A cylindrical chamber containing an ideal diatomic gas is sealed by a movable pi

Question

A cylindrical chamber containing an ideal diatomic gas is sealed by a movable piston with cross-sectional area A = 0.0015 m2. The volume of the chamber is initially V = 10-3 m3; the pressure outside the chamber constant at 105 Pa. Initially the gas pressure inside is 105 Pa and its temperature is 27°C.

A 20-kg mass placed on the piston causes the gas to undergo adiabatic compression. What is the final volume after the mass comes to rest?

(a) 4.2 × 10-4 m3
(b) 5.5 × 10-4 m3
(c) 1.2 × 10-4 m3
(d) 1.4 × 10-5 m3
(e) 8.8 × 10-5 m3

Explanation / Answer

The new Pressure on the outside is:
P2 = F/A + P1 = mg/A + P1 = (20 kg)(9.8 m/s2)/(0.0015 m2) + (105 Pa) = 130,772 Pa

P2V2 = P1V1 => V2 = (105 Pa)(103 m3)/(130,772 Pa) = 0.0827 m3

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