Final answer:
The assumption for Charles' law is that pressure and the amount of gas remain constant, whereas for Gay-Lussac's law, it is that volume and the amount of gas remain constant. Both laws assume a direct relationship between temperature and either volume or pressure, respectively, when all other variables remain unchanged.
Step-by-step explanation:
The assumption regarding Charles' and Gay-Lussac's law is that for Charles' law, the pressure and the amount of gas are constant, while the volume of a gas is directly proportional to its absolute temperature. Conversely, Gay-Lussac's law assumes that the volume and amount of gas are constant, while the pressure of a gas varies directly with the absolute temperature. The key concept here is the direct proportionality of temperature with another variable, under the condition that all other variables remain unchanged. Charles's law can be stated mathematically as V = const. × T, where V represents volume and T represents temperature in kelvins. In Gay-Lussac's law, a rigid container is used to ensure that volume remains constant, thereby only observing the relationship between pressure and temperature. Both of these laws convey the impact of changes in temperature on the behavior of gases, based on kinetic theory and the nature of gases under different conditions.