In his 1884 book Flatland, Edwin Abbot dreamed of a two-dimensional world. A) Find the two-dimensional ideal gas speed distribution for such a world analogous to the Maxwell speed distribution in three dimensions: m f(v) = 2лкBТ 3/2 4πv² e-mv²/2kBT A) Find the kinetic energy of a monatomic ideal gas in a two-dimensional world as a function of temperature, and show that your result is consistent with the equipartition theorem. Hint: Use the Standard Gaussian Integrals In = = So xne-ax^2 dx = 1 a = 1 2a 24-2-11-1 = 2a I2n+1 = n -I2n-1 a
In his 1884 book Flatland, Edwin Abbot dreamed of a two-dimensional world. A) Find the two-dimensional ideal gas speed distribution for such a world analogous to the Maxwell speed distribution in three dimensions: m f(v) = 2лкBТ 3/2 4πv² e-mv²/2kBT A) Find the kinetic energy of a monatomic ideal gas in a two-dimensional world as a function of temperature, and show that your result is consistent with the equipartition theorem. Hint: Use the Standard Gaussian Integrals In = = So xne-ax^2 dx = 1 a = 1 2a 24-2-11-1 = 2a I2n+1 = n -I2n-1 a
Question
Transcribed Image Text:In his 1884 book Flatland, Edwin Abbot dreamed of a two-dimensional world.
A) Find the two-dimensional ideal gas speed distribution for such a world
analogous to the Maxwell speed distribution in three dimensions:
m
f(v) =
2лкBТ
3/2
4πv² e-mv²/2kBT
A) Find the kinetic energy of a monatomic ideal gas in a two-dimensional world as a
function of temperature, and show that your result is consistent with the
equipartition theorem.
Hint: Use the Standard Gaussian Integrals
In
=
= So
xne-ax^2
dx
=
1
a
=
1
2a
24-2-11-1
=
2a
I2n+1
=
n
-I2n-1
a
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