Final answer:
The first law of thermodynamics or the law of energy conservation is applied when plant cells convert sunlight to chemical energy through photosynthesis.
Step-by-step explanation:
The law being applied when plant cells capture the sun's energy and convert it into chemical energy is the first law of thermodynamics. This principle, also known as the law of energy conservation, states that energy can neither be created nor destroyed; it can only be transformed or transferred from one form to another. In the case of plants, they convert the electromagnetic radiation from the sun, a form of light energy, into chemical energy that is stored within organic molecules through the process of photosynthesis. This process is a prime example of energy transformation and is fundamental to life on Earth, allowing plants to store energy that can later be used by themselves and by other organisms that consume them.