Final answer:
The pressure of an ideal gas increases when it's compressed isothermally due to Boyle's Law, which states that pressure is inversely proportional to volume at constant temperature.
Step-by-step explanation:
When an ideal gas in a cylinder is compressed isothermally, which means at a constant temperature, the pressure of the gas increases because of Boyle's Law. According to Boyle's Law, for a given mass at a constant temperature, the pressure of a gas is inversely proportional to its volume. This means that if you decrease the volume of the gas (by compressing it), the pressure must increase to maintain the same temperature.