(Solved): A piston-cylinder arrangement contains air at \( 250 \mathrm{kPa} \) and \( 300^{\circ} \mathrm{C} ...

A piston-cylinder arrangement contains air at \( 250 \mathrm{kPa} \) and \( 300^{\circ} \mathrm{C} \). The \( 50 \mathrm{~kg} \) piston has a diameter of \( 0.1 \mathrm{~m} \) and initially pushes against the stops. The atmosphere is at \( 100 \mathrm{kPa} \) and \( 20^{\circ} \mathrm{C} \). The cylinder now cools as heat is transferred to the ambient. (a) Show the process in a \( \mathrm{p}-\mathrm{v} \) and \( \mathrm{t}-\mathrm{v} \) diagram , (b) Determine at what temperature does the piston begin to move down, and (c) How far does the piston dropped when the temperature reaches ambient (35 pts) \[ \mathrm{R}=0.2870 \mathrm{~kJ} / \mathrm{kg} \mathrm{K} ; \quad \mathrm{P}_{\mathrm{cr}}=3.77 \mathrm{MPa} ; \quad \mathrm{T}_{\mathrm{cr}}=132.5 \mathrm{~K} \]