What is the mass of air in an auditorium with a height of 5 m, if the area is 200 m2, the temperature of the building

| September 11, 2021 | education

What is the mass of air in an auditorium with a height of 5 m, if the area is 200 m2, the temperature of the building is 17 degrees Celsius, the pressure is 750 mm of mercury, and the molar mass is 29 g / mol

To find out the mass of air in the audience in question, we use the formula: P * V = P * S * h = m * R * T / Mair, from where we express: m = P * S * h * Mair / (R * T).

Const: Мair – molar mass of air (according to the condition Мair = 29 * 10 ^ -3 kg / mol); R – universal gas constant (R = 8.31 J / (mol * K)).

Data: P – air pressure in the auditorium (P = 750 mm Hg; in the SI system P ≈ 10 ^ 5 Pa); S is the floor area of ​​the audience under consideration (S = 200 m2); h – audience height (h = 5 m); T – abs. air temperature (Т = 290.15 К (17 ºС)).

Let’s perform the calculation: m = P * S * h * Mair / (R * T) = 10 ^ 5 * 200 * 5 * 29 * 10 ^ -3 / (8.31 * 290.15) ≈ 1202.8 kg.

Answer: The mass of air in the audience under consideration is 1202.8 kg.



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