Air at 101 kPa is trapped in a piston-cylinder deviceoriented horizontally. Init

Question

Air at 101 kPa is trapped in a piston-cylinder deviceoriented horizontally. Initially the volume in the cylinderis 2.00 liters and the face of the piston is at x=0, a position atwhich the spring attached to the piston exerts noforce.    Atmospheric pressure is 101 kPa and thearea of the piston face is 0.018 m2.   The airexpands slowly until its volume is 3.00 liters.   Thespring is linear (F =kx) with a spring constant k = 16.2kN/m.   Determine the final pressure of the air and thework done by the air on the piston? I dont know where to start on this one.. Help with be appreciated... Air at 101 kPa is trapped in a piston-cylinder deviceoriented horizontally. Initially the volume in the cylinderis 2.00 liters and the face of the piston is at x=0, a position atwhich the spring attached to the piston exerts noforce.    Atmospheric pressure is 101 kPa and thearea of the piston face is 0.018 m2.   The airexpands slowly until its volume is 3.00 liters.   Thespring is linear (F =kx) with a spring constant k = 16.2kN/m.   Determine the final pressure of the air and thework done by the air on the piston? I dont know where to start on this one.. Help with be appreciated... I dont know where to start on this one.. Help with be appreciated...

Explanation / Answer

Pair*A = Patm*A +k*x                Pair = Pressure of air A*x = V = V - Vi    Vi= initial volume x = V/A - Vi/A Pair = Patm + kV/A2 - kVi/A2 = Patm +(k/A2)*(V - Vi) Final pressure, evaluate the above expression at V = 3 L Pair = 101 kPa + (16.2 kN/m /[0.018m2]2)*(3 L- 2L)*(1 m3/1000 L) Pair (final) = 151 kPa ================ Work = integral [P*dV] = integral [Patm + kV/A2 - kVi/A2]dV Work = (Patm- kVi/A2 )V +kV2/2A2      evaluated from 2 L to 3 L Vi = 2e-3 m3   (2 L = 2e-3 m3) Work = (101 kPa - 16.2 kN/m * 2e-3 m3/ [0.018m2]2)*(3e-3 m3 - 2e-3m3)             + {16.2kN/m /2*[0.018m2]2 }*([3e-3m3]2 - [2e-3 m3]2) Work = (0.001 + 0.125) kJ Work = 0.126 kJ PM me if you need more help with this. I won't be notifiedotherwise.

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