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Relationship between two specific heat ?
Sol: 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 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
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