Biosphere II is an experimental structure that was designed to be an isolated ecological space, intended for conducting experiments on managed, self-contained ecosystems. Biosphere II (so named because the earth itself was regarded as the first “Biosphere”) is covered by a rigid dome. One of the engineering challenges in designing Biosphere II stemmed from temperature fluctuations of the air inside the dome. To prevent this from resulting in pressure fluctuations that could rupture the dome, flexible diaphragms called “lungs” were built into the structure. These “lungs” expanded and contracted so that changes in air volume could be accommodated while pressure was maintained constant.

Transcribed Image Text:

For the purposes of this problem, assume that air is an ideal gas, with heat capacity equal to a weighted average of the ideal gas heat capacities of nitrogen and oxygen: Cpair= 0.79CPN₂ + 0.21CP0₂ A. Suppose the volume of air contained within the Biosphere II was 125,000 m³, there were no lungs, and the pressure of the air was 1 atmosphere when the temperature was 70°F. What air pres- sure would occur at a temperature of 0°F? B. Repeat part A, calculating the pressure resulting if the temperature were 105°F rather than 0°F. For parts C-E assume the Biosphere II has lungs, and that the total volume of air inside the dome is 125,000 m³ when the lungs are fully collapsed. C. If the lungs are designed to maintain a constant pressure of 1 atm at all temperatures between 0 and 105°F, what volume of air must the lungs hold when fully expanded? D. If the temperature inside the dome increases from 0°F to 105°F at a constant P = 1 atm, what change in internal energy does the air undergo? E. If the temperature inside the dome increases from 0°F to 105°F at a constant P = 1 atm, and the lungs are sized as calculated in part C, give your best estimate of the work done by the lungs on the surroundings.