Formula for Atmospheric Pressure

Barometric Formula

Barometric Formula:

\[ P = P_0 e^{-M g h / (R T)} \]

Sea Level Pressure (P₀):

Molar Mass (M):

kg/mol

Gravity (g):

m/s²

Height (h):

Gas Constant (R):

J/mol·K

Temperature (T):

Atmospheric Pressure (P):

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1. What is the Barometric Formula?

The Barometric Formula calculates atmospheric pressure at different altitudes based on the ideal gas law and the assumption of constant temperature. It describes how pressure decreases exponentially with height in the atmosphere.

2. How Does the Calculator Work?

The calculator uses the Barometric Formula:

\[ P = P_0 e^{-M g h / (R T)} \]

Where:

\( P \) — Atmospheric pressure at height h (Pa)
\( P_0 \) — Sea level pressure (Pa)
\( M \) — Molar mass of air (0.02896 kg/mol)
\( g \) — Gravitational acceleration (9.81 m/s²)
\( h \) — Height above sea level (m)
\( R \) — Universal gas constant (8.314 J/mol·K)
\( T \) — Absolute temperature (K)

Explanation: The formula models the exponential decrease in atmospheric pressure with increasing altitude, assuming constant temperature and gravitational acceleration.

3. Importance of Atmospheric Pressure Calculation

Details: Accurate atmospheric pressure calculation is crucial for aviation, meteorology, mountaineering, engineering design, and understanding weather patterns and climate science.

4. Using the Calculator

Tips: Enter sea level pressure in Pa, molar mass in kg/mol, gravity in m/s², height in meters, gas constant in J/mol·K, and temperature in Kelvin. Default values are provided for standard atmospheric conditions.

5. Frequently Asked Questions (FAQ)

Q1: What is standard sea level pressure?
A: Standard atmospheric pressure at sea level is 101,325 Pa (1013.25 hPa or 760 mmHg).

Q2: Why does pressure decrease with altitude?
A: Pressure decreases because there is less air above pushing down, and gravity's effect diminishes with height.

Q3: How accurate is the barometric formula?
A: It provides good approximations for altitudes up to about 10 km, but becomes less accurate at higher altitudes due to temperature variations.

Q4: What is the typical molar mass of air?
A: Dry air has a molar mass of approximately 0.02896 kg/mol, but this can vary with humidity and composition.

Q5: How does temperature affect atmospheric pressure?
A: Higher temperatures generally result in lower density and slightly different pressure profiles, though the formula assumes constant temperature.