for an isothermal expansion of an ideal gas
​change in E=0
change in V=0

1. The statement above showing:

     w = q= E = V=0

is for free isothermal expansion of an ideal gas.


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For an adiabatic process, in which no heat flows into or out of the gas because its container is well insulated, . If there is also no work done, i.e. a free expansion, there is no change in internal energy. For an ideal gas, this means that the process is also isothermal.
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