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?

  • 1
    $\begingroup$ It seems to me, Eqn. 5-7 is referring to molar quantities. $\endgroup$ Commented Sep 17, 2020 at 20:05

1 Answer 1


In general for a perfect or ideal gas,

$$C_p=C_V + R'$$

(using your notation) where the heat capacities are molar quantities.

It follows that for a perfect gas mixture $(C_p)_\text{mix}=(C_V)_\text{mix} + R'$.

  • 1
    $\begingroup$ 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! $\endgroup$
    – John Ortiz
    Commented Sep 17, 2020 at 20:01

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.