Question

Measurements of pressure and temperature at various stages in an adiabatic air turbine show that the states of air lie on the line pv^1.25 = constant. If kinetic and gravitational potential energy is neglected, prove that the shaft work per kg as a function of pressure is given by the following relation 

\(W = 3.5p_1v_1 \left[1 - \left(\frac{p^2}{p_1}\right)^{1/5}\right]\)

Take γ for air as 1.4.

Answer 1

Using S.F.E.E.

Here adiabatic process

∴ Q → 0 and as

So