Solar radiation of 15,000 kcal/m²/yr reaches a meadow. Producers are 20% efficient and supply a net primary productivity of 60,000 cal/m² over a year. What is the efficiency of pho... Solar radiation of 15,000 kcal/m²/yr reaches a meadow. Producers are 20% efficient and supply a net primary productivity of 60,000 cal/m² over a year. What is the efficiency of photosynthesis in this region?
Understand the Problem
The question is asking for the efficiency of photosynthesis in a meadow given specific solar radiation and productivity values. To solve it, we need to calculate the actual productivity based on the efficiency and compare it with the provided net primary productivity.
Answer
The efficiency of photosynthesis is $2\%$.
Answer for screen readers
The efficiency of photosynthesis in this region is $2%$.
Steps to Solve
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Understanding the variables
We have the following values:
- Solar radiation: $15,000 , \text{kcal/m}^2/\text{yr}$
- The efficiency of producers: $20%$ or $0.20$
- Net primary productivity (NPP): $60,000 , \text{cal/m}^2$
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Convert solar radiation to cal/m²
We need to convert solar radiation from kcal to cal:
$$ 15,000 , \text{kcal/m}^2 = 15,000 \times 1,000 , \text{cal/m}^2 = 15,000,000 , \text{cal/m}^2 $$ -
Calculate the theoretical maximum productivity
Using the efficiency formula, we can find the maximum productivity:
$$ \text{Maximum Productivity} = \text{Solar Radiation} \times \text{Efficiency} $$
Substituting in the values:
$$ \text{Maximum Productivity} = 15,000,000 , \text{cal/m}^2 \times 0.20 = 3,000,000 , \text{cal/m}^2 $$ -
Calculate the efficiency of photosynthesis
Efficiency of photosynthesis can be determined by the net primary productivity divided by the maximum productivity:
$$ \text{Efficiency} = \frac{\text{Net Primary Productivity}}{\text{Maximum Productivity}} $$
Substituting in values:
$$ \text{Efficiency} = \frac{60,000 , \text{cal/m}^2}{3,000,000 , \text{cal/m}^2} $$ -
Perform the calculation
Now we calculate the efficiency:
$$ \text{Efficiency} = \frac{60,000}{3,000,000} = 0.02 $$
Converting to percentage:
$$ \text{Efficiency} = 0.02 \times 100% = 2% $$
The efficiency of photosynthesis in this region is $2%$.
More Information
In this context, the efficiency of photosynthesis is relatively low compared to typical values seen in different ecosystems, which can range from 1% to 5% or more depending on various environmental conditions.
Tips
- Not converting units: Forgetting to convert kcal to cal or ignoring unit conversions can lead to incorrect calculations. Always check units before performing calculations.
- Misunderstanding efficiency calculations: It's important to distinguish between actual productivity and maximum potential productivity when calculating efficiency.
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