Project ForgeThermodynamics
First Law of Thermodynamics
GATE 2022
Hard
A polytropic process is carried out from an initial pressure of 110 kPa and volume of 5 m³ to a final volume of 2.5 m³. The polytropic index is given by n=1.2. The absolute value of the work done during the process is ___________ kJ (round off to 2 decimal places).
408.92 kJ(± 1.5 accepted)
Explanation
P2 = P1(V1/V2)ⁿ = 110×2^1.2 ≈ 110×2.2974 ≈ 252.71 kPa. W = (P1V1−P2V2)/(n−1) = (550 − 252.71×2.5)/0.2 = (550−631.78)/0.2 ≈ −408.92 kJ. Absolute value ≈ 408.92 kJ (negative sign indicates work is done ON the gas during compression, consistent with V decreasing).
Source: GATE ME 2022 Session 1 (ME-1) (2022)
This question is part of a 15-day revision cycle — sign in and Project Forge will bring it back the day before you'd forget it.