https://physics.stackexchange.com/questions/552250/compressing-and-cooling-air-in-a-coolgardie-safe-then-decompressing/552275?noredirect=1#comment1246830_552275

I'm a 10th grader so it would help to explain how, in the answer to the link above, $$T_{cool}\left(\frac{V_{final}}{V}\right)\left(\frac{P_{ambient}}{P_{cool}}\right)$$ became... $$T_{cool}\left(\frac{P_{ambient}}{P_{cool}}\right)^{2/7}$$

Where did 2/7 come from?