You're right, the expanding and cooling universe seems to contradict the increasing entropy, but there's a deeper explanation why both can still be true. Here's why:
Entropy: While the universe cools down, it also spreads out, becoming less "clumped" in terms of energy distribution. This spreading out contributes significantly more to entropy than the cooling effect does. Imagine hot coffee. It starts ordered and hot, but as it cools and spreads, it becomes more disordered and spreads its heat energy everywhere, ultimately increasing entropy.
Second Law of Thermodynamics: This law states that in an isolated system (like the universe), entropy can only increase or stay the same, never decrease. This holds true regardless of specific events like cooling or expansion.
Implications for the Universe's End: While entropy increases, it doesn't necessarily signal an immediate "end" to the universe. The current understanding suggests two possible final states depending on its ultimate fate:
1. Heat Death: In this scenario, the universe continues expanding forever, eventually reaching a state of maximum entropy where everything is at the same temperature, with no usable energy left for work or processes. This "heat death" wouldn't involve the universe disappearing but rather becoming inert and unchanging.
2. Big Rip: More speculative, this scenario suggests the universe's expansion could accelerate infinitely due to dark energy, eventually ripping apart even atoms. While intriguing, evidence currently seems against this outcome.
Understanding: It's important to remember that our understanding of the universe's ultimate fate is still evolving. New discoveries and theories might change our current models.
As for your specific question, the universe's end wouldn't come directly from increasing entropy alone. It's one factor impacting its evolution, but other aspects like dark matter and energy play significant roles in determining its ultimate destiny.