Water droplets gathered and formed into cloud which gets heavier then does the entropy of the system decreases? If so why 2nd law of thermodynamics allowed it?
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2 Answers
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The second law of thermodynamics says that the entropy of an isolated (or closed) system left to spontaneous evolution cannot decrease with time. A cloud is not an isolated system - it interacts with the surrounding atmosphere, which in turn interacts with the wider atmosphere. So to get to an isolated system that includes the cloud we must at least include the whole atmosphere of the Earth.
But the Earth's atmosphere is not an isolated system either. It interacts with the land, the sea and the ice caps. The sea in turn is influenced by the gravity of the Moon and the Sun. And the Sun also heats the Earth and its atmosphere. So to get to an isolated system that includes the cloud, we must at least include the Earth, the Moon and the Sun.
The entropy of this whole system does not decrease over time, so the second law of thermodynamics is not broken. The entropy of individual components of this system (such as the cloud) may decrease, but this decrease will be matched by a greater increase in entropy elsewhere in the system.
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Clouds are not closed objects, butt rather a part of a dynamic atmosphere, which is far from thermodynamic equilibrium (to which the Laws of thermodynamics/statistical physics apply.) In this sense, there is nothing wrong with entropy being locally reduced, provided that the overall entropy (of the atmosphere or the earth as a whole) increases (see, e.g., Maximum Principle vs. Minimum Principle in Non-equilibrium Thermodynamics.)
Locally, the transition between water vapor, water droplets and ice crystals can be indeed described using equilibrium thermodynamics. Again, these transitions are accompanied by release of latent heat, i.e., the increase of entropy of the surrounding environment (air, kinetic energy of water droplets, etc.)
For more see: Twelve Lectures on Cloud Physics, A short course in cloud physics
Related:
Why do clouds have well-defined boundaries?
Why are snowflakes flat?
