Project ForgeThermodynamics
First Law of Thermodynamics
GATE 2016
Medium
A piston-cylinder device initially contains 0.4 m³ of air (ideal gas) at 100 kPa and 80°C. The air is isothermally compressed to 0.1 m³. The work done during this process is __________ kJ. (Take the sign convention such that work done on the system is negative.)
-55.45 kJ(± 0.15 accepted)
Explanation
For an isothermal ideal-gas process, W=∫p dV=p1V1 ln(V2/V1). p1V1=100×0.4=40 kJ. W=40×ln(0.1/0.4)=40×ln(0.25)=40×(-1.386)≈-55.45 kJ — negative, consistent with work done ON the gas during compression.
Source: GATE ME 2016 Set-2 (2016)
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