During an expansion process a piston-cylinder system, the volume of gas containe

Question

During an expansion process a piston-cylinder system, the volume of gas contained in the cylinder changes from 0.1 to 0.3 m^3. The pressure changes during the quasi-equilibrium process according to the relation, p = 2.4V + 0.4, where the units of P and V are [bar] and [m^3] respectively. a. Derive the symbolic formula for work by integration and find the work done by the gas in [J]. b. Check the answer by plotting the process by hand on a PV diagram and calculating the work using geometry relations. c. If there is friction in the between the piston and cylinder with a constant force of 2000 N for the entire process and the area of the piston is 0.2 m^3, what is actual useful work done by the piston during the process?

Explanation / Answer

a)Work = Integral PdV = Integral (2.4V+0.4)dV = 1.2V^2+0.4V+C, where C is integration constant. Apply limits to get, Work = 17828.8J Actual useful work = 17828.8-(10000*1)= 7828.8J

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