You are working on a team designing a new wastewater treatment facility that intends to generate a portion of its own electricity using methane produced by bacteria breaking down compounds in the wastewater. Your team is developing a prototype pressure vessel to capture gaseous methane produced by methanogens. The apparatus is used to estimate the amount of PV work that can be generated by the bacteria into a balloon with a certain level of tensile strength. For this effort, a pressure sensor is fitted at the inlet to an expanding spherical balloon looped over a container with simulated wastewater slurry. The current balloon'sdiameterwill slowly increase as methane is produced from 1 in to 2 ft with an error in measurement of theradiusof about 2%. There are two potential pressure sensors you can use over the expected range of 0 to 50 psig. One sensor is less expensive and has an error in measurement of 5% and the other is more expensive and has an error of 0.1%. Calculate the maximum total errors in the PV work obtained with each sensor. In order tojustify purchasing the more expensive pressure sensor, you would like to reduce total errors by at least half. Is it worth the expense? Why/why not?