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) $k_{\text{mix}} = \frac{(C_{p})_{\text{mix}}}{(C_{p})_{\text{mix}}-R'}$


(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?

  • $\begingroup$ 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 $\endgroup$ – finnmglas Sep 17 '20 at 15:50
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    $\begingroup$ On topic here, on topic on chemistry (or physics?). OP decides where to post in that case. And OP posted here. $\endgroup$ – SE - stop firing the good guys Sep 17 '20 at 16:12
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    $\begingroup$ Good question and congrats on going through the details. My 4th edition doesn't have these equations in it. And I learned something. $\endgroup$ – 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.).

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    $\begingroup$ Since $C_{p}$ is the molar specific heat, my mistake is equation (4). It should be: $R' = (C_{p}) - (C_{v})$ $\endgroup$ – John Ortiz Sep 17 '20 at 19:48

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