Relationship between two specific heat, Mechanical Engineering

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

 

Posted Date: 10/15/2012 2:21:27 AM | Location : United States







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