Calculate the heat required to ralse the temperature of $1$ mol of methane from $260$ to $600C$ in a steady$-$flow process at a pressure sufficiently low that the ideal$-$gas state is a suitable approximation for methane.

Table C$\mathrm{.}1$: Heat Capacities of Gases in the Ideal$-$Gas State ${?}^{}$

Constants in equation $\frac{C_P^{ig}}{R}=A+BT+C{T}^2+D{T}^{-2}$ for $T(K)$ from $298K$ to $T_{\text{m}\text{a}\text{x}}$

$\backslash$table$[[$Chemical species,,T$\_($max$),$C$\_($P$\_(29$s$))^($ig$)/$R$,$A$,10^(3)$B$,10^(6)$C$,10^(-5)$D$],[$Alkanes:$],[$Methane$,$CH$\_(4),1500,4\mathrm{.}217,1\mathrm{.}702,9\mathrm{.}081,-2\mathrm{.}164,$dots$],[$Ethane$,$C$\_(2)$H$\_(6),1500,6\mathrm{.}369,1\mathrm{.}131,19\mathrm{.}225,-5\mathrm{.}561,$dots$],[$Propane$,$C$\_(3)$H$\_(8),1500,9\mathrm{.}011,1\mathrm{.}213,28\mathrm{.}785,-8\mathrm{.}824,$dots$],[$n$-$Butane,C$\_(4)$H$\_(10),1500,11\mathrm{.}928,1\mathrm{.}935,36\mathrm{.}915,-11\mathrm{.}402,$dots$],[$iso$-$Butane,C$\_(4)$H$\_(10),1500,11\mathrm{.}901,1\mathrm{.}677,37\mathrm{.}853,-11\mathrm{.}945,.],[$n$-$Pentane,C$\_(5)$H$\_(12),1500,14\mathrm{.}731,2\mathrm{.}464,45\mathrm{.}351,-14\mathrm{.}111,$dots$],[$n$-$Hexane,C$\_(6)$H$\_(14),1500,17\mathrm{.}550,3\mathrm{.}025,53\mathrm{.}722,-16\mathrm{.}791,$dots$],[$n$-$Heptane,C$\_(7)$H$\_(16),1500,20\mathrm{.}361,3\mathrm{.}570,62\mathrm{.}127,-19\mathrm{.}486,......],[$n$-$Octane,CoH$\_(18),1500,23174,4108,70567,-22208,-]]$