Answer:
The change in the density of the air inside the syringe is due to the change in temperature. When the air inside the syringe is cooled, it contracts, causing the density to increase.
The principle that explains this phenomenon is known as Charles's Law, which states that the volume of a gas is directly proportional to its temperature, provided the pressure and the amount of gas remain constant.
In this case, the density of the air doubles when the syringe is cooled, implying that the volume of the air inside the syringe is halved. Therefore, if the density of the air when cooled is 2.4 kg/m³, the density of the air at room temperature (when the volume is twice as much) would have been half of this value, or 1.2 kg/m³.
So, the density of the air at room temperature was 1.2 kg/m³.