By how much does the density of air increase when it is compressed to half its volume?
Solution 13RQ Step 1 In this problem, we should find out the increase in density when air is compressed to half of its exact volume. Density, = mass, m / volume, v = m/v In this problem, consider “m” kg is the mass of the air. “v” is the volume of air. When it is compressed to half of its original volume, the new volume, v ’ = v/2 The mass remains same and it is “m” kg since there is no change for the mass when air is compressed. So, the new density would be, ‘ = m / v ’ We know that, the new volume, v ‘ = v/2 ‘ = m / (v/2) = 2m/v But we know that, = m/v So, changing the new density equation, ‘ = 2 Conclusion The density of air will be doubled when the volume of air is halved.