Numerical Problems/ICSE/Class 10
Created by Titas Mallick
Biology Teacher • M.Sc. Botany • B.Ed. • CTET (CBSE) • CISCE Examiner
BioNotesBioNotesCreated by Titas Mallick
Biology Teacher • M.Sc. Botany • B.Ed. • CTET (CBSE) • CISCE Examiner
Online
Numerical Problems - Energy Flow
Understanding energy flow in an ecosystem relies primarily on two fundamental principles:
Energy Flow:
- Sunlight (e.g., 1,000,000 J) ➔ (1% Absorbed) ➔ Producers [T1] (10,000 J)
- Producers [T1] ➔ (10% Transferred, 90% Lost as Heat) ➔ Primary Consumers [T2] (1,000 J)
- Primary Consumers [T2] ➔ (10% Transferred, 90% Lost as Heat) ➔ Secondary Consumers [T3] (100 J)
- Secondary Consumers [T3] ➔ (10% Transferred, 90% Lost as Heat) ➔ Tertiary Consumers [T4] (10 J)
In a forest ecosystem, 5,000,000 Joules of solar energy falls on the green plants. Calculate the amount of energy that will be available to the secondary consumers in the food chain: Plants → Deer → Tiger.
Step 1: Calculate energy absorbed by Producers (Plants)
Step 2: Apply the 10% Law for Primary Consumers (Deer)
Step 3: Apply the 10% Law for Secondary Consumers (Tiger)
Final Answer: The tiger will receive 500 Joules of energy.
[!WARNING] Common Pitfall A very common mistake is to apply the 10% law directly to the solar energy (e.g., taking 10% of 5,000,000 J for plants). Always remember: Sun to Plant is 1%, Plant to Consumer is 10%.
A snake (tertiary consumer) in a grassland food chain has 2.5 Joules of energy available to it. The food chain is: Grass → Grasshopper → Frog → Snake
Calculate:
We must work backwards through the trophic levels, multiplying by 10 (the inverse of taking 10%) for consumer levels, and multiplying by 100 (the inverse of taking 1%) for the sun.
Step 1: Assign trophic levels and known values
Step 2: Calculate backward from Tertiary to Secondary Consumer (Frog)
Step 3: Calculate backward from Secondary to Primary Consumer (Grasshopper)
Step 4: Calculate backward from Primary Consumer to Producer (Grass)
Step 5: Calculate incident Solar Energy
Final Answers:
In an aquatic ecosystem, phytoplankton generate 80,000 J of energy. They are eaten by zooplankton, which are then eaten by small fish. How much energy is lost to the environment as heat and metabolic work during the transfer from zooplankton to small fish?
Step 1: Determine energy at Phytoplankton (Producers - T1)
Step 2: Determine energy at Zooplankton (Primary Consumers - T2)
Step 3: Determine energy at Small Fish (Secondary Consumers - T3)
Step 4: Calculate the energy lost during the T2 to T3 transfer
Final Answer: 7,200 Joules of energy is lost to the environment during this specific transfer.
If a hypothetical ecosystem starts with 1,000,000 J of solar energy, explain mathematically why food chains rarely exist beyond 4 or 5 trophic levels. Calculate the energy available for a quaternary consumer (T5).
Let's model the energy flow step-by-step:
Conclusion: By the time energy reaches the 5th trophic level, only 1 Joule remains from the original 1,000,000 Joules of sunlight (a mere 0.0001% of the original energy). This minimal amount of energy is insufficient to sustain a viable population of top predators. Organisms at this level would have to spend more energy hunting for food than they would gain from eating it. Therefore, massive energy loss at each step limits the length of food chains.
[!TIP] Conceptual Check Because energy decreases so rapidly, organisms occupying higher trophic levels usually need to consume large quantities of prey, making them highly vulnerable to habitat loss and changes in prey populations.