Answer to Question #283801 in Molecular Physics | Thermodynamics for Pratz

Question

A 0.5 kg of air is compressed reversibly and adiabatically from 80 kPa and 60°C to 0.4 MPa and is then expanded at constant pressure to the original volume. Sketch the process on p-V and T-S diagrams, compute work transfer, heat transfer and change in entropy for whole path

Answer 1

$V_0=\frac{mRT_0}{p_0}=0.514~m^3,$

$\gamma=\frac{c_p}{c_V}=1.4,$

$W_c=-\frac 52mRT_0((\frac{p_1}{p_0})^{1-\frac 1{\gamma}}-1)=-60~kJ,$

$V_1=V_0(\frac{p_1}{p_0})^{\gamma}=0.163~m^3,$

$T_1=\frac{p_1V_1}{mR}=527.3~K,$

$T_2=\frac{p_2V_2}{mR}=1664.8~K,$

$Q_c=0,$

$Q_e=mc_p\Delta T=571.7~kJ,$

$W_e=p\Delta V=140.5~kJ,$

$Q=Q_c+Q_e=571.7~kJ,$

$W=W_c+W_e=80.5~kJ.$