# Specific Heat Ratio for a perfect gas mixture

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?

• The question doesn't seem to be a bad one, however, I believe it is not really suited for this site... For chemistry questions, check out chemistry.stackexchange.com – finnmglas Sep 17 '20 at 15:50
• On topic here, on topic on chemistry (or physics?). OP decides where to post in that case. And OP posted here. – SE - stop firing the good guys Sep 17 '20 at 16:12
• Good question and congrats on going through the details. My 4th edition doesn't have these equations in it. And I learned something. – Organic Marble Sep 17 '20 at 20:32

Universal gas constant R' is correct. Sutton uses $$C_p$$ for molar specific heat and $$c_p$$ for mass specific heat. See table of symbols at end of chapter (I have the 7th ed.).
• Since $C_{p}$ is the molar specific heat, my mistake is equation (4). It should be: $R' = (C_{p}) - (C_{v})$ – John Ortiz Sep 17 '20 at 19:48