Final answer:
The new absolute pressure of an ideal gas when the volume changes to 0.9 m^3 at constant temperature can be found using Boyle's Law. The calculation yields approximately 222.22 kPa, which is not present among the provided options, hinting at a potential error.
Step-by-step explanation:
The question involves the application of the ideal gas law, which is a fundamental concept in chemistry and physics. Since the temperature remains constant, Boyle's Law, which is a special case of the ideal gas law, can be applied to solve for the new pressure.
Boyle's Law states that the product of the pressure and volume of a fixed amount of an ideal gas, at a constant temperature, is constant. Mathematically, P1V1 = P2V2, where P1 and V1 represent the initial pressure and volume, and P2 and V2 represent the final pressure and volume. Substituting the given values:
P1 = 500 kPa
V1 = 0.4 m3
V2 = 0.9 m3
To find the final pressure (P2), we rearrange the equation to: P2 = (P1V1) / V2 = (500 kPa * 0.4 m3) / 0.9 m3 = 222.22 kPa (approximately).
Therefore, the new absolute pressure when the volume changes to 0.9 m3 would be 222.22 kPa. However, this value is not provided in any of the multiple-choice options given in the question, suggesting there might be an error in the options provided or a misunderstanding in the calculation.