"I don’t trust myself to be an effective inquiry-based teacher if I’m not living an inquiry-based life. I don’t trust either of us." Dan MeyerOn that theme, I have recently been sharing a series of posts about my own inquiry into light and water, which began with a simple juxtaposition of two photos. This inquiry has led me to seek out and further juxtapose a range of natural and contrived phenomena. It has also led me to try to sort through various pieces of explanation, which have arisen through contemplation and conversation with peers.
In this post, I want to share another piece of inquiry that I think is important and important to infuse into one's inquiry life: seeking coherence and spotting inconsistency. This puzzle has stuck with me as fun and engaging.
If we (a) approximate a shallow chunk of water (near earth) as being incompressible
and (b) we assume that piece of water is in thermal equilibrium
and (c) that piece of water is in a constant gravitational field
then (d) macroscopically, we can show that the pressure increases linearly with depth.
but (e) microscopically, the particle density and kinetic energy would appear to be the same be, via our starting assumptions (a) and (b);
so (f) how can the pressure be different, if the particles have the same kinetic energy and particle density?
You have a couple of options here to approach trying to sort this out, and I encourage you to explore this a bit before you settle on a quick answer. Any takers?