A gas mixture with the composition CO$2=9\%,$ CO$=2\%,$ O$2=7\%$ and N$2=82\%,$ with Cp respectively:

CO$2$: Cp$=7+0\mathrm{.}8$T$-0\mathrm{.}004$T$2$

CO : Cp$=6+0\mathrm{.}9$T$-0\mathrm{.}005$T$2$

O$2$ : Cp$=8+0\mathrm{.}5$T$-0\mathrm{.}003$T$2$

N$2$ : Cp$=7+0\mathrm{.}7$T$-0\mathrm{.}009$T$2$

Calculate the difference in enthalpy at temperatures of $2000$F and $5000$F with units of Cp: BTU$/$lbmol $0$F