I am reading Rocket Propulsion Elements by George P. Sutton & Oscar Biblarz, 9th Edition. In the fifth chapter, I was introduce to the specific heat ratio k for the perfect gas mixture, Eq. 5-7:
(1) $k_{\text{mix}} = \frac{(C_{p})_{\text{mix}}}{(C_{p})_{\text{mix}}-R'}$
Since,
(2) $k_{j} = \frac{(C_{p})_{\text{j}}}{(C_{v})_{\text{j}}}$
(3) $R_{j} = \frac{R'}{\mathfrak{M}_{j}} $ $\text{&}$
(4) $R_{j} = (C_{p})_{\text{j}} - (C_{v})_{\text{j}}$
It seems to me that this equation should instead include the mixture gas constant $R_{\text{mix}}$ in the place of the Universal gas constant, $R'$.
I tried to derive it without success. Can someone clarify this to me?