A Mars habitat module maintains pressure via a feedback system. The oxygen generator adds 4.5% of current pressure each hour, while leaks reduce it by 1.2% per hour. Starting at 100 kPa, what is the pressure after 5 hours?

Sun, 03 May 2026 18:44:31 +0000

A Mars habitat module maintains pressure via a feedback system. The oxygen generator adds 4.5% of current pressure each hour, while leaks reduce it by 1.2% per hour. Starting at 100 kPa, this dynamic balance shapes long-term habitat viability—explaining why accurate tracking of atmospheric stability matters for space exploration and advanced life support research. In light of growing interest in sustainable off-world living and climate-controlled environments, this system exemplifies precision engineering inspired by both terrestrial and extraterrestrial needs. Why A Mars habitat module maintains pressure via a feedback system. The oxygen generator adds 4.5% of current pressure each hour, while leaks reduce it by 1.2% per hour. Starting at 100 kPa, this dynamic balance shapes long-term habitat viability—explaining why accurate tracking of atmospheric stability matters for space exploration and advanced life support research. In light of growing interest in sustainable off-world living and climate-controlled environments, this system exemplifies precision engineering inspired by both terrestrial and extraterrestrial needs. Calculating the pressure after five hours reveals how feedback mechanisms maintain stability. Each hour, the pressure rises by 4.5% of the current level, but simultaneous losses due to leaks reduce it by 1.2%. The net gain per hour is therefore 3.3% of the initial value—though applying this incrementally respects the compounding effect of each hour’s balance. Starting from 100 kPa: - After Hour 1: 100 × 1.033 = 103.3 kPa
- After Hour 2: 103.3 × 1.033 ≈ 106.7 kPa
- After Hour 3: 106.7 × 1.033 ≈ 110.1 kPa
- After Hour 4: 110.1 × 1.033 ≈ 113.4 kPa
- After Hour 5: 113.4 × 1.033 ≈ 116.7 kPa