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To maintain a constant temperature in the context of Boyle's Law, an isolated system is necessary. Boyle's Law states that for a given amount of gas at constant temperature, the pressure of the gas is inversely proportional to its volume. In order for this relationship to hold true, the system must not exchange heat with the environment, meaning it must be insulated from external influences.
An isolated system prevents heat transfer, ensuring that the internal energy of the gas remains constant. This stability is crucial because any heat exchange could result in temperature changes, which would violate the premise of Boyle's Law. By keeping the system isolated, the gas can be allowed to expand or compress under varying pressures without losing or gaining heat, thereby enabling the pressure-volume relationship described by Boyle's Law to be accurately observed and maintained.