dQ = dU + dW; for a perfect gas
dQ at constant pressure
dU at Constant volume; = mCvdT = mCv(T2 – T1)
dW at constant pressure = PdV = P(V2 – V1) = mR(T2 – T1)
Putting all the values we get
dQ = mCv(T2 – T1) + mR(T2 – T1)
dQ = m(CV + R)(T2 – T1)
but dQ = mCp(T2 – T1)
mCp(T2 – T1) = m(CV + R)(T2 – T1)
Cp = CV + R; Cp - CV = R ...(i)
Now divided by Cv; we get
Cp /CV – 1 = R/Cv; Since Cp /CV = y (gama = 1.41)
y – 1 = R/Cv;
or Cv = R/ (y – 1); CP = yR/ (y – 1); CP>CV; y>1
