Heats of Formation

Standard Heat of Reaction (at $T^{\circ }$)

$$\Delta H_{\text{rxn}}^{\circ }(T^{\circ })=\sum _{\text{prod}}{\nu }_i\Delta H_f^{\circ }(i,T^{\circ })-\sum _{\text{react}}{\nu }_j\Delta H_f^{\circ }(j,T^{\circ }).$$

Temperature Correction (Kirchhoff’s law)

For general $T$,

$$\Delta H_{\text{rxn}}(T)=\Delta H_{\text{rxn}}^{\circ }(T^{\circ })+{\int }_{T^{\circ }}^T\sum _k{\nu }_k{c}_{p,k}(\tau )\mathrm{d}\tau .$$

If $c_{p,k}$ are polynomial in $T$, this integral is analytic.

Performance link: chamber $T_0$ and $\Delta H_{\text{rxn}}$ influence $c^{\ast }\propto \sqrt{R{T}_0/\gamma }$ and therefore $I_{sp}=C_f{c}^{\ast }/g_0$.