When 2 litre of ideal gas expands isothermally into vacuum to a total volume of 6 litre, the change in internal energy is ______ J. (Nearest integer)

When an ideal gas expands isothermally into vacuum, we need to find the change in internal energy.

Key concepts:

In free expansion (expansion into vacuum):

- No external pressure opposes the expansion, so work done $$W = 0$$.

- The expansion is rapid and adiabatic in nature, with no heat exchange: $$Q = 0$$.

For an ideal gas:

The internal energy depends only on temperature: $$U = nC_vT$$.

In free expansion of an ideal gas, the temperature remains constant (Joule's experiment).

Therefore: $$\Delta U = 0$$ J

The change in internal energy is $$\boxed{0}$$ J.