Final answer:
The piston in the gas cylinder will move up when the temperature increases from 273 K to 303 K and the pressure increases from 1.00 atm to 1.20 atm because the pressure increase is less than it would be if the volume remained constant, indicating expansion.
Step-by-step explanation:
The student's question involves understanding how changes in temperature and pressure affect the volume of a gas within a cylinder with a piston. Given that the initial conditions are a volume of 30.0 mL, pressure of 1.00 atm, and a temperature of 273 K, and upon heating, the temperature rises to 303K and pressure increases to 1.20 atm, we need to determine the direction of piston movement.
According to Gay-Lussac's law, for a given mass of gas at constant volume, the pressure of the gas is directly proportional to its absolute temperature. Thus, when the temperature increases from 273 K to 303 K, if the volume were to stay constant, the pressure would indeed increase as observed. However, since the cylinder has a piston and the pressure increase is less than what would be expected (a direct proportion would result in a pressure of approximately 1.11 atm), it indicates that the volume must have increased to accommodate the extra pressure. Therefore, the piston will move up to allow the gas to expand as the temperature rises.