Final answer:
To determine the decreased gas volume when a piston compresses gas in a cylinder, one can calculate the volume change using the given measurements of the piston's diameter and stroke distance. The change in volume is found using the volume formula for a cylinder, and the uncertainty is computed by combining relative uncertainties of the measurements. The answer is 143.6 ± 0.005 cm³ for the volume change and its uncertainty.
Step-by-step explanation:
When a piston with a circular cross section moves to compress gas in a cylinder, the change in gas volume can be calculated. The diameter of the piston is given as 7.500 ± 0.002 cm. Using the formula for the volume of a cylinder, V = πr^2h, where r is the radius and h is the stroke distance, we can find the volume change. The radius is half of the diameter, and the stroke distance is given as 3.250 ± 0.001 cm.
To find the uncertainty in this volume, one would use the rule for multiplication which combines the relative uncertainties of the diameter and stroke distance. The calculation of the decreased volume in cubic centimeters is as follows: V = π · (7.500 cm / 2)^2 · 3.250 cm. Using this method, the uncertainty in the total volume can be determined by summing the relative uncertainties and applying them to the calculated volume.
The correct answer to the volume change question is 143.6 ± 0.005 cm³, which takes into account both the uncertainties in the diameter and the stroke distance of the piston.