2.122 A cylinder has a thick piston initially held by a pin, as shown in Fig. P.

Question

2.122 A cylinder has a thick piston initially held by a pin, as shown in Fig. P.2.122. The cylinder contains carbon dioxide at 200 kPa and ambient temperature of 290 K. The metal piston has a density of 8000 kg/m^3 and the atmospheric pressure is 101 kPa. The pin is now removed, allowing the piston to move, and after a while the gas returns to ambient temperature. Is the piston against the stops?

Explanation / Answer

Solution: Force balance on piston determines equilibrium float pressure. Piston mp = Ap × l × ? ?piston = 8000 kg/m3 Pext on CO2 = P0 + mpgAp = 101 + Ap × 0.1 × 9.807 × 8000Ap × 1000 = 108.8 kPa Pin released, as P1 > Pext piston moves up, T2 = To & if piston at stops, then V2 = V1 × ?2/?1 = V1 × 150 / 100 Ideal gas with T2 = T1 then gives ? P2 = P1 × V1 / V2 = 200 × 100150 = 133 kPa > Pext ? piston is at stops, and P2 = 133 kPa

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