posted by kb on .
A primitive diving bell consists of a cylindrical tank with one end open and one end closed. The tank is lowered into a freshwater lake, open end downward. Water rises into the tank, compressing the trapped air, whose temperature remains constant during the descent. The tank is brought to a halt when the distance between the surface of the water in the tank and the surface of the lake is 38.0 m. Atmospheric pressure at the surface of the lake is 1.01 multiplied by 105 Pa. Find the fraction of the tank's volume that is filled with air.
I need help getting started. Ive looked in the book and have no idea where to begin.
Hint: What do you think is the pressure of the air in the tank?
just guessing but normal atmospheric pressure
PV=nRT ideal gas law is the only thing i got n R T will stay constant i believe so that leaves me with PV so PV of initial vs. PV of final... maybe
The ideal gas law:
PV = NRT
is certainly valid, but this equation simply tells you that temperature, volume and pressure are related. In this problem the temperature is constant, so what you need to know is the pressure. If you know the pressure then the equation will tell you by what factor the volume has changed.
So, you need to think about the fact that the oressur at a certain dept is higher than at the surface of the water. Why is that? Can you calculate the pressure at a certain dept from first principles (don't look in your book for an equation, you can't learn physics that way)
Hint: forget this particlar problem with the tank for a moment. Consider the water in the lake between the surface and some dept h. This water has a certain weight. Gravity acts on the water. Why doesn't the water accelerate downward? Clearly it doesn't, so there must be a force acting on it in te opposite direction.
This must be the force exerted by the water below accros the surface, i.e. the pressure times the area. But note that the air above the surface also exerts a downward force on the water.
So, you can find the pressure at some dept by demanding that the total force is zero.