Mass of escaped air from a cylinder

[moenste]

Homework Statement

A cylinder containing 19 kg of comperessed air at pressure 9.5 times that of the atmosphere is kept in a store at 7 °C. When it is moved to a workshop where the temperature is 27 °C a safety valve on the cylinder operates, releasing some of the air. If the valve allows air to escape when the its pressure exceeds 10 times that of the atmosphere, calculate the mass of air that escapes.

Answer: 0.33 kg

2. The attempt at a solution
Density of air = 1.293 kg m^-3

Mass = Volume * Density
Volume_Store = 19 / 1.293 = 14.7 m³

V_Workshop = (p_Store * V_Store * T_Workshop) / (T_Store * p_Workshop) = (9.5 p₀ * 14.7 * 300.15) / (280.15 * 10 p₀) = 14.95 m³

Mass_Workshop = 14.95 * 1.293 = 19.33 kg

19.33 - 19 = 0.33 kg... fits the answer but why the mass is 19.33 after the escape? What's wrong?

 

[SteamKing]

Homework Statement

A cylinder containing 19 kg of comperessed air at pressure 9.5 times that of the atmosphere is kept in a store at 7 °C. When it is moved to a workshop where the temperature is 27 °C a safety valve on the cylinder operates, releasing some of the air. If the valve allows air to escape when the its pressure exceeds 10 times that of the atmosphere, calculate the mass of air that escapes.

Answer: 0.33 kg

2. The attempt at a solution
Density of air = 1.293 kg m^-3

This appears to be the density of air at standard temperature and pressure. It's not clear how this relates to the problem.

When air is compressed to 9.5 times atmospheric pressure, its density increases.

Mass = Volume * Density
Volume_Store = 19 / 1.293 = 14.7 m³

The air is compressed and kept in a cylinder in a store, or storage room. It's not clear why you are calculating the volume of 19 kg of air at standard pressure and temperature. (See above)

V_Workshop = (p_Store * V_Store * T_Workshop) / (T_Store * p_Workshop) = (9.5 p₀ * 14.7 * 300.15) / (280.15 * 10 p₀) = 14.95 m³

Mass_Workshop = 14.95 * 1.293 = 19.33 kg

19.33 - 19 = 0.33 kg... fits the answer but why the mass is 19.33 after the escape? What's wrong?

Your approach to solving this problem is puzzling.

 

[SteamKing]

Homework Statement

A cylinder containing 19 kg of comperessed air at pressure 9.5 times that of the atmosphere is kept in a store at 7 °C. When it is moved to a workshop where the temperature is 27 °C a safety valve on the cylinder operates, releasing some of the air. If the valve allows air to escape when the its pressure exceeds 10 times that of the atmosphere, calculate the mass of air that escapes.

Answer: 0.33 kg

2. The attempt at a solution
Density of air = 1.293 kg m^-3

Mass = Volume * Density
Volume_Store = 19 / 1.293 = 14.7 m³

V_Workshop = (p_Store * V_Store * T_Workshop) / (T_Store * p_Workshop) = (9.5 p₀ * 14.7 * 300.15) / (280.15 * 10 p₀) = 14.95 m³

Mass_Workshop = 14.95 * 1.293 = 19.33 kg

19.33 - 19 = 0.33 kg... fits the answer but why the mass is 19.33 after the escape? What's wrong?

As far as the mass of air escaping from the cylinder is concerned, the pressure inside the workshop is immaterial, unless you assume the workshop is airtight, which few are.

The ambient temperature difference between the store room and the workshop is what is causing the air to want to expand inside the cylinder.

Concentrate on what is happening inside the compressed air cylinder. Use the perfect gas law, PV = nRT, to find out the details.