Subtopic: Thermodynamic principles of I.C. engines
Question Statement:
At an initial pressure of 100 kPa, 1 kg of air is compressed reversibly from 15 litres to 1 litre at a final pressure of 2000 kPa. Neglecting other losses, the Polytropic Exponent (n) is ________. (Rounded off to three decimal places)
Official Answer Key:
1.100 to 1.111
Step-by-Step Solution & Explanation
A reversible polytropic process obeys:
p₁V₁ⁿ = p₂V₂ⁿ
Rearranging:
(p₂/p₁) = (V₁/V₂)ⁿ
Taking logarithms:
n = ln(p₂/p₁)/ln(V₁/V₂)
Substituting:
n = ln(2000/100)/ln(15/1) = ln(20)/ln(15) = 2.99573/2.70805 = 1.106
(The mass of 1 kg is not required — the exponent depends only on the pressure and volume ratios.)
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