The pressure of an ideal gas undergoing isothermal change is increased by 10%. The volume of the gas must decrease by about

For an ideal gas undergoing an isothermal change, the temperature remains constant. According to Boyle's Law, the pressure (P) and volume (V) of an ideal gas are inversely proportional, meaning the product PV is constant. If the initial pressure is P1 and the initial volume is V1, then P1V1 = P2V2. When the pressure is increased by 10%, the new pressure P2 becomes 1.10P1. Substituting this into the equation gives P1V1 = (1.10P1)V2, which simplifies to V2 = V1 / 1.10. Calculating this value, V2 ≈ 0.909V1. The percentage decrease in volume is calculated as ((V1 - V2) / V1) × 100, which is ((1 - 0.909) / 1) × 100 = 9.09%. Therefore, the volume must decrease by approximately 9% [1].

Sources

1. [1] https://www.sciencedirect.com/topics/engineering/ideal-gas-equation