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What is the mass of air in a room measuring 5m X 10m X 10m?

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mahmuda092569 | Student | (Level 2) Honors

Posted December 20, 2009 at 12:50 AM via web

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What is the mass of air in a room measuring 5m X 10m X 10m?

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pohnpei397 | College Teacher | (Level 3) Distinguished Educator

Posted December 20, 2009 at 1:19 AM (Answer #1)

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In order to find the answer to this question, you need to know the following equation:

m = dv

Where m is mass, d is density, and v is volume.  In this case, you are looking for mass, you have volume.  So you need to know the density of air.

As is turns out, the approximate density of air at sea level (and at 20 C) is 1.2 kilograms per cubic meter.

First, we must find the the volume of the room, which you get by multiplying its dimensions.  That tells us that the room is 500 m^3.  Now we can plug in the numbers

m = 500*1.2

Which gives us

m = 600 kilograms.

So, the air in your room weighs approximately (depending on how wet it is, what temperature, etc) 600 kg.

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neela | High School Teacher | (Level 3) Valedictorian

Posted December 20, 2009 at 2:41 AM (Answer #2)

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The mass of the air at the room is obtained as th product of its volume and its density. The volume of the air is clearly  the volume of the room equal to the product the length, breadth and height of the room=5m*10m*10m = 500 cubic meter = 500 M^3

So, the air mass in the room is = 500m^3 * ro., where ro is the density of the air.

Again, the density ro of the air for any temperature and pressure is given by, ro = P/(R*T)  where, P is the atmospheric air pressure , R is the gas constant and T is the temperature in kelvin scale. For T = 20 deg C T = 273.15 +20 =293.15 and T = 101.325 and R = 0.28705 J/kg. So ro = 1.2041 kg/m^3

So the mass of the air in the room is 500*1.20412 =602.06 kg

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