Chapter 3.4, Problem 31P

Experimental measurements of heat capacities are often represented in reference works as empirical formulas. For graphite, a formula that works well over a fairly wide range of temperatures is (for one mole) $C_p=a+bT-\frac{c}{T^2}$, where $a=16.86J/K,b=4.77\times {10}^{-3}J/K^2$, and $c=8.54\times {10}^{5}J\cdot K$. Suppose, then, that a mole of graphite is heated at constant pressure from 298 K to 500 K. Calculate the increase in its entropy during this process. Add on the tabulated value of $S\left(298K\right)$ (from the back of this book) to obtain $S\left(500K\right)$.