Mechanical Engineering - Thermodynamics - Discussion

K-means Boltzmann's constant and T means the temperature in kelvin.

I also think option C is the right answer.

I think Option C is correct.

I want the correct explanation for this question. Please someone describe it clearly.

Then how to find most probable velocity?

Please mention the method just like you explained about root mean square velocity.

μ rms = √ (3RT/M).

where
μrms = root mean square velocity in m/sec.
R = ideal gas constant = 8.3145 (kg.m2/sec2)/Kmol.
T = absolute temperature in Kelvin.
M = mass of a mole of the gas in kilograms.

I think answer is option C.

@Venkatarao, P K Nag and Cengel.

Which book is good for thermodynamics? Can anyone tell me?

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.