A cylinder of internal diameter 75mm is closed at one end an

A cylinder of internal diameter 75mm is closed at one end and sealed by a fricitonless piston loaded by a spring of stiffness 20 kN/m. The cylinder initially contains 3 x10^-4 m^3 of air at 3 bar. Heat is added to the air such that the piston moves outwards by 30mm. Calculate the work done by the air, the change in internal energy of the air, and the heat transfered to the air. Subject is basic engineering thermodynamics.

Solution

Work done by the air   = Work done on the spring + Work done against atmosphere

                                 = 0.5 * k * x^2 + Patm * area of piston * x

                                = 0.5 * 20000 * (30 * 10^-3)^2 + 101325 * pi * 0.075^2 * 0.03 / 4

                                = 22.43 J

Final pressure   = 3 * 10^5 + 20000 * 0.03 / (pi * 0.075^2 / 4)    = 4.358 bar

Initial temperature     T1 = 3 * 10^5 / (1.225 * 287 ) = 853.303 K

P1 * V1 / T1 = P2 * V2 / T2

3 * 3 * 10^-4   / 853.303   = 4.358 * 4.325 * 10^-4 / T2

T2 = 1787.04 K

Change in internal energy = m * Cv * (T2 - T1)

                                      = 1.225 * 3 * 10^-4 * 718 * (1787.04 - 853.303)

                                      = 246.38 J

Heat transferred = 246.38 + 22.43 = 268.81 J