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Various types of speeds of ideal gases is considered one of the most asked concept.
43 Questions around this concept.
At room temperature, a diatomic gas is found to have an r.m.s. speed of 1930 ms-1. The gas is :
Which of the following statements is true for gas?
(i) For a certain temperature, the average speed is always greater than the most probable speed.
(ii) Ratio of Vrms: Vav: Vmp is: 1.77: 1.6: 1.41
The root mean square velocity of molecules of gas is
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Maxwell distribution curve at a particular temperature shows that
1. As the Pressure due to an ideal gas is given as
Where
R = Universal gas constant
M = molar mass
P = pressure due to gas
= density
2. I.e With the rise in temperature, rms speed of gas molecules increases.
3. I.e With the increase in molecular weight, rms speed of the gas molecule decreases.
4. The rms speed of gas molecules does not depend on the pressure of the gas (if the temperature remains constant)
I.e
and according to the kinetic theory of gases
Maxwell’s Law -
The (Root mean square velocity) gives us a general idea of molecular speeds in a gas at a given temperature. So, it doesn't mean that the speed of each molecule is
.
Many of the molecules have speed less than and many have speeds greater than
. So, Maxwell derived an equation that describes the distribution of molecules in different speeds as -
So, from this formula, you have to remember a few key points -
1.
2.
Conclusions from this graph -
1. This graph is between number of molecules at a particular speed and speed of these molecules.
2. You can observe that the is maximum at most probable speed.
3. This graph also represent that .
4. This curve is asymmetric curve.
5. From this curve we can calculate number of molecules corresponds to that velocity range by calculating area bonded by this curve with speed axis.
Effect of temperature on velocity distribution :
With rising of temperature, the curve starts shifting right side and become broader as shown as -
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