= Solution
For a reversible <isothermal expansion> of one mole of an <ideal gas>, <internal energy> depends only on <temperature>, so $\Delta U=0$. The <first law of thermodynamics> gives
$$
Q=W=\int_{V_i}^{2V_i}\frac{RT_0}{V}\,dV=\boxed{RT_0\ln2.}
$$
This uses quasistatic expansion against the gas pressure. Specifying only the initial and final volumes and constant <temperature> would not fix heat for an arbitrary irreversible process: an insulated ideal-gas free expansion has $Q=W=0$.
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