ##C_p/C_v## = 7/5 for a diatomic gas.
The article above goes on to provide an explanation for the relationship.
 

FAQ: Can we use molecular speed of gas formula also for the air?

What is the molecular speed of gas formula?

The molecular speed of gas formula is given by the root-mean-square (RMS) speed equation, which is v = √(3RT/M), where v is the molecular speed, R is the gas constant, T is the temperature in Kelvin, and M is the molar mass of the gas.

Can this formula be used for air?

Yes, this formula can be used for air because air is a mixture of gases and the molecular speed of each gas can be calculated using this formula. However, the average molecular speed of air will be slightly different due to the varying molecular weights of the gases present in air.

What is the significance of using the molecular speed of gas formula?

The molecular speed of gas formula is used to calculate the average speed of gas molecules in a given sample. This information is important in understanding the behavior of gases and can be used in various scientific applications such as in the study of gas diffusion and gas pressure.

Is this formula applicable to all types of gases?

Yes, this formula is applicable to all types of gases as long as the temperature and molar mass of the gas are known. However, the average molecular speed may vary depending on the specific gas being studied.

Can this formula be used to compare the molecular speeds of different gases?

Yes, this formula can be used to compare the molecular speeds of different gases. The higher the temperature, the faster the average molecular speed will be for all gases. However, the molar mass of the gas will also affect the final result, with lighter gases having higher molecular speeds compared to heavier gases at the same temperature.

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