A vertical cylinder is divided into 2 equal parts by a heavy insulating piston of mass m. The top contains Nitrogen at temperature T 1 and pressure P 1 . The bottom part has oxygen at a temperatur

Question

A vertical cylinder is divided into 2 equal parts by a heavy insulating piston of mass m. The top contains Nitrogen at temperature $T_{1}$ and pressure $P_{1}$ . The bottom part has oxygen at a temperature $2 T_{1}$ . The cylinder is turned upside down. To keep the piston in the middle, oxygen must be cooled to $\frac{T _{1}}{3}$ . Temperature of nitrogen remains at $T_{1}$ . What is the initial pressure of oxygen.

TestHub · Accepted Answer

Initially (N2 on top): P O 2 ​ ​ = P 1 ​ + A m g ​ . After inversion: P 1 ​ = P O 2 ​ ′ ​ + A m g ​ and T 1 ​ /3 P O 2 ​ ′ ​ ​ = 2 T 1 ​ P O 2 ​ ​ ​ ⇒ P O 2 ​ ′ ​ = 6 P O 2 ​ ​ ​ . Solving: P 1 ​ = 6 P 1 ​ + m g / A ​ + A m g ​ ⇒ P 1 ​ = 5 7 ​ A m g ​ and P O 2 ​ ​ = 5 12 ​ A m g ​ = 7 12 ​ P 1 ​ .

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