Ideal gas law in combustion engine analysis

Question

I'm studying this derivation of the Diesel engine theoretical efficiency:

http://hyperphysics.phy-astr.gsu.edu/hbase/thermo/diesel.html

Here the ideal gas law is used in many occasions. Why is it applicable here? I've been taught that the ideal gas law is a useful approximation only when gas pressures and densities are small. But aren't the pressures of combusting gasses inside cylinders of engines quite high if they are able to provide enough torque to move heavy vehicles? I understand that overall there derivations assume highly ideal conditions are are only idealizations of true engines but why can we apply the ideal gas law to combustion engines?

I've also seen ideal gas approximation used in analysis of jet engines, so I could ask the same question here: Aren't the pressures and temperatures too high so that the ideal gas law is not a very good approximation?

Answer 1

Pressures inside the cylinder are quite high, but so are temperatures. To determine how applicable the ideal gas law is, use the law of corresponding states. This law calculates a reduced temperature ($T/T_c$) and a reduced pressure ($P/P_c$) to arrive at a compressibility factor of z. This factor is used in the ideal gas law to make it applicable to real gases. Thus, the modified ideal gas law becomes $PV=znRT$.

If your calculated value of z is "reasonably" close to 1, the ideal gas law applies. For more info, see https://en.wikipedia.org/wiki/Compressibility_factor