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 worldanalogous to the Maxwell speed distribution in three dimensions:mf(v) =2лкBТ3/24πv² e-mv²/2kBTA) Find the kinetic energy of a monatomic ideal gas in a two-dimensional world as afunction of temperature, and show that your result is consistent with theequipartition theorem.Hint: Use the Standard Gaussian IntegralsIn== Soxne-ax^2dx=1a=12a24-2-11-1=2aI2n+1=n-I2n-1a

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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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