Answer:
Isothermal expansion W₁ =-37198.9 J
Polytropic Compression W₂ =-34872.82 J
Isobaric Compression W₃ = -6974.566 J
The net work for the cycle = -79046.29 J
Explanation:
Mass of air = 0.15 kg = 150 g
Molar mass = 28.9647 g/mol
Number of moles = 150 g /28.9647 g/mol = 5.179 moles of air
PV = nRT therefrore V = nRT/(P) = 5.179*8.314*(350+273.15)/(2×10⁶) = 0.0134167 m³
For isothermal expansion we have
P₁V₁ = P₂V₂ or V₂ = P₁V₁/P₂ = 2×10⁶*0.0134167 / (5×10⁵) = 0.0536668 m³
Therefore work done
W₁ = -nRTln(V₂/V₁) = -26833ln(4) = -37198.9 J
Stage 2
Compression polytropically we have
where P₃ = 2 MPa
Therefore V₃ = = 1.6904×10⁻² m³
Work = W₂ = = -34872.82 J
or T₃ =
= 785.12 K
Isobaric compression we have thus
Work done W₃ = P(V₁ -V₃) = -6974.566 J
Total work = W₁ + W₂ + W₃ = -37198.9 J + -34872.82 J + -6974.566 J = -79046.29 J