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[Thermodynamics] Density of Air

2021-09-27 16:36 作者:AoiSTZ23 0人讀過 | 我要投稿

By: Tao Steven Zheng (鄭濤)

【Problem】

The composition of air is roughly 80% nitrogen and 20% and oxygen. Calculate the density of air under normal temperature and pressure conditions (NTP).

NTP is defined as the condition when temperature is 20 degrees Celsius and the pressure is 1 atmosphere.

【Solution】

Step 1: Calculate Mass
Nitrogen and oxygen gas are diatomic, so the molar mass is

$%200.80%20%5Cleft(2%20%5Ccdot%2014.01%20%5C%2C%20%5Cfrac%7Bg%7D%7Bmol%7D%20%5Cright)%20%2B%200.20%20%5Cleft(2%20%5Ccdot%2016.00%20%5C%2C%20%5Cfrac%7Bg%7D%7Bmol%7D%20%5Cright)%20%3D%2028.80%20%5C%2C%20%5Cfrac%7Bg%7D%7Bmol%7D%20$

To calculate the mass of 1 mole of air is

$%20%5Cleft(1%20%5C%2C%20mol%20%5Cright)%20%5Cleft(28.80%20%5C%2C%20%5Cfrac%7Bg%7D%7Bmol%7D%20%5Ctimes%20%5Cfrac%7B1%20%5C%2C%20kg%7D%7B1000%20%5C%2C%20g%7D%20%5Cright)%20%3D%200.02880%20%5C%2C%20kg%20$

Thus 1 mole of air weighs 0.02880 kg.

Step 2: Calculate Volume
To calculate the volume of 1 mole of air at NTP

$P%20%3D%201%20%5C%2C%20atm%20%3D%20101325%20%5C%2C%20Pa$

$T%20%3D%20%7B20%7D%5E%7B%5Ccirc%7D%20C%20%2B%20273.15%20%3D%20293.15%20%5C%2C%20K$

$PV%20%3D%20nRT%20$

$%20(101325%20%5C%2C%20Pa)V%20%3D%20(1%20%5C%2C%20mol)%5Cleft(8.31%20%5C%2C%20%5Cfrac%7BJ%7D%7BK%5Ccdot%20mol%7D%5Cright)(293.15%20%5C%2C%20K)%20$

$V%20%3D%200.024%20%5C%2C%20m%5E3$

Step 3: Calculate Density
The density of air is simply the mass divided by the volume:

$%7B%5Crho%7D_%7Bair%7D%20%3D%20%5Cfrac%7B0.02880%20%5C%2C%20kg%7D%7B0.024%20%5C%2C%20m%5E3%7D$

$%7B%5Crho%7D_%7Bair%7D%20%3D%201.2%20%5C%2C%20%5Cfrac%7Bkg%7D%7Bm%5E3%7D$

標簽：

[Thermodynamics] Density of Air的評論 (共條)

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