What mass of air will leave a room with a volume of 100 m³ when the temperature rises from 7 ° C to 17 ° C?

| August 8, 2021 | education

What mass of air will leave a room with a volume of 100 m³ when the temperature rises from 7 ° C to 17 ° C? Pressure 100 kPa. For air, the molar mass is 29 g / mol.

We will proceed from the Mendeleev-Clapeyron equation:
PV = mRT / M, where P is pressure, R is universal gas constant, m is gas mass, T is temperature, M is molar mass.
Let us find from this equation the expression for the mass m:
m = MPV / RT.
T1 = 273.16 + 7 = 280.16 K;
T1 = 273.16 + 17 = 290.16 K.
For the difference in masses at different temperatures, the following expression will be valid:
m1 –m2 = MPV / (R * T1) – MPV / (R * T2) = (MPV / R) (1 / T1-1 / T2) =
= ((0.029 mol / kg * 10000 Pa * 100 m ^ 3) / (8.3144 J / mol * K)) * (1 / 280.15 K – 1 / 290.16 K) = 4.28 kg.
Answer: 4.28 kg.



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