Heat calculations are frequently used in chemical engineering, as well as in many other engineering fields. One common issue is determining the amount of heat needed to increase the temperature of a material. The characteristic that is needed to carry out this computation is the heat capacity $(c_p).$ This parameter represents the quantity of heat required to raise a unit mass by a unit temperature. If $c_p$ is constant over the range of temperatures being examined, the required heat $(H)$ can be calculated by$.$

$H=m{c}_{p}T$

Such a computation is adequate when $T$ is small. However, for large ranges of temperature, the heat capacity varies as a function of temperature and can be calculated by$.$

$H=m{\displaystyle \underset{T_1}{\overset{T_2}{}}}{c}_p(T)dT$

Consider heating $36$ grams of steam from $200C$ at $1$MPa to $500C$ and $1$MPa. Choose and use the appropriate six$-$segment Newton$-$Cote integration formula to numerically compute the heat required $($in $J)$ to raise the steam to $500C.$

State all assumptions and utilize your chemical engineering knowledge and resources to find data points.