Final answer:
Doubling the length of the cylinder does not change the density of the air, which would remain at 1.4 kg/m3. However, if the radius of the cylinder is halved, the air density would quadruple to 5.6 kg/m3, since the volume decreases to a quarter.
Step-by-step explanation:
Density of Air in a Cylinder
The student asks two questions about changes in the density of air enclosed in a cylinder under different conditions. For both scenarios, it's important to understand that the density of a gas is directly proportional to its pressure when the temperature is held constant (Gay-Lussac's Law).
Part A: Doubling the Cylinder's Length
If the length of the cylinder is doubled while the radius remains unchanged, the volume of the cylinder would double.
However, since the mass of air remains the same and density is mass per unit volume (density = mass/volume), the density of the air would not change.
It remains at 1.4 kg/m3.
Part B: Halving the Cylinder's Radius
If the radius of the cylinder is halved and the length remains unchanged, the volume of the cylinder decreases to one quarter of its original volume (since the volume of a cylinder is proportional to the square of the radius).
Again, assuming the mass of the air inside the cylinder is constant,
the density of the air would quadruple to 5.6 kg/m3.