Final answer:
The statement that doubling both the pressure and temperature of a gas quadruples the volume is false. In reality, according to the combined gas laws, doubling both would keep the volume unchanged. The volume of a gas is directly proportional to temperature per Charles's law, and inversely proportional to pressure per Boyle's law, but not in the way the false statement describes.
Step-by-step explanation:
The statement 'if the pressure of a gas sample is doubled and its temperature is also doubled then the volume will be quadrupled' is false according to the combined gas law, which is derived from Boyle's law, Charles's law, and Gay-Lussac's law. These laws describe the relationship between pressure, volume, and temperature of a given amount of gas when one of the variables is kept constant.
According to Charles's law, when the temperature of a gas sample is doubled at constant pressure, the volume also doubles. Boyle's law states that at constant temperature, the volume of a gas is inversely proportional to its pressure. Therefore, if we double the pressure, the volume would halve, not quadruple.
Based on Gay-Lussac's law, which states that the pressure of a gas is directly proportional to its temperature at constant volume, simply doubling the pressure while also doubling the temperature would keep the volume constant, not quadruple it. The correct result of doubling both the pressure and temperature of a gas sample, holding the amount of gas constant, would be that the volume remains unchanged, not quadrupled.