$(6$ points$)$ Carbon dioxide initially at $50$kPa,$300K,$ undergoes a process in a closed system until its pressure and temperature are $1$ MPa and $700$ K $,$ respectively. Assuming ideal gas behavior, find the entropy change of the carbon dioxide by a$)$ first assuming constant specific heats $($approximate method$),$ and b$)$ then assuming variable specific heats $($exact method$).$ Which method do you expect to be more correct and why? $($please see Table on next page$)$

Note: $C_{p,av,CO2}=0\mathrm{.}846k\frac{J}{k}{g}^{-1}{K}^{-1}$ at $300K,M_{CO2}=44k\frac{g}{k}$mol,$R_{CO2}=0\mathrm{.}1889kJk{g}^{-1}{K}^{-1}.$