шпора по физике за первый семестр / Распределения Больцмана

яю 0A?@545;5=8O >;LF<0=0. A=>2=>5 C@02=5=85 " 8 <0:A25;A:85 @0A?@545;5=8O <>;5:C; ?> A:>@>AB8 1K;8 ?>;CG5=K ?@54?>;>65=85<, GB> <>;5:C;K @02=><5@=> @0A?@545;5=K ?> >1J5<C 8 2A5 =0?@02;5=8O 42865=8O <>;5:C; @02=><5@=> @0A?@545;5=K ?> >1J5<C 8 2A5 =0?@02;5=8O 42865=8O <>;5:C; @02=>25@>OB=K. "0:85 CA;>28O <>3CB 1KBL @50;87>20=K B>;L:> 2 B>< A;CG05, 5A;8 =0 <>;5:C;K =5 459AB2CNB =8:0:85 2=5H=85 A8;>2K5 ?>;O. 4=0:> <>;5:C;K ;N1>3> 3070 2 75<=KE CA;>28OE =0E>4OBAO 2 ?>B5=F80;L=>< 3@028B0F8>==>< ?>;5 5<;8, GB> ?@82>48B : =0@CH5=8N @02=><5@=>3> @0A?@545;5=8O <>;5:C; ?> >1J5<C. P = pgh  402;5=85 2 684:>AB8 ; dP = - pgdh  B.:. A C25;8G5=85< 2KA>BK 402;5=85 C<5=LH05BAO.

PV = mRT / ј => p = m / V = Pј / RT ; dP = - Pј g dh / RT = P m0 g dh / kT ; dP/ P = - m0 g dh / kT ; @>8=B53@8@C5< MB> 2K@065=85:

(8=B53@0; P0 - P) dP / P = - (m0 g / kT) (8=B53@0; 0 - h) dh ; ln (P / P0) = - (m0 gh / kT) ; P = R0 e (AB. m0 gh / kT) ; P = P0 e (AB.  ј n / RT) ; -B> 2K@065=85 >?8AK205B @0A?@545;5=85 G0AB8F ?> 2KA>B5 2 3@028B0F8>==>< ?>;5. m0 gh = W?, ?>MB><C n = n0 e (AB.  W? / kT). -B> 8 5ABL @0A?@545;5=8O >;LF<0=0. => >?8AK205B @0A?@545;5=85 G0AB8F ?> 2KA>B5 2 3@028B0F8>==>< ?>;5, 0 =5 B>;L:> 2 3@028B0F8>==>< ?>;5 5<;8. -B> @0A?@545;5=85 ?@85<;5<> : G0AB8F0<, =0E>4OI8<AO 2 A>AB>O=88 70>B8G5A:>3> B5?;>2>3> 42865=8O.