You partially fill a graduated cylinder with cold water. You measure the pressure at the bottom with a sensitive barometer. You heat the water until it is nearly boiling and measure the pressure at the bottom again. What happens to the reading of the barometer?
A) It increases a lot. B) It increases a bit. C) It remains the same. D) It decreases a bit. E) It decreases a lot.
Solution: It remains the same. The water expands which decreases the density and increases the depth. So two variables change in the usual formula for pressure as a function of depth in a static fluid. But the mass and the weight force remain the same. So the force of the bottom of the container on the water must remain the same. So the pressure must remain the same. This means that the increased depth and decreased density balance out.