A U-tube with 30 cm of water is set up vertically and 12 cm of olive oil is poured carefully into the left-hand limb of the tube as shown below. It is observed that water will be pushed up in the other limb. The density of water and olive oil are 1000 kg m-3 and 920 kg m-3 respectively.
Given A is at same level as the boundary between olive oil and water.a) What is the length of water column above point A?b) A further 6 cm of olive oil is added into the left-hand limb. How much further will the water level rise in the right limb?
Solutions: View video tutorial for part (b)a)
Poil = Pwater above A
ρgh = ρgh920 x 10 x 12 = 1000 x 10 x h
h = 11.04 cm
b) Pressure of water = pressure of olive oil
1000 x 10 x (2x + 11.04)/100 = 920 x 10 x 18/100
x = 2.76 cm
Gas inside a cylinder is heated slowly to a higher temperature. The pressure inside the cylinder remains constant as the piston moves outwards.
How do the speed of the gas molecules and their rate of collision with the piston compare with their initial values at the lower temperature?
In short: Temperature increases, Kinetic Energy increases, Rate of Collision decreases, Average Force on wall increases, Pressure constant.
As temperature increases, the speed of molecules increases, the kinetic energy of the air molecules increases.
As piston is free to move, it will move to the right such that the pressure remains constant (equal to atmospheric pressure outside). As the piston moves to the right, the volume inside the piston increases.
Surface area in which the air molecules collide increases.
The rate of collision decreases as the number of molecules remains constant. With higher KE of molecules, the molecules will collide the wall with greater force. Though rate of collision decreases, with each collision having greater impact force, the average force acting on the wall of piston increases.
Since P = F / A, with greater force F, over a bigger area A, the pressure P remains constant. (Compared with previously, smaller F over smaller A, but P constant)
Misconception: Many think that the rate of collision remains the same, which is wrong. Apparently the effect of volume increases is more significant, hence rate of collision decreases, even though they collide with greater impact force. Hence overall force on wall still increases. If the speed of the molecules increases but the pressure remains constant, then the molecules must collide less frequently. If the rate of collision stayed the same, the pressure would increase. If the rate of collision increased, the pressure would increase even more.