Question

7. Show that the distributions of speed for a two dimensional gas is given by the expression muſzkat Flu) = u koT use V (again, some books notation instead of u What does F(u) du for the above, represent 9. Use the above relation for Fra) to derive <u>, <už, <u²7 <u² in 2-dim expressions for

I just need help with number 9, posting 7 & 8 for references on relation for F(u).

Answer 1

- т а) F(u) ие. 2KoT КЕТ mur т xиx e kBT Plu) x du КТ ор <u. 1 u PCu) mur - 1 "2 т du. их хих е КОТ о mu7201 е ет- 2 du. КОТ о - z 2keT п. XZ) va 2 • та dz mur 2kТ differentiating, ar m x Zu du = кот Substituting Әи 2 az x 31. mu U' values with Z, ю T e Х 2T x Sz dz. х т. T г о о ( - ) - 2 43Т Z е. dz то ор Szé с (, ) = "п, Applying I function, {u7° 2%т x ) п Aus 2 2n kgT апот X X <p> T CS Scanned with CamScanner Caus) Пл

542) un plu) 24 /2kgT u х -mu u e m KBT du. 6 m -mur/2KBT e du. KBT mur 2KBT Z 2KBT * Z differentiating, x 2u du a dz IKBT m duz KBT X d2 Туха Substituting the value of u on J u² x e ² x kot da. 137 myu 89 Z ure d.Z 2 KBT -Z ze dz 2KBT (Appling I funtion (ganna furiction) to solke integration. 712) T(171) = IPCI) j zl2-1) -Z e de - 1 12) 2KBT (Aus) CS Scanne CamScanner