A mass of 5 kilograms of air in a piston-cylinder assembly undergoes two processes in series from an initial state where p1 = 4 MPa, T1 = 264°C: Process 1–2: Constant-temperature expansion until the volume is twice the initial volume. Process 2–3: Constant-volume heating until the pressure is again 4 MPa. Sketch the two processes in series on a p-v diagram. Assuming ideal gas behavior, determine (a) the pressure at state 2, in MPa, (b) the temperature at state 3, in oC, and for each of the processes (c) the work and heat transfer, each in kJ.

Aloaded platform of total mass 500 kg is supported by a dashpot and by a set of springs of effective stiffness 72 kn/m. it is observed that when the platform is depressed through a distance x = 12.5 cm below its equilibrium position and then released without any initial velocity; it reaches its equilibrium position in the shortest possible time without overshoot. find the position and velocity of the loaded platform 0.10 sec. after its release. if a further load of 400 kg is added to the platform, find, i) the frequency of damped vibrations, and i) the amplitude of vibration after 2 complete oscillations, given that the initial amplitude is 15 cm.

Awall of 0.5m thickness is to be constructed from a material which has average thermal conductivity of 1.4 w/mk. the wall is to be insulated with a material having an average thermal conductivity of 0.35 w/mk so that heat loss per square meter shall not exceed 1450 w. assume inner wall surface temperature of 1200°c and outer surface temperature of the insulation to be 15°c. calculate the thickness of insulation required.

The characteristic roots of a dynamic system are: 1.7920 1.8160 i, -1.7920 1.8160 i, -0.4160 what is the order of this system? what are the settling time and damping ratio of the system?