Atmospheric pressure is the force exerted by the weight of air above a specific area. It is measured in pascals (Pa), where 1 Pa equals 1 newton per square meter (N/m²). The standard atmospheric pressure at sea level is approximately 101,325 Pa.
Equation for Atmospheric Pressure
To calculate atmospheric pressure in newtons per square meter (Pascals) at a specific elevation, you can use the barometric formula:
P = Po * e^(-Mgh/RT)
Where:
- P = atmospheric pressure in pascals at height ‘h’
- Po = standard atmospheric pressure at sea level (101,325 Pa)
- M = molar mass of Earth’s air (approximately 0.029 kg/mol)
- g = acceleration due to gravity (approximately 9.81 m/s²)
- h = height above sea level (meters)
- R = universal gas constant (approximately 8.314 J/(mol·K))
- T = absolute temperature in kelvins (K)
Example Calculation
To find the atmospheric pressure at an elevation of 1,000 meters, assuming a temperature of 288°K (15°C):
Insert values into the equation:
- Po = 101325 Pa
- M = 0.029 kg/mol
- g = 0.81 m/s^2
- h = 1000 m
- R = 8.314 J/(mol·K))
- T = 288K
Below is the calculation of atmospheric pressure at 1000 meters height.
P = 101325 * e**(-0.029 * 9.81 * 1000 / 8.314 * 288)
This will yield the atmospheric pressure at that elevation in pascals (N/m²)
Molar Mass:
A mol is a fundamental unit in chemistry used to measure the amount of a substance. Mol is defined as the quantity of any chemical substance that contains 6.022 X10**23 entities such as such as atoms, molecules, or ions. This number is known as Avogadro’s number.
Molar mass is the mass of one mole of a substance, expressed in kilograms per mole (kg/mol).
Gas Constant:
The gas constant (symbol R) is a fundamental physical constant that relates the energy scale to the temperature scale for a mole of particles in the ideal gas law.
Its value is approximately 8.314 J/(K·mol) in SI units, and it is used in various equations in chemistry and physics.
