At sea level, the atmospheric pressure is 1.04×10 to the power 5 pa.Assuming g=10ms sq and density of air to be uniform and equal 2 1.3kg m cube find the height of the atmosphere.
Ok if it is 1.04*10^5 N/m^2 what would be the answere in kN/cm^2
of course, the air does not have constant density, but under the given assumptions, you want to convert pressure to meters:
1 pa = 1N/m^2
1.04*10^5 N/m^2 * 1m^3/1.3kg * 1kg/9.8N = 8163m or 8.163km
The folks who have climbed Mt. Everest (7855m) would be interested to know this. They were so close to outer space!
The answer is 8000m
To find the height of the atmosphere, we can use the barometric formula, which relates the atmospheric pressure to the height. The formula is given by:
P = P0 * exp(-mgh/RT)
Where:
P = Pressure at height h
P0 = Pressure at sea level
m = Mass of air per unit area
g = Acceleration due to gravity
h = Height above sea level
R = Universal gas constant
T = Temperature
Given:
P0 = 1.04 × 10^5 Pa
g = 10 m/s^2
m = density of air = 1.3 kg/m^3
We can rewrite the formula as:
h = (RT / mg) * ln(P0 / P)
Now, let's plug in the values:
R = 8.31 J/(mol·K) (Universal gas constant)
T = Standard temperature at sea level = 273 K (Assuming standard conditions)
P = Atmospheric pressure at a certain height (unknown)
To proceed, we need to determine the molar mass of air. Air is a mixture of various gases, with nitrogen (N2) and oxygen (O2) being the main components. The average molar mass of air is approximately 29 g/mol.
Now we can calculate the height.
Step 1: Convert the density of air to kg/m^3:
Density of air = 1.3 kg/m^3
Step 2: Calculate the molar mass of air:
Molar mass of air = 29 g/mol = 0.029 kg/mol
Step 3: Calculate the mass of air per unit area:
m = Density * g
= 1.3 kg/m^3 * 10 m/s^2
= 13 kg/(m^2·s^2)
Step 4: Calculate the height using the barometric formula:
h = (RT / mg) * ln(P0 / P)
= (8.31 J/(mol·K) * 273 K) / (13 kg/(m^2·s^2) * g) * ln(P0 / P)
Now, we need the value of P at the height of the atmosphere. Without that information, it is not possible to calculate the height accurately.