Chapter 3, Problem 3.67E

Plots of $C_p/T$ versus $T$ are used to determine the entropy of a material, as the entropy value would be the area under the curve. For sodium sulfate, ${\text{Na}}_{\text{2}}{\text{SO}}_{\text{4}}$, the following data are available:

$T\left(\text{K}\right)$	$C_p\left(\text{cal}/\text{K}\right)$
$\text{13}\text{.74}$	$\text{0}\text{.171}$
$16.25$	$\text{0}\text{.286}$
$\text{20}\text{.43}$	$\text{0}\text{.626}$
$\text{27}\text{.73}$	$\text{1}\text{.615}$
$\text{41}\text{.11}$	$\text{4}\text{.346}$
$\text{52}\text{.72}$	$\text{7}\text{.032}$
$\text{68}\text{.15}$	$\text{10}\text{.48}$
$\text{82}\text{.96}$	$\text{13}\text{.28}$
$\text{95}\text{.71}$	$\text{15}\text{.33}$

Source: G.N. Lewis and M.Rabdall, Thermodynamics, rev.

K. Pitzer and L.Brewer, McGraw-Hill, New York, $1961$.

Extrapolate to $\text{0}\text{K}$ using a function $f\left(T\right)=k{T}^3$, where $k$ is some constant. Using your plot, numerically evaluate the experimental entropy of ${\text{Na}}_{\text{2}}{\text{SO}}_{\text{4}}$ at $\text{90}\text{K}$.