Specific Heat Ratio

So I've been researching about designing a rocket engine, when I came across the specific heat ratio. I found on the Braeuig.us website that they were able to get a number by finding the heat capacity $C_p$ and the constant volume specific heat $C_v$.

Shouldn't the size of the combustion chamber pressure be taken into account? As it gets smaller, won't the fuel/oxydizer combustion be hotter due to the high pressure? I'm pretty much a novice in rocketry so please excuse my question if it's a little dumb. Thanks in advance!

• The specific heat ratio is a physical property of the gas mixture, independent of equipment the gas is passing through. – Chet Miller Feb 7 '18 at 1:00