Compression vs Temp

P*T^(n-1)=C

P=pressure(pascal)

T=temperature(Kelvin)

n= a constant

for isentropic compression n=k k=1,4 for air

isentropic means no heat is added or removed. Because heat is always added by the compressor, it doesn't have 100% efficiency, this isn't 100% accurate, but a good guess.

For better accuracy you should read some Thermodynamics

Hope this will help

You are right with your last sentence:

(1) p*v=R*T

(2) p*v^m=C m = k if isentropic process and m=1 if isotherm

from (2) → v^m= C*p^(-1) → v= C^(1/m)*p^(-1/m) introduce in (1)

p*[C^(1/m)*p^(-1/m)]/R= T → p^(1-1/m)*(C^(1/m)/R)=T →

p^(1-(1/m))/T= Constant