IGNOU BPHCT 135 2026 - What is most probable speed? Using the expression of the number of mol

Question

What is most probable speed? Using the expression of the number of molecules in a Maxwellian gas in the range v to v + dv as
$$dN_v = 4\pi N \left( \frac{m}{2\pi k_BT} \right)^{3/2} v^2 \exp \left[ - \left( \frac{mv^2}{2k_BT} \right) \right] dv$ $
Obtain an expression for most probable speed.

19 Jan 2026

Answer :

Word Count : 258

In thermal physics and statistical mechanics, the most probable speed of molecules in a gas is the speed at which the maximum number of molecules is moving. For a gas in thermal equilibrium, the distribution of molecular speeds is given by the Maxwell-Boltzmann distribution. The number of molecules having speeds between (v) and (v + dv) is expressed as [ dN = N f(v) dv = N 4 \pi \left(\frac{m}{2 \pi k_B T}\right)^{3/2} v^2 \exp\left(-\frac{mv^2}{2k_B T}\right) dv

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