= Solution
A <state function> is determined by the equilibrium state, rather than the path used to reach it. Its differential is exact and its change around a closed <thermodynamic cycle> is zero. <Internal energy>, <entropy> and <enthalpy> are examples; transferred <heat> and <work> are not <state functions>.
For slow expansion in contact with a large <thermal reservoir>, the fixed <temperature> of that reservoir maintains an <isothermal process>. For a fixed amount of <ideal gas>, <internal energy> and <enthalpy> depend only on <temperature>, so
$$
\boxed{T=\mathrm{constant},\qquad U=\mathrm{constant},\qquad H=\mathrm{constant}.}
$$
The <ideal gas law> also gives $pV=\mathrm{constant}$. For a reversible expansion the absorbed <heat> equals the <work> done by the gas, while its <entropy> increases by $n_{\rm mol}R\ln(V_2/V_1)$; constant <internal energy> does not mean zero <heat transfer>.
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