In discussing the velocity distribution of molecules of an ideal gas, a functionF(x, y, z) = f(x)f(y)f(z) is needed such that d(ln F) = 0 when φ = x2 + y2 + z2 =const. Then by the Lagrange multiplier method d(ln F + λφ) = 0. Use this to show that F(x, y, z) = Ae−(λ/2)(x2+y2+z2).
In discussing the velocity distribution of molecules of an ideal gas, a functionF(x, y, z) = f(x)f(y)f(z) is needed such that d(ln F) = 0 when φ = x2 + y2 + z2 =const. Then by the Lagrange multiplier method d(ln F + λφ) = 0. Use this to show that F(x, y, z) = Ae−(λ/2)(x2+y2+z2).
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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 = x2 + y2 + z2 =
const. Then by the Lagrange multiplier method d(ln F + λφ) = 0. Use this to show that F(x, y, z) = Ae−(λ/2)(x2+y2+z2).
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