To solve this problem, we can use Boyle's Law, which states that the pressure and volume of a gas are inversely proportional when the temperature remains constant.
Boyle's Law can be expressed as: P1 * V1 = P2 * V2
Where: P1 and P2 are the initial and final pressures, respectively V1 and V2 are the initial and final volumes, respectively
Let's substitute the given values into the equation and solve for V2:
P1 = 3000 N/m^2 V1 = 250 cm^3 P2 = 100 mm Hg = 100/760 * 11325 N/m^2 (converting mm Hg to N/m^2) ≈ 1490.13 N/m^2
Plugging in these values:
3000 N/m^2 * 250 cm^3 = 1490.13 N/m^2 * V2
Simplifying the equation:
V2 = (3000 N/m^2 * 250 cm^3) / (1490.13 N/m^2) V2 ≈ 504.02 cm^3
Therefore, the volume of the gas will be approximately 504.02 cm^3 when the pressure is changed to 100 mm Hg at the same temperature.