GATE AG 2017 • Q10 NAT • 2 Marks

Section 3: Farm Power

Farm Power

Subtopic: Thermodynamic principles of I.C. engines

Question Statement:

Air temperature at the beginning of adiabatic compression in an IC engine is 27 °C and the engine compression ratio is 16:1. The temperature of air at the end of the compression in °C will be __________.

Official Answer Key:

635 to 637

Step-by-Step Solution & Explanation

• Isentropic (adiabatic) compression relation: T2/T1 = r^(γ–1), with air standard γ = 1.4. • T1 = 27 + 273 = 300 K, r = 16. • T2 = 300 × 16^0.4. 16^0.4 = e^(0.4×ln16) = e^(0.4×2.7726) = e^1.109 ≈ 3.031. • T2 = 300 × 3.031 ≈ 909.4 K = 909.4 – 273 = 636.4 °C, inside the accepted range 635–637.

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