Question

2 On Thermodynamic Equilibrium In class, we saw that the velocity (u) distribution of non-relativistic particles with number-density n and temperature T in thermodynamic equilibrium is the Maxwellian distribution No = n4mv? (2.) e-mo?/KT, so long as quantum effects may be neglected. 1) It was claimed that the most probable speed for a particle is Umg(T) = 247 ni

Answer 1

Summary :

To find the most probable velocity we differentiate expression with respect to velocity and found out the maximum of v i.e., v at which expression becomes maximum. This gives most probable speed. Next to find the wein's displacement law we again differentiated the expression to find maximum value of lambda which gives wein's law.

Mus = (400*) Germany % me 447 * No te potironey (urmet me 370747 απιτ) 1 molt This expression represents the probability that there are speed of molecule will be in the interval af of dro to find most probable speed , we just need to differentiate this expression wort.o to find out the maxima. ve to [(4 093 ) ant) 5 *mJ * 1 ts [ve*) que totes with long e *27047 totes les moing a HO 2k T 2kT or U 12k7 . m

f at B.(t) 2.hc²/15 exp (hq KT)-| Wein's displacement law says that Amax le. which planck's distribution attains maxima is inversely related to tenperatione T. . 2. We need to know the maxim of B, (T) 7, 8,61) = ale ang mga] = 24 Sep on the heart that che/12) = 2he² 0 2) rearranging terus girs exy Chesdkt) = 5 oxp(be/4K7) + - 0 yn.o becomes which is a transcendental its root can be found with gh. : computer

It turns out 'u ~ 4.96 : ho ² yigo AKT * Aman T = Goh k) - cout. Thus Amax T = consta which is wein's Law. de Bolo dd = 2hc-7 exp (hel lkt) | - p= f : Jdala :: By(1) dy = elevi 2hey (t) cha de . est hindi 12 ay 2 y 3 est harita