Let's say you have a box that is made of a material that can change in volume. The box is 1kg. If you push it down from ground level to 10metres underwater, how much percentage does the volume of the box change due to the pressure change?
assuming temperature and moles of gas are constant then let's assume the following:
-every 10 m under water, pressure changes 1 atm. you can verify this with pgh, where p is the density of water, g is acceleration due to gravity, and h is height of the water.
-when the box is above water, it has p1=1 atm, under water it has p2=p1+pwater, where pwater is the pressure due to water. since it is 10 meters under water, the pressure due to water is 1 atm, but the water is also being pushed by the air above it (1 atm). so p2=2 atm.
from Boyle's Law, P1V1=P2V2. you don't even need to know this law by name, you just need to recognize in PV=nRT that n, R, and T are constant.
2*p1=p2 or p1= 1 atm, and p2= 2 atm
(p1*v1)/(p2)=v2, so, (p1*v1)/(2p1)= (1/2*v1)=v2.
the final volume of the box under water is half the volume of the box above water.
