A simple open U-tube contains mercury. When 11.9 cm of water is poured into the right arm of the tube, how high above its initial level does the mercury rise in the left arm? Take the density of mercury to be 13.6 g/cm3 and the density of water to be 1.00 g/cm3.
[ (0.5)*11.9 ]/ 13.6= 0.428 cm
Take half of what is added (since it must rise one side and fall is height on the other)- in this case 11.9/2
Divide that by the density of mercury.
Don't ask me why that's right. It just is. #Physics/Chemistry.
Lol.
To find the height to which the mercury rises in the left arm of the U-tube when water is poured into the right arm, we can use the principle of Pascal's law and the concept of hydrostatic pressure.
Here's how we can calculate it step by step:
Step 1: Determine the difference in pressure between the two arms of the U-tube:
Since the U-tube is open to the atmosphere, the pressure at the surface of the mercury in both arms is atmospheric pressure, which we can consider to be constant. Therefore, the difference in pressure between the two arms of the U-tube is due to the difference in height of the columns of liquid.
Step 2: Calculate the hydrostatic pressure of the water column in the right arm:
The hydrostatic pressure of a liquid depends on its density, height, and gravitational acceleration. In this case, the density of water is 1.00 g/cm3, and the height of the water column is 11.9 cm. The gravitational acceleration is approximately 9.8 m/s2. By using the equation P = ρgh, where P represents pressure, ρ represents density, g represents gravitational acceleration, and h represents height, we can calculate the pressure exerted by the water column.
P_water = (1.00 g/cm3) * (9.8 m/s2) * (11.9 cm)
Convert cm to meters and g to kg: P_water = (0.01 kg/L) * (9.8 m/s2) * (0.119 m)
P_water ≈ 0.113 kg/m·s2
Step 3: Calculate the height of the mercury column in the left arm:
Similarly, we can use the same equation to calculate the height of the mercury column in the left arm by converting the pressure difference into height.
Let's assume the height of the mercury column in the left arm is h_mercury.
P_mercury = (13.6 g/cm3) * (9.8 m/s2) * (h_mercury)
Convert g to kg: P_mercury = (0.136 kg/L) * (9.8 m/s2) * (h_mercury)
P_mercury ≈ 1.333 h_mercury kg/m·s2
Step 4: Equate the pressures and solve for the height of the mercury column:
Since the pressure difference between the two arms of the U-tube is equal to the pressure of the water column, we can set the equations equal to each other and solve for h_mercury:
0.113 kg/m·s2 = 1.333 h_mercury kg/m·s2
Divide both sides by 1.333:
h_mercury ≈ 0.085 m
Therefore, the mercury rises approximately 0.085 meters above its initial level in the left arm of the U-tube when 11.9 cm of water is poured into the right arm.