A ruptured pressure relief valve on a large R-744 (CO₂) system in a machinery room discharges into the atmosphere. The relief capacity is 12 kg/min and the room volume is 80 m³. If the emergency ventilation system fails, how quickly could the CO₂ concentration reach a hazardous level (e.g., 5% by volume, which causes rapid breathing and symptoms)? (Assume uniform mixing, CO₂ density at STP = 1.98 kg/m³)

Question: A ruptured pressure relief valve on a large R-744 (CO₂) system in a machinery room discharges into the atmosphere. The relief capacity is 12 kg/min and the room volume is 80 m³. If the emergency ventilation system fails, how quickly could the CO₂ concentration reach a hazardous level (e.g., 5% by volume, which causes rapid breathing and symptoms)? (Assume uniform mixing, CO₂ density at STP = 1.98 kg/m³)

Answer options:

• Less than 30 seconds ✅ Approximately 1 minute
• Approximately 5 minutes
• Over 10 minutes

Correct answer: Approximately 1 minute

Explanation: Target CO₂ volume = 80 m³ * 0.05 = 4 m³. Mass of CO₂ at 5% = 4 m³ * 1.98 kg/m³ = 7.92 kg. Time to reach hazardous level = 7.92 kg / (12 kg/min) ≈ 0.66 minutes, or approximately 40 seconds. This demonstrates rapid onset of oxygen displacement and health hazards. This highlights the dangers of CO2.