A cylinder with a safety valve contains oxygen at a temperature of 20 degrees Celsius under a pressure of 110 kPa.

| September 9, 2021 | education

A cylinder with a safety valve contains oxygen at a temperature of 20 degrees Celsius under a pressure of 110 kPa. When the cylinder is heated to 60 degrees, oxygen weighing 1.8 kg is released through the valve. Find the volume of the balloon.

Data: T1 (initial absolute oxygen temperature) = 293 K; P (pressure in the indicated cylinder) = 110 kPa = 11 * 104 Pa; T1 (initial absolute oxygen temperature after heating) = 333 K; Δm (mass of released oxygen) = 1.8 kg.

Constants: R (universal gas constant) = 8.31 J / (K * mol)); MO2 (molar mass) = 0.032 kg / mol.

1) The initial mass of oxygen: P * Vb = mn * R * Tn / MO2 and P * Vb = (mn – Δm) * R * Tk / MO2, whence we express: P * Vb * MO2 / R = 1 / (mn * Tn) = 1 / ((mn – Δm) * Tc).

(mn – Δm) * Tc = mn * Tn.

(mn – 1.8) * 333 = mn * 293.

333mn – 293mn = 599.4.

mn = 599.4 / 40 = 14.985 kg.

2) The volume of the indicated cylinder: Vb = mn * R * Tn / (P * MO2) = 14.985 * 8.31 * 293 / (11 * 104 * 0.032) = 10.365 m3 ≈ 10.4 m3.

Answer: The volume of the indicated cylinder is 10.4 m3.



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