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When an ideal gas expands isothermally into a vacuum, it undergoes free expansion. In free expansion, no external pressure is exerted on the gas, so the gas performs no work on its surroundings. Additionally, since the temperature remains constant during isothermal expansion, the change in internal energy (ΔUΔU) of the gas is also zero.
Therefore, in free expansion:
W=0W=0
ΔU=0ΔU=0
So, in this case, for the expansion of 1 litre of ideal gas into vacuum until its total volume is 5 litres:
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