Respuesta :
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
[tex]\frac{P_2}{P_3} = (\frac{V_3}{V_2} )^n[/tex] where P₃ = 2 MPa
Therefore V₃ = [tex](\frac{1}{4} )^{\frac{1}{1.2} }*V_2[/tex] = 1.6904×10⁻² m³
Work = W₂ = [tex]\frac{P_2V_2-P_3V_3}{n-1}[/tex] = -34872.82 J
[tex]\frac{P_2}{P_3} = (\frac{T_2}{T_3} )^\frac{n}{n-1}[/tex] or T₃ = [tex]T_2*(\frac{P_3}{P_2})^\frac{n-1}{n}[/tex] = 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
