$4.$ The entropy change to bring a sample from $0$ K $($absolute zero$)$ to a given state is called the absolute entropy of the sample in that state. Using Simpson's rule, calculate the absolute entropy of $1\mathrm{.}000$ mol of solid silver at $270$ K$.$ For the region $0$ K to $30$ K$,$ use the approximate relation Cp$=$aT$3($Note that dS $=($Cp$/$T$)$ dT$)$

where a is a constant that you can evaluate from the value of Cp at $30$ K$.$ For the region $30$ K to $270$ K$,$ use the following data:

T$/$K

Cp$/$JK$+$mo$1-1$

$30$

$4\mathrm{.}77$

$70$

$16\mathrm{.}33$

$110$

$20\mathrm{.}96$

$150$

$22\mathrm{.}97$

$190$

$24\mathrm{.}09$

$230$

$24\mathrm{.}73$

$270$

$25\mathrm{.}31$

Simpson's Rule

$[$f$($x$)$dx$=[6+4+2/2+4,+2,+...+4/20-1+20]$The entropy change to bring a sample from $0K($absolute zero$)$ to a given state is

called the absolute entropy of the sample in that state. Using Simpson's rule,

calculate the absolute entropy of $1\mathrm{.}000$mol of solid silver at $270K.$ For the region

$0K$ to $30K,$ use the approximate relation

$C_p=a{T}^3,($ Note that $dS=(C\frac{p}{T})dT)$

where $a$ is a constant that you can evaluate from the value of $Cp$ at $30K.$ For

the region $30K$ to $270K,$ use the following data:

Simpson's Rule

${\displaystyle \underset{a}{\overset{b}{}}}f(x)dx$~~$\frac{h}{3}[f_0+4f_1+2f_2+4f_3+2f_4+$cdots$+4f_{2n-1}+f_{2n}]$