Apply the Legendre transformation to the Entropy S as a function of E, specifically for the ideal gas according to the Sackur-Tetrode equation: S(E, = KBN(2 mkN) -AK/ + 2 k277r3h6/ e5m3 )).

the Legendre transform g of a function f is:
g(m) = f(x(m))- m • x(m) mit
x(m) = (r)-1(m).
Show that h(y) := f(-y) is f Legendre-transformed twice. This demonstrates that no information is lost during the Legendre trans-formation.

Apply the Legendre transformation to the Entropy S as a function of E, specifically for the ideal gas according to the Sackur-Tetrode equation:
S(E, = KBN(2 mkN) -AK/ + 2 k277r3h6/ e5m3 ))

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