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find entropy change for free expantion of ideal gas

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entropy = jouls/kelvin
supose 1 liter of ideal gas is allowed to freely expand into a 2 liter volume in an isolated system
the energy in the system would remain the same,
the temperature in the system would remain the same
therefore if entropy =jouls/kelvin the entropy would remain the same
howerer if 1 liter of ideal gas is allowed to freely expand into a 2 liter volume in an isolated system the entropy does increase.
how dose entropy=jouls/kelvin ?

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