A space habitat’s life support system must maintain oxygen, recycling 85% of it daily. If the system starts with 1,000 kg of oxygen and the crew consumes 60 kg per day, how much oxygen remains after 5 days? - NBX Soluciones

Understanding the Context

The Daily Oxygen Cycle in Space

Daily oxygen consumption in space typically includes not only breathing but also metabolic byproducts that the system must counteract. In this scenario:

• Initial oxygen supply: 1,000 kg
  
• Daily consumption: 60 kg
  
• Recovery rate: 85% of consumed oxygen is recycled each day

Key Insights

This means that 15% of the oxygen used each day must be replenished through onboard generators like electrochemical oxygen production or CO₂ reduction.

Calculating Oxygen Remaining After 5 Days

Let’s step through each day to model the oxygen balance:

• Day 0 (start): 1,000 kg
  
• Daily consumption: 60 kg
  
• Daily recovery: 85% of 60 kg = 51 kg recycled oxygen
  
• Net oxygen loss per day: 60 kg – 51 kg = 9 kg

Final Thoughts

However, because recycled oxygen reduces the amount needing generation, the net loss changes daily:

• The system recovers part of the consumed oxygen, but not all — only 85%. The remaining 15% must be supplied externally (or generated from other processes), but here we assume generation meets the deficit except for losses inherent in recycling inefficiencies.

But in standard modeling for closed life support systems, the daily oxygen balance working only on the consumed amount (with 85% recovery sufficient to offset loss) simplifies to:

Each day, the system must compensate for 15% of the consumed oxygen (i.e., 60 × 0.15 = 9 kg net loss), but recycling supports the remainder.

Thus, the total oxygen consumed over 5 days:
60 kg/day × 5 days = 300 kg

But due to 85% recycling efficiency, the system only needs to generate 15% of that — the non-recoverable portion:
300 kg × (15%) = 45 kg of new oxygen generated (or produced)