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I am confused when I apply Euler's equation on the free expansion of an ideal gas.

Consider a free expansion (expansion of gas in vaccum) where the volume is doubled (V->2V)

The classical free expansion of an ideal gas results in increase in entropy by an amount of nR ln(2), a decrease in pressure (P->P/2), and the temperature T is constant.

The Euler equation of thermodynamics writes U=-PV+TS.

Before free expansion S=(U+PV)/T.

After free expansion S=(U+(P/2)(2V))/T.

It looks like that from Euler equation the entropy should remain unchange.

However it must not be the case from what we know about free expansion.

Can anyone give me some clue where am i wrong?