a mercury column in a simple barometer at a height of 75.9cm. An amount of pure water is introduced into the barometer column and form a 1.20cm layer on top of mercury. The mercury column now stand at height of 78.08cm . what is the pressure in the space above water at a particular temperature.(density of mercury = 13600kg/m2, density of water =1000kg/m2)
To find the pressure in the space above the water, we can use the hydrostatic pressure equation:
P = ρgh
Where:
P = Pressure
ρ = Density
g = Acceleration due to gravity
h = Height of the column
First, we need to find the pressure due to the mercury column. The density of mercury is given as 13600 kg/m^3 and the height of the mercury column is (78.08 - 75.9) cm = 2.18 cm = 0.0218 m.
So, the pressure due to the mercury column can be calculated as:
P_mercury = ρ_mercury * g * h_mercury
= 13600 kg/m^3 * 9.8 m/s^2 * 0.0218 m
= 2876.64 Pa
Next, we calculate the pressure due to the water layer on top of the mercury. The density of water is given as 1000 kg/m^3 and the height of the water layer is 1.20 cm = 0.012 m.
So, the pressure due to the water layer can be calculated as:
P_water = ρ_water * g * h_water
= 1000 kg/m^3 * 9.8 m/s^2 * 0.012 m
= 117.6 Pa
Finally, we add the pressures due to the mercury column and the water layer to get the total pressure in the space above the water:
P_total = P_mercury + P_water
= 2876.64 Pa + 117.6 Pa
= 2994.24 Pa
Therefore, the pressure in the space above the water at the particular temperature is approximately 2994.24 Pa.
To find the pressure in the space above the water in the barometer column, we need to consider the pressure exerted by both the mercury and the water. Let's break down the steps to get the answer:
1. Determine the pressure exerted by the mercury column:
Given that the height of the mercury column is 75.9 cm, we can convert it to meters by dividing by 100: 75.9 cm ÷ 100 = 0.759 m.
The density of mercury is given as 13600 kg/m^3.
To find the pressure exerted by the mercury column, we use the formula P = ρgh, where P is the pressure, ρ is the density, g is the acceleration due to gravity (approximately 9.8 m/s^2), and h is the height.
So, the pressure exerted by the mercury column is: P_h = 13600 kg/m^3 * 9.8 m/s^2 * 0.759 m.
2. Determine the pressure exerted by the water layer:
Given that there is a 1.20 cm layer of water on top of the mercury, we need to account for this.
The height of the water layer is 0.012 m (1.20 cm ÷ 100).
The density of water is given as 1000 kg/m^3.
Using the same formula as before, the pressure exerted by the water layer is: P_w = 1000 kg/m^3 * 9.8 m/s^2 * 0.012 m.
3. Calculate the total pressure in the space above the water:
Since pressure is additive, the total pressure is the sum of the pressure exerted by the mercury column and the pressure exerted by the water layer: P_total = P_h + P_w.
4. Find the pressure in the space above the water:
The pressure in the space above the water is given by the total pressure, P_total.
Therefore, the pressure in the space above the water is P_total.
Now that we have all the necessary values, we can substitute them into the formulas and perform the calculations to find the pressure in the space above the water at a particular temperature.