Subtopic: Thermodynamic principles of I.C. engines
Question Statement:
One kilogram of air is subjected to polytropic compression from a volume of 28 m³ and a pressure of 101 kPa to a volume of 2 m³ and pressure of 2 MPa. The external work required to make this compression possible is
Options:
(A) 1.66 MJ
(B) 2.93 MJ
(C) 3.04 MJ
(D) 8.92 MJ
Official Answer Key:
D
Step-by-Step Solution & Explanation
Polytropic index from p₁V₁ⁿ = p₂V₂ⁿ: n = ln(p₂/p₁)/ln(V₁/V₂) = ln(2000/101)/ln(28/2) = ln(19.80)/ln(14) = 2.986/2.639 = 1.131. Work of compression, W = (p₁V₁−p₂V₂)/(n−1) = (101×28 − 2000×2)/(1.131−1) = (2828−4000)/0.131 = −8945 kJ; magnitude of external work required ≈ 8.92 MJ.
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