Final answer:
The gas decreased in volume by 0.67 cm³. The uncertainty in this volume is 0.003 cm³.
Step-by-step explanation:
To find the decrease in volume of the gas, we can calculate the initial volume and subtract the final volume. The initial volume can be calculated using the formula for the volume of a cylinder, V = πr²h, where r is the radius and h is the height. With a circular cross-section of 7.500 cm diameter, the radius is half of that, which is 3.750 cm. The height is given as 3.250 cm. Plugging these values into the formula, we get:
Vinitial = π(3.750 cm)²(3.250 cm) = 144.27 cm³
The final volume is given as 143.6 cm³. To find the decrease in volume, we subtract the final volume from the initial volume:
Decrease in volume = Vinitial - Vfinal = 144.27 cm³ - 143.6 cm³ = 0.67 cm³
Therefore, the gas decreased in volume by 0.67 cm³.
The uncertainty in this volume can be found by adding the uncertainties of the initial and final volumes:
Uncertainty = Uncertainty of Vinitial + Uncertainty of Vfinal = 0.002 cm + 0.001 cm = 0.003 cm
Therefore, the uncertainty in the volume is 0.003 cm³.