Mercury has a density of 13600 kg/m3. At what depth in millimetres is the pressure in mercury equal to that of standard atmospheric pressure? (take std pressure= 101 Pa)
(rho)* g* h = 101*10^3 N/m^2
h = 0.758 m = 758 mm
The correct answer is 760 mm. There are too few significant figures in the input data
To calculate the depth at which the pressure in mercury is equal to standard atmospheric pressure, we can use the formula for pressure in a fluid:
Pressure = ρ × g × h
Where:
- Pressure is the pressure in the fluid (in Pa)
- ρ is the density of the fluid (in kg/m³)
- g is the acceleration due to gravity (approximately 9.8 m/s²)
- h is the depth in the fluid (in meters)
We need to solve for h. Given that the density of mercury is 13600 kg/m³ and standard atmospheric pressure is 101 Pa, we can substitute these values into the equation:
101 = 13600 × 9.8 × h
To solve for h, rearrange the equation:
h = 101 / (13600 × 9.8)
Calculating this value gives:
h ≈ 0.0000733 meters
To convert this to millimeters, multiply by 1000:
h ≈ 0.0733 millimeters
Therefore, the depth at which the pressure in mercury is equal to standard atmospheric pressure is approximately 0.0733 millimeters.
To determine the depth in millimeters at which the pressure in mercury is equal to standard atmospheric pressure, we can use the concept of hydrostatic pressure.
Hydrostatic pressure is given by the formula: P = ρgh
Where:
P is the pressure,
ρ is the density of the fluid,
g is the acceleration due to gravity, and
h is the height or depth of the fluid.
In this case, we need to find the depth (h) at which the pressure (P) is equal to standard atmospheric pressure (101 Pa), and the density (ρ) of mercury is given as 13600 kg/m³.
First, we need to determine the acceleration due to gravity (g). The standard value usually used is approximately 9.8 m/s².
Next, we can rearrange the hydrostatic pressure formula to solve for h:
h = P / (ρg)
Converting the pressure from Pascals (Pa) to Newtons per square meter (N/m²):
1 Pa = 1 N/m²
Substituting the known values into the equation, we get:
h = 101 N/m² / (13600 kg/m³ * 9.8 m/s²)
Simplifying further:
h = 101 / (13600 * 9.8)
Now we can calculate the depth (h) in meters. To convert it to millimeters, we multiply it by 1000:
h = (101 / (13600 * 9.8)) * 1000
Using a calculator, we can evaluate this expression:
h ≈ 0.077 meters ≈ 77 millimeters
Therefore, the depth at which the pressure in mercury is equal to standard atmospheric pressure is approximately 77 millimeters.