Expand $1.00$ mol of an monatomic gas initially at $5.00 \mathrm{kPa}$ and $600 \mathrm{~K}$ from initial volume $V_{i}=1.00 \mathrm{~m}^{3}$ to final volume $V_{f}=$ $2.00 \mathrm{~m}^{3}$. At any instant during the expansion, the pressure $p$ and volume $V$ of the gas are related by $p=5.00 \exp \left[\left(V_{i}-V\right) / a\right]$, with $p$ in kilopascals, $V_{i}$ and $V$ in cubic meters, and $a=1.00 \mathrm{~m}^{3}$. What are the final (a) pressure and (b) temperature of the gas? (c) How much work is done by the gas during the expansion? (d) What is $\Delta S$ for the expansion? (Hint: Use two simple reversible processes to find $\Delta S .$ )