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)
Pressure = height * density * gravity
101 Pa = height * (13600 kg / m3) * (9.81 m/s2)
** note that kg * m/s2 = N
101 Pa = height * 133416 N/m3
** Pa = N/m2
therefore,
(101 N/m2) / (133416 N/m3) = height
height = 0.00075703 m = 0.75703mm
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HOWEVER!!! from my knowledge the standard atmospheric pressure is 101.325 KILO Pascal... so if that's the case, assuming you mistyped and meant 101 kPA...
101 kPa = height * 133416 N/m3
(101000 N/m2) / (133416 N/m3) = height
height = 0.757030641 m = 757.030641 mm
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Why did the math book go to the therapist? Because it had too many problems! But don't worry, I'll help you solve this one.
To calculate the depth at which the pressure in mercury is equal to standard atmospheric pressure, we can use the formula:
Pressure = density * gravitational acceleration * height
Given that the density of mercury is 13600 kg/m^3 and the standard atmospheric pressure is 101 Pa, we can set up the equation as:
101 Pa = 13600 kg/m^3 * 9.8 m/s^2 * height
Let's solve for height:
height = 101 Pa / (13600 kg/m^3 * 9.8 m/s^2)
height ≈ 0.077 meters or 77 millimeters
So, at a depth of approximately 77 millimeters, the pressure in mercury would equal standard atmospheric pressure.
To determine the depth at which the pressure in mercury is equal to standard atmospheric pressure, we can use the hydrostatic pressure formula:
Pressure = Density x gravitational acceleration x depth
First, we need to convert the standard atmospheric pressure from Pascals (Pa) to kilograms per square meter (kg/m²):
Standard pressure = 101 Pa
Next, we rearrange the formula to solve for depth:
Depth = Pressure / (Density x gravitational acceleration)
Density of mercury = 13600 kg/m³
Gravitational acceleration = 9.8 m/s²
Now we can substitute the given values into the formula:
Depth = 101 Pa / (13600 kg/m³ x 9.8 m/s²)
Simplifying:
Depth = 101 Pa / 133280 kg/(m²·s²)
Now, let's convert this depth to millimeters by multiplying by 1000:
Depth = (101/133280) m x 1000 mm/m
Calculating:
Depth = 0.757 mm (approximately)
Therefore, the pressure in mercury is equal to standard atmospheric pressure at a depth of approximately 0.757 millimeters.
To determine the depth at which the pressure in mercury is equal to standard atmospheric pressure, we need to use the concept of hydrostatic pressure and the formula for pressure. The hydrostatic pressure is the pressure exerted by a fluid at a given depth, which increases with increasing depth.
The formula for hydrostatic pressure is given by:
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 depth.
In this case, the fluid is mercury, and its density is given as 13600 kg/m^3. The standard atmospheric pressure is given as 101 Pascals.
We can rearrange the formula to solve for the depth, h:
h = P / (ρg)
Substituting the known values:
h = 101 Pascals / (13600 kg/m^3 * 9.8 m/s^2 * 1000 mm/m)
Calculating this, we get:
h = 0.00743 mm
Therefore, at a depth of approximately 0.00743 millimeters, the pressure in mercury is equal to the standard atmospheric pressure.