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computational_physics
lectures
Commits
181a56e7
Commit
181a56e7
authored
Mar 11, 2021
by
Michael Wimmer
Browse files
clarify specific heat
parent
518d247e
Pipeline
#56026
passed with stages
in 1 minute and 42 seconds
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src/proj1moldynweek4.md
View file @
181a56e7
...
...
@@ 136,11 +136,13 @@ However, as derived by [Lebowitz](https://journals.aps.org/pr/abstract/10.1103/P
it can be calculated from fluctuations in the kinetic energy instead:
$$
\f
rac{
\l
angle
\d
elta K^2
\r
angle}{
\l
angle K
\r
angle^2} =
\f
rac{2}{3N}
\l
eft(1
\f
rac{3N}{2 C_V}
\r
ight)
\l
eft(1
\f
rac{3N}{2 C_V}
\r
ight) =
\f
rac{2}{3N}
\l
eft(1
\f
rac{3}{2 c_V}
\r
ight)
$$
where $K$ is the kinetic energy, and $
\l
angle
\d
elta K^2
\r
angle=
\l
angle K^2
\r
angle 
\l
angle K
\r
angle^2$ the fluctuations of the
kinetic energy.
kinetic energy. In this formula $C_V$ is the total specific heat capacity
for all $N$ atoms, whereas $c_V=C_V/N$ is the specific heat per atom.
#### Diffusion
...
...
@@ 179,4 +181,4 @@ if you want to observe these different types of behaviour.
 Implement the initialization of positions onto an fcc lattice.
 Show that the initial velocities obey a MaxwellBoltzmann distribution.
 Perform the rescaling of temperature and show how the desired temperature is attained after a certain amount of rescaling and equilibrating.

Study at least one observable, and compare its behaviour to literature.
\ No newline at end of file
 Study at least one observable, and compare its behaviour to literature.
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