A container (cylindrical, base area = 821 cm^2) fitted with frictionless, massless piston consist of — States of Matter and Gaseous State Chemistry Question
Question
A container (cylindrical, base area = 821 cm^2) fitted with frictionless, massless piston consist of five valves - I, II, III, IV and V. The distance of valves from the initial position of piston is 15, 30, 40, 45 and 50 cm, respectively. The initial height of piston from the base of container was 60 cm. These valves open automatically if pressure exceeds over 1.5, 2.2, 2.5, 4.4 and 4.8 atm, respectively. Under the given conditions (shown in the diagram), the system is in state of equilibrium. Piston is now compressed (moved downward) slowly and isothermally. Neglect the volume of valve connectors. Select the correct option(s):
💡 Solution & Explanation
Initially, P = 1 atm, h = 60 cm. Isothermal compression: P × h = constant. Let's calculate the heights at which each valve's opening pressure is reached: Valve I (P = 1.5 atm): h = 1 × 60 / 1.5 = 40 cm (distance moved = 20 cm, which is past Valve I at 15 cm, so Valve I opens first). Since the process is isothermal, the average kinetic energy and thus the average molecular momentum (which depends only on temperature) remains constant. The increase in pressure during compression is entirely due to the increased frequency of collisions per unit wall area.