The sun supplies energy at a rate of about 1.0 kilowatt per...

The sun supplies energy at a rate of about $1.0$ kilowatt per square meter of surface area ( 1 watt $=1 \mathrm{~J} / \mathrm{s}$ ). The plants in an agricultural field produce the equivalent of $20 . \mathrm{kg}$ sucrose $\left(\mathrm{C}_{12} \mathrm{H}_{22} \mathrm{O}_{11}\right)$ per hour per hectare ( $1 \mathrm{ha}=10,000 \mathrm{~m}^{2}$ ). Assuming that sucrose is produced by the reaction $12 \mathrm{CO}_{2}(g)+11 \mathrm{H}_{2} \mathrm{O}(l) \longrightarrow \mathrm{C}_{12} \mathrm{H}_{22} \mathrm{O}_{11}(s)+12 \mathrm{O}_{2}(g)$ $\Delta H=5640 \mathrm{~kJ}$ calculate the percentage of sunlight used to produce the sucrosethat is, determine the efficiency of photosynthesis.

The sun supplies energy at a rate of about $1.0$ kilowatt per square meter of surface area ( 1 watt $=1 \mathrm{~J} / \mathrm{s}$ ). The plants in an agricultural field produce the equivalent of $20 . \mathrm{kg}$ sucrose $\left(\mathrm{C}_{12} \mathrm{H}_{22} \mathrm{O}_{11}\right)$ per hour per hectare ( $1 \mathrm{ha}=10,000 \mathrm{~m}^{2}$ ). Assuming that sucrose is produced by the reaction
$12 \mathrm{CO}_{2}(g)+11 \mathrm{H}_{2} \mathrm{O}(l) \longrightarrow \mathrm{C}_{12} \mathrm{H}_{22} \mathrm{O}_{11}(s)+12 \mathrm{O}_{2}(g)$
$\Delta H=5640 \mathrm{~kJ}$
calculate the percentage of sunlight used to produce the sucrosethat is, determine the efficiency of photosynthesis.

Key Concepts

Solar Energy Flux

Solar energy flux refers to the amount of solar power received per unit area, typically measured in watts per square meter. This concept is essential in understanding the total energy input available from the sun for various Earth systems, including photosynthetic processes in plants.

Photosynthesis Process

Photosynthesis is the biochemical process by which plants, algae, and some bacteria convert light energy from the sun into chemical energy, stored in the bonds of sugars. This process involves the absorption of solar radiation and its conversion into forms of energy that can be used to drive the synthesis of complex organic molecules.

Reaction Enthalpy

Reaction enthalpy (?H) is a measure of the energy change that occurs during a chemical reaction, often expressed in kilojoules per mole. In the context of photosynthesis, it quantifies the energy stored in the chemical bonds of the sugars produced, providing a basis for comparing the chemical energy output with the solar energy input.

Energy Conversion Efficiency

Energy conversion efficiency in photosynthesis is determined by comparing the chemical energy stored in the synthesized sugars to the total solar energy received. This efficiency calculation assesses how effectively plants convert light energy into chemical energy, which is critical for understanding and improving crop yields and bioenergy production.

Unit Conversions

Unit conversions are necessary for aligning measurements of energy, time, and area. Converting units such as kilowatts to joules per second, area measurements like hectares to square meters, and time intervals enables the precise computation of energy inputs and outputs, facilitating accurate efficiency calculations.

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