Question

A system contains 0.25 m3 of air pressure of 4.8 bars and 160⁰ C. It is expanded adiabatically till the pressure falls to 1.5 bar. The air is then heated at a constant pressure till its enthalpy increases by 80 kJ. Sketch the process on a P-V diagram and determine the total work done. Use Cp=1.005 kJ/kg.K and Cv=0.714 kJ/kg.K

Answer 1

Volume of system contains= 0.25 m³, Air pressure= 4.8 bars and Temperature T₁=160⁰C. P₂= 1.5 bar, h=80 kJ,Cp=1.005 kJ/kg.K and Cv=0.714 kJ/kg.K

$P_1V_1^{\gamma}=P_2V_2^{\gamma}$

$\frac{V_2}{V_1}=\frac{P_2}{P_1}^{\frac{1}{\gamma}}$

$\gamma=\frac{C_p}{C_v}=1.41$

$V_2=$ .1095 m³

Work done in adiabatic process= $\frac{P_1V_1-P_2V_2}{\gamma -1}=\frac{4.8 \times .25 - .1095\times 1.5}{1.41-1}=252.6 kJ$

Work don in constant pressure = Pdv= h=80 kJ

Total work done= 252.6+80=332.6 kJ