A chamber fitted with a piston contains \(1.00 \mathrm{~mol}\) of a monatomic ideal gas that is taken from an initial state i to a final state \(f\) via states 1 and 2 . The chamber volume is initially \(V_{i}=0.100 \mathrm{~m}^{3}\), and the temperature is \(T_{i}=273{ }^{\circ} \mathrm{C}\). To take the gas to state 1 , it is heated isochorically to \(T_{1}=373{ }^{\circ} \mathrm{C}\). To take it to state 2 , it is heated isobarically to \(T_{2}=473{ }^{\circ} \mathrm{C}\). Finally, the gas is allowed to expand isothermally until its volume is \(V_{\mathrm{f}}=2 V_{2}\). What is the change in entropy of the gas?