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In finding enthalpy change $\Delta H$ during adiabatic, reversible expansion of mixture of two ideal gases $n_1$ mol of $\ce{A}$ ($C_{\mathrm{m},v}=\frac{3}{2}R$) and $n_2$ mol of $\ce{B}$ ($C_{\mathrm{m},v}=3R$) taken in a container and during this temperature change is $T_\mathrm{i}$ to $T_\mathrm{f}$. Then what should be the value of $\Delta H$?

It can be $$\Delta H=\left(n_1\right)\frac{5}{2}R\left(T_\mathrm{f}-T_\mathrm{i}\right)+\left(n_2\right)4R\left(T_\mathrm{f}-T_\mathrm{i}\right)$$ taking individully for each gas. Or let say average molar heat capacity of gaseous mixture at constant pressure be $C_{\mathrm{m},p,\mathrm{avg}}$ then it can be $$\Delta H=\left(n_1+n_2\right)C_{\mathrm{m},p,\mathrm{avg}}\left(T_\mathrm{f}-T_\mathrm{i}\right)$$ so please help which is correct one. As per suggestion both are same. $$C_{\mathrm{m},p,\mathrm{avg}}=\frac{\left(n_1\right)\frac{5}{2}R+\left(n_2\right)4R}{n_1+n_2}$$

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They both are same.

If you plug $C_{\mathrm{m},p,\mathrm{avg}}$ in your second equation, you will get your first equation. The average $C$ is calculated as a mole fraction weighted average.

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