a derive the mathematical equation for work done, Mechanical Engineering

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a derive the mathematical equation for work done

(a) Derive the mathematical equation for work done in a polytropic process (i.e.) PVⁿ =c)

(b) A mass of gas is compressed in a quasi-static process from 80KPa, 0.1m³ to 0.4MPa, 0.03m³. Assuming that pressure and volume are related by PVⁿ = const., Determine the work done by the gas system.

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