# Thermodynamic Ideal Gas Law. Laws of Thermodynamics

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## Introduction

We can use the ideal gas law to compute the mass of air inside your room.

To do so, find the volume of 1 mol of any gas, and then use this along with the volume of your room to compute n, the number of moles. Knowing the relationship between n and the mass of a sample, we can find our final result.

The following assumptions are in order:

1. The gas behaves like an ideal gas.

2. P = 1 atm = 1.013 x 105 N/m2, which is the average, standard atmospheric pressure on Earth (not in the mountains or inside the ocean).

3. T = 273 K, which is 20oC or 68oF.

## Step One

From the ideal gas equation we found in part one, solve for V to find the volume of a gas.

1. V = nRT/P

Thus V = (1.00 mol) (8.315 J/mol.K ) (293 K) / (1.013 x 105 N/m2) = 0.024 m3. This is the same as 24 L (liters).

## Step Two

Estimate the volume of your room. Suppose your bedroom is 10 by 11 feet. In metric units of meters, this is 3.1 m by 3.4 m. Let’s assume the height of your bedroom is 2.5 m (8 feet). The volume is then length x width x height = 3.1 m * 3.4 m * 2.5 m. To find the number of moles, divide the volume of your room by the volume of 1 mol of air.

1. n = (3.1m) (3.4 m) (2.5 m) / 0.024 m3 = 1098 mol

## Step Three

From the previous article on Avogadro’s number, we learned how to compute the molecular mass of a sample. For air, 1 mol = 0.029kg. Using M = n * m, where M is the mass of the sample and m is the molecular mass, we have

1. M = 1098 mol * 0.029 kg ≈ 32 kg

So, for the dimensions we used, the mass of air in the room is 32 kg or about 71 lbs!

In part three, we will learn how to derive Boyle’s, Charles’, and Gay-Lussac’s Laws from the ideal gas law equation.

Physics for Scientists and Engineers by Douglas Giancoli

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