In discussing the velocity distribution of molecules of an ideal gas, a function F ( x , y , z ) = f ( x ) f ( y ) f ( z ) is needed such that d ( ln F ) = 0 when ϕ = x 2 + y 2 + z 2 = const. Then by the Lagrange multiplier method d ( ln F + λ ϕ ) = 0. Use this to show that F ( x , y , z ) = A e − ( λ / 2 ) x 2 + y 2 + z 2 .
In discussing the velocity distribution of molecules of an ideal gas, a function F ( x , y , z ) = f ( x ) f ( y ) f ( z ) is needed such that d ( ln F ) = 0 when ϕ = x 2 + y 2 + z 2 = const. Then by the Lagrange multiplier method d ( ln F + λ ϕ ) = 0. Use this to show that F ( x , y , z ) = A e − ( λ / 2 ) x 2 + y 2 + z 2 .
In discussing the velocity distribution of molecules of an ideal gas, a function
F
(
x
,
y
,
z
)
=
f
(
x
)
f
(
y
)
f
(
z
)
is needed such that
d
(
ln
F
)
=
0
when
ϕ
=
x
2
+
y
2
+
z
2
=
const. Then by the Lagrange multiplier method
d
(
ln
F
+
λ
ϕ
)
=
0.
Use this to show that
F
(
x
,
y
,
z
)
=
A
e
−
(
λ
/
2
)
x
2
+
y
2
+
z
2
.
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