Show that h(y) := f(-y) is f Legendre-transformed twice.

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 ))