Mechanical Engineering - Thermodynamics - Discussion

The most probable speed, vp, is the speed most likely to be possessed by any molecule (of the same mass m) in the system and corresponds to the maximum value or mode of f(v). To find it, we calculate df/dv, set it to zero and solve for v:

\frac{df(v)}{dv} = 0

which yields:

v_p = \sqrt {\frac{2kT}{m}} = \sqrt {\frac{2RT}{M}}


The root mean square speed is the second-order moment of speed:

= \sqrt {\langle v^2 \rangle} = \left(\int_0^{\infty} v^2 \, f(v) \, dv \right)^{1/2}.

= \sqrt {\frac{3kT}{m}} = \sqrt {\frac{3RT}{M} } = \sqrt{\frac{3}{2}} v_p.

Answer B is right.

Most probable velocity vp = root of 2kT/m.

k = The molar gas constant has the value 8.3143 J/mol K.

T = Temperature.

Formula for most probable velocity.

vp = option B.

And for root mean square velocity.

Vrms=option C.

I think still in doubt but probably B is best option.

Guys option B is right.

And option C is root mean square velocity (rms velocity).

While here many got doubts about B & C options. I goggled it and found that the word 'Probable velocity makes the difference here.

Option : B is correct.

Option C is RMS velocity of molecules.

Please tell me what is "k" and "T"?

Please give me brief explanation. I am not understand the above explanation.

Answer 2 is correct. The third answer (C) is for root mean square velocity. And 2nd (B) is the most probable velocity.