A lake has a volume of 2 × 10⁶ L and the dissolved oxygen concentration is 9 mg L⁻¹. A sudden heatwave raises the temperature by 5 °C, causing the dissolved oxygen to drop by 15 %. If a fish consumes 0.3 g of oxygen per hour, how many fish can survive in the lake for 5 days before the oxygen is completely depleted? Assume no other sources or sinks of oxygen.

Step-by-step solution

1. Step 1: Calculate total initial dissolved oxygen: $9,\text{mg/L}\times 2\times 10^6,\text{L}=18\times 10^6,\text{mg}=18,\text{kg}$.
2. Step 2: Apply 15 % drop due to heatwave: $18,\text{kg}\times 0.85=15.3,\text{kg}$ remaining.
3. Step 3: Convert remaining oxygen to grams: $15.3,\text{kg}=15,300,\text{g}$.
4. Step 4: Calculate daily consumption per fish: $0.3,\text{g/h}\times 24,\text{h}=7.2,\text{g/day}$.
5. Step 5: Compute total consumption by one fish over 5 days: $7.2,\text{g/day}\times 5=36,\text{g}$.
6. Step 6: Determine number of fish that can be supported: $\frac{15,300,\text{g}}{36,\text{g}}=425$ fish.
7. Step 7: Round to whole number (no partial fish) and report the answer.

Concept tested: Oxygen availability and fish survival

Published 10 October 2026 · How this solution was prepared and checked