# 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. Without explanation the Equation was stated as follows:

(5-7) $$k_{\text{mix}} = \frac{(C_{p})_{\text{mix}}}{(C_{p})_{\text{mix}}-R'}$$

From Thermodynamics I know,

(a) $$k_{j} = \frac{(C_{p})_{\text{j}}}{(C_{v})_{\text{j}}}$$ ; Species specific heat ratio

(b) $$R_{j} = \frac{R'}{\mathfrak{M}_{j}};$$ Species Gas constant equal to Univ. Gas constant over Molar Mass of species $$\text{&}$$

(c) $$R_{j} = (C_{p})_{\text{j}} - (C_{v})_{\text{j}}$$ ;Mayer's Formula for species

So, it seems to me that Eq. (5-7) should instead include the mixture gas constant $$R_{\text{mix}}$$ in the place of the Universal gas constant, $$R'$$.

I tried to derive Eq. (5-7) from Eqs. a, b, and c without success. Can someone clarify the derivation of Eq. (5-7) to me?

• It seems to me, Eqn. 5-7 is referring to molar quantities. – Chet Miller Sep 17 '20 at 20:05

$$C_p=C_V + R'$$
It follows that for a perfect gas mixture $$(C_p)_\text{mix}=(C_V)_\text{mix} + R'$$.
• I agree. I believe my issue was due to a misunderstanding. $C_{p}$ is the molar specific heat, and $c_{p}$ is the mass-basis specific heat. Thank you! – John Ortiz Sep 17 '20 at 20:01