A liquid is used to make a mercury-type barometer. The barometer is intended for spacefaring astronauts. At the surface of the earth, the column of liquid rises to a height of 2185 mm, but on the surface of Planet X, where the acceleration due to gravity is one-fourth of its value on the earth, the column rises to only 725 mm. Find the (a) the density of the liquid, (b) the atmospheric pressure at the surface of Planet X.
A beaker has a mass of 125g what is the mass of a liquid if the beaker plus liquid have a mass of 232g
To find the density of the liquid used in the barometer, we can use the concept of pressure and the difference in heights of the liquid column between the Earth and Planet X.
(a) Let's start by finding the density of the liquid.
We know that the atmospheric pressure at the surface of the Earth supports a liquid column of 2185 mm in height. In this case, we can assume that the atmospheric pressure's contribution is equal to the weight of the liquid column.
On the other hand, on Planet X, the liquid column is only 725 mm high due to the lower acceleration due to gravity. Again, we can assume that the atmospheric pressure's contribution is equal to the weight of the liquid column.
The difference in height of the liquid column between the two scenarios is 2185 mm - 725 mm = 1460 mm.
Now, let's consider the pressure exerted by a liquid column. The pressure is given by the equation:
Pressure = Density × Gravity × Height
Since the acceleration due to gravity is different for both scenarios, we can express the pressure as:
Pressure = Density × Gravity × Height
On Earth, the pressure is equal to the atmospheric pressure, which we can denote as P₁:
P₁ = Density × Gravity (Earth) × 2185 mm
On Planet X, the pressure is also equal to the atmospheric pressure, which we can denote as P₂:
P₂ = Density × Gravity (Planet X) × 725 mm
Since the densities are the same, we can equate P₁ and P₂ and rearrange the equation to find the density, denoted by ρ:
P₁ = P₂
Density × Gravity (Earth) × 2185 mm = Density × Gravity (Planet X) × 725 mm
Simplifying the equation:
Density × Gravity (Earth) = Density × (Gravity (Planet X) / 4)
Dividing both sides by Gravity (Earth):
Density = [Density × (Gravity (Planet X) / 4)] / Gravity (Earth)
Substituting the known values:
Density = Density × (1/4)
To solve for density, we can cancel out the density on both sides of the equation:
1 = (1/4)
Since the density does not affect the equation, we can't determine the exact value of the density using this method. However, we can conclude that the density of the liquid is not affected by the change in gravity.
(b) To find the atmospheric pressure at the surface of Planet X, we need to calculate it separately.
Using the equation from above:
P₂ = Density × Gravity (Planet X) × 725 mm
Since we can't determine the exact value of the density, we can't calculate the atmospheric pressure on Planet X.