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A container of gas with temperature $300\text{ K}$ is placed on top of a cold reservoir that is kept at $200\text{ K}$. The movable lid of the container gradually moves downward as the gas cools and its pressure decreases.

Which of the following statements below is true about the entropy of the gas and why?


The entropy of the gas increases. Entropy always increases with any thermodynamic process.


The entropy of the gas remains the same. Even though the gas cools, it has less volume to occupy, leading to constant entropy.


The entropy of the gas would decrease, but only if the gas cools to less than $200\text{ K}$.


The entropy of the gas decreases. The gas is not a closed system because it is transferring heat to the cold reservoir.

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